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Critic2 user's guide

1. CRYSTAL name struct LOAD name clmsum name struct e Quantum ESPRESSO CRYSTAL name cube LOAD name cube ZPSP C 4 H 1 CRYSTAL name scf out LOAD name cube ZPSP C 4 H 1 CRYSTAL CARTESIAN celldm 1 CELL_PARAMETERS matrix ENDCARTESIAN NEQ x0 yO z0 C ZPSP 4 rest of the ATOMIC_POSITIONS list 38 ENDCRYSTAL LOAD name cube CRYSTAL name scf in LOAD name cube ZPSP C 4 H 1 e Abinit CRYSTAL name_DEN LOAD name_DEN e VASP CHGCAR format divided by cell volume CRYSTAL POSCAR POTCAR LOAD CHGCAR ZPSP C 4 H 4 CRYSTAL POSCAR POTCAR LOAD AECCARO LOAD AECCAR2 LOAD AS S1 S2 REFERENCE 3 CRYSTAL POSCAR POTCAR LOAD CHG LOAD ELFCAR e elk CRYSTAL GEOMETRY OUT LOAD STATE OUT GEOMETRY OUT e aiPI CRYSTAL CELL a b c alpha beta gamma SPG space group NEQ x y z atom ENDCRYSTAL LOAD atl ion atl at2 ion at2 e Any code that writes Gaussian cubes 39 CRYSTAL name cube LOAD name cube e Gaussian molecules MOLECULE name wfn LOAD name wfn MOLECULE name wfx LOAD name wfx e Promolecular procrystal density calculations CRYSTAL name cif MOLECULE name xyz e Conversion between crystal formats CRYSTAL name cif WRITE name scf in WRITE name xyz MOLMOTIF e Conversion between grid formats CRYSTAL name cif LOAD rhoup_DEN LOAD rhodn_DEN LOAD AS 1 2 nl n2 n3 CUBE GRID FILE rhospin cube FIELD 3 8 Simple graphical representations points
2. PROXIMATE keyword the atomic contributions to the density are calculated by interpolating from a radial grid that is precomputed at the beginning of the run EXACT calculates the fully analytical values of the field with no approximations Applies to PI Default APPROXIMATE RHONORM VNORM In WIEN2k the clmsum and other files representing the electron density have different normalization The 1 0 m 0 radial component is divided by sqrt 4 pi The option VNORM can be used if the file in the input does not present this normalization e g a potential file Applies to WIEN2k Default RHONORM NUMERICAL Calculate the derivatives of the field numerically Mostly used for testing the implementa tion of new field types Applies to all Default no ANALYTICAL 35 Calculate the derivatives of the field analytically Opposite of NUMERICAL Applies to all Default yes TYPNUC 3 3 Controls whether the nuclei are maxima 3 or minima 3 of the field Applies to all Default 3 maxima NORMALIZE n r Normalize the grid integral over the unit cell to n r Applies to grids 6 3 Field arithmetics New fields can be defined as combinations of the existing ones using the LOAD AS keyword This allows the creation of fields that are not directly computed by the electronic structure program and is very useful in combination with the cube writing facilities keyword CUBE in Simple graphical representations points lines
3. OFF OBJ PLY BASIN DBASIN npts i PHASE phtheta r phphi ROOT root s PREC delta r VERBOSE MAP id i expr Plot a primary bundle starting from a point in its interior given by x r y r z r The bisection algorithm is used with precision delta r PREC keyword The rays traced are obtained by a recursive subdivision lvl i cycles a cube CUBE an octahedron TRIANG or using a uniform distribution of ntheta i nphi i points on the unit sphere SPHERE The output file has root root s and its format may be OFF OBJ PLY BASIN or DBASIN with npts i points sampled along each ray The initial polyhedron may be rotated a phase given by phtheta r polar angle and phphi r azimuthal angle If a 3d model format is used OFF OBJ PLY the MAP keyword can be utilized to col ormap a given field given by number id i or field containing expression expr onto the surface The color scale limits are the minimum and the maximum value of the field or ex pression on all the points of the surface The mapping function is the same as in gnuplot r sqrt x g x 3 b sin 360 x with x from 0 to 1 Default values TRIANG lvl i 3 ntheta i nphi i 5 OBJ output phtheta r Od0 phphi r 0d0 root s lt root gt bundle 12 Integration of atomic basins 12 1 Overview Critic2 provides several methods to integrate the attractor basins associated to the maxima of a field In QTAIM theory this field is the electron density the at
4. That is the name of the file without the extension If no input file is known for instance because critic2 was run as critic2 lt inputfile then the root defaults to stdin The default root can be changed with the keyword ROOT 14 e The critical points of a field can be classified by their rank 1 and signature s The rank is the number of non zero eigenvalues of the Hessian In the vast majority of cases r 3 The signature is the number of positive eigenvalues minus the number of negative eigenvalues s 3 is a maximum s 1 is a first order saddle point s 1 is a second order saddle point and s 3 is a minimum All these critical points necessarily appear in a periodic field and receive special names nuclear CP bond CP ring CP and cage CP respectively The abbreviations ncp bcp rcp and ccp are also used throughout the manual Note that a maximum is a nuclear critical point even though it may not be associated to any nucleus 4 Arithmetic expressions variables and functions in critic2 4 1 Basic usage In critic2 an arithmetic expression can be used almost everywhere in the input where a real or integer number is expected Arithmetic expressions that appear in the input without an associated keyword are evaluated and their result is written to the output For instance you can start critic2 and write 3 2xsin pi 4 i 3 2xsin pi 4 o 4 4142135623731 In the same way variables can be d
5. cause the volume of each tetrahedron is exactly known This implies that the integrated cell volume for a periodic integration region will always be exact if it is not then it is an error The integrated cell charge on the contrary is a measure of how well the tetrahedra are being integrated but not of how well the IAS is being determined e For very high levels of QTREE say 10 11 depending on the amount of memory your computer has memory usage may turn out to be a problem The COLOR ALLOCATE keyword controls the amount of memory allocated for the color and property arrays The syntax is COLOR_ALLOCATE 0 1 72 Using a zero value the color vector and possibly the properties vectors depending on PROP_MODE is allocated only for the current IWST This saves memory but makes the computation slower specially if the GRADIENT MODE is 2 or 3 In addition setting COLOR_ALLOCATE to 0 deactivates the passing of colors through the contacts DO CONTACTS and NOCONTACTS keywords and the plotting sets PLOT_MODE to 0 If COLOR_ALLOCATE is 1 the color and optionally the properties of all the IWST are saved By default COLOR_ALLOCATE is 1 if maxlevel i lt 8 and 0 if the maximum level is higher e In cases where only the properties of some of the atoms are interesting there exists the possibility of deactivating the integration of some atoms by using the INACTIVE and ACTIVE keywords Tetrahedra belonging to an inactive atom are not in
6. the integer type is that which is the result of se lected_int_kind 2 63 The subdivision level is the main input parameter for QTREE controlling the accuracy and cost of the integration For small medium sized systems 4 5 are low cost inte grations seconds 6 7 are medium cost minutes and 8 9 are the slowest and most accurate hours The level is input in the call to the QTREE integration QTREE 6 gtree_lvl is 6 By default the integration level is 5 In addition to trm more work space can be allocated if the integration is restricted to the volume and charge or to the volume charge and Laplacian The number and type of properties to be integrated is controlled by the PROP_MODE keyword The following values are allowed 0 only volume is integrated This amounts to canceling the finite elements inte gration of tetrahedra and is equivalent to INTEG_MODE 0 see below 1 only charge and volume If the integration uses the value of the density at the grid points INTEG_MODE 11 see below In addition to trm another real 8 array fgr is allocated strictly it is selected_real_kind 14 not real 8 In fgr the value of the density at the grid points is stored 2 charge volume and Laplacian In a similar way to 1 if the information on the grid points is used during the integration INTEG_MODE 11 an additional real 8 array lapgr is allocated It contains the value of the Laplacian of the electron density
7. 0 000000 0 500000 0 500000 Vector 3 0 500000 0 000000 0 500000 Vector 4 0 500000 0 500000 0 000000 Centering type p 1 a 2 b 3 c 4 1i 5 f 6 r 7 6 The Cartesian crystallographic transformation matrices are the transformation operations between the vector basis formed by the cell vectors crystallographic coordiantes and the in ternal Cartesian axes used in critic2 Cartesian coordinates The crystallographic to cartesian matrix crystocar gives the cell vectors in Cartesian axes The metric tensor is the crystocar matrix times its transpose Cartesian crystallographic transformation matrices Car to crys xcrys A x xcar 0 0968639067 0 0000000000 0 0000000000 0 0000000000 0 0968639067 0 0000000000 0 0000000000 0 0000000000 0 0968639067 9 Crys to car xcar B x xcrys 10 3237628366 0 0000000000 0 0000000000 0 0000000000 10 3237628366 0 0000000000 0 0000000000 0 0000000000 10 3237628366 Metric tensor 106 5800791057 0 0000000000 0 0000000000 0 0000000000 106 5800791057 0 0000000000 0 0000000000 0 0000000000 106 5800791057 Some more information about crystal symmetry follows including the list of operations in chemical notation and their principal axes the crystal point group the Laue class and the cyrstal system Symmetry operations in chemical notation 1 E 0 00
8. 8 4 4703204 2 F 12 7 3000027 1 Ca 24 8 5600119 2 F 6 10 3237628 Ca 11 24 11 2500597 2 F 24 12 6439756 1 Ca 32 13 4109613 2 F 12 14 6000054 1 Ca 48 15 2690512 2 F Kra 24 16 3233023 1 Ca 2 F 4 4 4703204 1 Ca 6 5 1618814 2 F 12 7 3000027 2 F 12 8 5600119 1 Ca 8 8 9406409 2 F 6 10 3237628 2 F 12 11 2500597 1 Ca 24 11 5423177 2 F 24 12 6439756 2 F 16 13 4109613 1 Ca List of nearest neighbor distances id atom rnn 2 bohr 1 Ca 2 2351602 2 F 2 2351602 Wigner Seitz neighbors hee UO I 22 0 S12 50 ss sy 05 20 die Q 10 5 0 1 0 Gre 0 Ora Is the cell orthogonal T Critic2 always has a reference scalar field defined The reference field is the one that for instance provides the attraction basins tha are integrated or whose critical points are determined by AUTO In absence of any external field loaded by the user critic2 defaults to the promolecular density the sum of atomic densities calculated using the internal density tables The information that follows in the output shows how critic2 builds the promolecular density First the atomic numbers and charges are identified the number of electrons is counted and then the density tables for the appropriate atoms are loaded from external files x Atomic radial density grids 12 List of atoms and charges id atom Z O ZPSP if Ca 20 0 S 2 F 9 0 Number of elec
9. INCREMENTS x r y r z r X I y r and z r are the step lengths in each direction NSTEP nx i ny i nz i NSTEP defines the number of steps in each direction If plotting the whole unit cell is not convenient a parallelepipedic region can be extruded from the crystal with the keyword CUBE x0 r yO r z0 r xl r yl r zl r where x0 r y0 r z0 r and x1 r yl r z1 r are the cube limits in crystallographic coordi nates A region much larger than one periodic cell can also be selected with this method In addition it is possible to define the cube containing a fragment of the crystal using CUBE filel xyz file2 xyz Define the limits of the cube using the crystal fragments contained in file1 xyz file2 xyz A small border RTHRES is added around the region exactly containing all the atoms The xyz files have the usual xyz format in angstrom in the same spirit as the FRAGMENT keyword The xyz however are not used as fragments for the NCI calculation Some cutoffs are relevant to the visualization of the NCI CUTOFFS rhocut r dimcut r These cutoffs apply to the writing of density and reduced density gradients respectively to the dat file If at a given point the density is above rhocut r or the reduced density gradient is above dimcut r then the point is not written to the dat file Defaults rhocut r 0 2 and dimcut r 2 0 for loaded densities and 1 0 for promolecular densities CUTPLOT rhoplot r dimplot r When th
10. Lattice parameters bohr 10 3237 Lattice parameters ang 5 463100 Lattice angles degrees 90 000 Molecular formula Ca 1 F 2 Number of Number of non equivalent atoms in atoms in the unit cell 63 10 323763 10 323763 5 463100 5 463100 90 000 90 000 the unit cell 2 12 Number of electrons in the unit cell 152 Next comes the non equivalent atom list In this case the whole crystal is generated by replicating two atoms one Ca and one F The positions multiplicities and the atomic numbers are indicated List of non equivalent atoms X y Z name mult Z 0 00000 0 00000 0 00000 Ca 4 20 0 25000 0 25000 0 25000 F 8 9 The next table is the complete atom list Here critic2 lists all the atoms in the unit cell 4 Ca and 8 F The exact same list is repeated in Cartesian coordinates referred to the internal coordinate framework used in critic2 List of atoms in the unit cell cryst x y Z name 0 0000000000 0 0000000000 0 0000000000 Ca 0 0000000000 0 5000000000 0 5000000000 Ca 0 5000000000 0 0000000000 0 5000000000 Ca 0 5000000000 0 5000000000 0 0000000000 Ca 0 2500000000 0 2500000000 0 2500000000 F 0 2500000000 0 7500000000 0 7500000000 F 0 7500000000 0 2500000000 0 7500000000 F 0 7500000000 0 7500000000 0 2500000000 F 0 7500000000 0 7500000000 0 7500000000 F 0 7500000000 0 2500000000 0 2500000000 F 0 2500000000 0 7500000000 0 2500000000 F 0 2500000000 0 2500000000 0 7500000000
11. a sphere of radius rad r in bohr and cen tered around the crystallographic coordinates x0 r y0 r z0 r If no center is given 0 0 0 is used The similar keyword CUBE writes all atoms inside a cube of side side r centered around x0 r yO r z0 r default 0 0 0 There is an important application of the xyz format WRITE keyword the coordinates written to the xyz file are consistent with the transformation to Cartesian coordinates in critic2 so it is possible to give back all or part of these coordinates to critic2 in order to represent a subset of the atoms in the crystal This is incredibly useful when generating fragments for an NCIPLOT calculation see FRAGMENT keyword in section Non covalent interaction visualization NCIPLOT The OBJ output is similar to xyz critic2 will write a finite piece of the crystal to a file with Wavefront OBJ format The OBJ format is a three dimensional model representation that is it uses vertices and faces instead of atoms This file format is understood by many visualizers such as view3dscene meshlab blender and others The keywords have the same meaning as in the xyz format The additional CELL keyword instructs critic2 to write a stick representa tion of the unit cell In the case of a molecular structure loaded using the MOLECULE instead of the CRYSTAL keyword the MOLCELL keyword can be used to represent the molecular cell that is the region around the molecule outside which critic2 considers
12. at each one of its four faces are copied to the corresponding neighboring IWST using the information found in section 3 Of course this is only done if DOCONTACTS is active e Once the integration of the IWST is completed the atomic properties are scaled and summed to the integrals inside the beta spheres The final result is output together with an analysis of the contribution of each subdivision level to the total integrated properties e It is possible to plot the basins obtained by QTREE using the PLOT_MODE keyword It can assume the values 0 no plotting is done 1 asingle tess file is written containing a description of the unit cell CPs the IWS and balls corresponding to all the grid points that have been sampled 2 same as 1 but only the balls that are either on the face of an IWST or close to a IAS are output 3 the full WS cell 4 a file for the full WS cell and several files containing a description of each of the integrated basins Note that the basins need not be connected 5 same as 4 but only balls belonging to faces of IWST and IAS are output The default value is O If PLOT MODE is gt 0 then it is possible and it is active by default to plot the sticks that form the tetrahedra inside stick files The PLOTSTICKS and NOPLOTSTICKS keywords control this behaviour Some additional considerations e The integration of the volume is not done using the beta sphere basin separation be
13. at the grid points 3 all the integrable properties calculated by the module The number of proper ties varies with the interface being used No fgr or lapgr are allocated as the grid points need to be recomputed during integration The default value for PROP_MODE is 2 The termini of the grid points contained in a beta sphere is marked previous to the beginning of the subdivision Each tetrahedron is subdivided recursively up to a level qtree lvl and integrated at the same time The IWST integration is relatively independent of one another so for the moment we will focus on just one IWST which we will call the base tetrahedron The IWST integration is not exactly independent of one another for two reasons When the integration ends the termini of the four faces of a base tetrahedron are copied to its neighbors trm according to the contacts determined previously Depending of the method chosen see GRADIENT MODE below the gradient path integration may be aware of the neighboring grid points that may very well 64 belong to other IWST In particular the gradient mode number 3 integrates a gra dient path following grid points When the endpoint is reached all the grid points that have been traversed by the path are assigned the same common terminus Therefore there is the possibility that gradient paths starting inside a given base tetrahedron write the trm of other IWST Nevertheless both features can be avoi
14. different fields e g clmup for the spin up density but the same format In those cases the keywords WIEN ELK can be used to force critic2 to read in a specific format The LOAD COPY keyword can be used to make a copy of the field in slot id i to the next available slot or to slot id2 i if it is given with the keyword TO 6 2 Additional options The definition of a field can be supplemented by additional optional keywords that depend on the type of field in the input and that come after the file name They are NEAREST TRILINEAR TRISPLINE Choose the grid interpolation mode in a grid field e g a cube file NEAREST use the field at the nearest grid point TRILINEAR trilinear interpolation TRISPLINE 3d spline interpolation adapted from the abinit code this part was coded by A Lherbier according to the source If some derivatives are not available first and second in NEAREST second in TRISPLINE they are taken as zero IN B the code for grid and qub file extensions all of them corresponding to grids is not very well tested Same thing goes for elk OUT files with a third file different from the density I think a dirty hack I did to elk once wrote these If you are planning on using these fields please send me an e mail A 34 By default TRISPLINE is used but this may require a lot of memory in very large cube files say 400 3 However the memory allocation for the TRISPLINE interpolation only happens if th
15. eses siate a SS a Re ES 14 4 Scanning Tunneling Microscope STM plots 14 5 The exchange hole dipole moment XDM model of dispersion 38 40 40 41 41 42 43 43 47 48 50 50 50 52 55 55 55 56 56 57 58 59 73 74 75 14 6 Control commands and options o o 84 15 Appendix 86 15 1 Related programs and output file formats 86 A AE Ge amp Sa ae A 86 BASIN files si 65 4 ee amp Pik E a SES Eee S amp Rac e ER 86 BBASIN Miles si ron ee ws Se ew a a ee 87 OFF and COFF Hee us corras SER ee eS we SE ESSERE SS SES 88 16 Copyright notice 88 1 Introduction Critic2 is a program for the analysis and representation of solid state electron densities and other scalar fields This program provides an interface to many solid state electronic structure programs and makes it possible to analyze manipulate and interconvert scalar fields electron densities and others and crystal structures The types of analyses critic2 is able to perform are based on Bader s Quantum Theory of Atoms in Molecules QTAIM Critic2 encapsulates common methods for topological analy sis under periodic boundary conditions and applies them irrespective of the source of the electron density This primarily includes locating the complete set of critical points topol ogy and integrating atomic regions basins Several specialized algorithm for the latter are availabl
16. for crystallographic computation NEWCELL xl r yl r zl r x2 r y2 r z2 r x3 r y3 r z3 r INV INVERSE Transform the crystal structure description by using a new unit cell given by the vectors x1 x2 x3 in crystallographic coordinates relative to the old unit cell The x1 x2 x3 78 vectors must be pure translations of the old cell either lattice vectors centering vectors or combinations of the two NEWCELL unloads all fields except the promolecular density and clears the critical point list If the INV or INVERSE keyword is used the input vectors correspond to the crystallographic coordinates of the old cell in the new coordinate system The NEWCELL keyword is useful for building supercells or for performing routine but tedious crystallographic transformations For instance given a face centered cubic lattice and the conventional cubic cell one can find the primitive rhombohedral cell by doing CRYSTAL LIBRARY mgo NEWCELL 1 2 1 2 0 1 2 0 1 2 0 1 2 1 2 Likewise if the current cell is rhombohedral the same NEWCELL order but including the INVERSE keyword transforms to the cubic That is CRYSTAL LIBRARY mgo NEWCELL 1 2 1 2 0 1 2 0 1 2 0 1 2 1 2 NEWCELL 1 2 1 2 0 1 2 0 1 2 0 1 2 1 2 INVERSE gives a unit cell and crystal structure description that is equivalent to the initial one read from the library WS Find the Wigner Seitz cell of the system and print information about its partition in tetr
17. formulas For instance gtf 1 is the Thomas Fermi kinetic energy den sity for field 1 which is assumed to be the electron density for the system In all instances etf 1 is equivalent to writing the formula in full 3 10 3 pi 2 2d0 3d0 1 5 3 but obviously much more convenient The library of chemical functions includes 17 gtf id GTF Thomas Fermi kinetic energy density The kinetic energy density for a uniform electron gas with its density given by the value of field id at the point The argument field can be of any type See Yang and Parr Density Functional Theory of Atoms and Molecules vtf id VIF the potential energy density calculated using the Thomas Fermi kinetic energy density and the local virial theorem 2g r v r 1 4 lap in au htf id HTF the total energy density calculated using the Thomas Fermi kinetic en ergy density and the local virial theorem 2g r v r 1 4 lap r in au gtf_kir id GTF_KIR Thomas Fermi kinetic energy density with the semiclassical gra dient correction proposed by Kirzhnits for the not so homogeneous electron gas The electron density and its derivatives are those of field id at every point in space See Kirzhnits 1957 Sov Phys JETP 5 64 72 Kirzhnits Field Theoretical Methods in Many body Systems Pergamon New York 1967 Abramov Y A Acta Cryst A 1997 264 272 and also Zhurova and Tsirelson Acta Cryst B 2
18. give the pseudopotential charges using the ZPSP keyword for all types of atoms in the system e TAU the kinetic energy density It is used in the calculation of B and can be extracted from the ELF Hence it is required except if the ELF or the B is given If the ELF is used instead of TAU a cube file tau cube is written e ELF the electron localization function Can be used in place of TAU This is useful because most programs e g QE VASP generate cubes for the ELF but not for the kinetic energy density e PDENS the promolecular density It is generated by critic2 if not present in the XDM call and written to a cube file pdens cube for future use e CORE the core density It is generated by critic2 if not present in the XDM call and written to a cube core cube unless the B and RHOAE are given in which case it is ignored The ZPSP of all atoms is required in order to calculate this quantity e LAP the Laplacian of the electron density It is generated by Fourier transform of RHO unless it is given or B is given in which case it is not needed and its calculation is skipped 82 e GRAD the gradient of the electron density It is generated from RHO unless B is given If B is available the calculation of GRAD is skipped e RHOAE the all electron density on a cube If given replaces the pseudo density plus core in the calculation of the atomic volumes e XB the exchange hole dipole moment in the Becke Roussel mode
19. in the input For instance if the first field 1 is the spin up density and the second 2 is the spin down density the total density can be calculated with the expression 1 2 The expression 0 represents the promolecular density which is always available once the crystal structure is known so 1 2 0 would represent the density difference between the actual crystal density and the sum of atomic densities Between the and the field number it is possible to specify an identifier to access the derivatives of the field The identifier can be e v valence only value of the field it is usually employed to access the valence density in a grid field in which core augmentation is active e c core only value of the field x y z first derivatives XX XY XZ yy yz ZZ second derivatives e g norm of the gradient e Laplacian lv valence Laplacian Laplacian without core augmentation lc core Laplacian 16 Therefore for instance 12 is the Laplacian of field 2 and xy3 is the xy component of the Hessian of field 3 There is a clear divide between expressions that reference fields and those that do not and for certain keywords critic2 will decide what to do with an expression based on this distinction For instance a 2 CUBE CELL FIELD ax 1 calculates a grid spanning the entire cell for a scalar field that is built as two times the field number 1 but a 2 CUBE CELL FIELD ax1 uses fie
20. integration is performed by quadrature The qtree algorithm is accessed through the QTREE keyword Lastly integration algorithms based on grid discretization are very popular nowadays thanks to the widespread use of pseudopotential plane waves DFT methods Critic2 provides the integration method of Yu and Trinkle YT described in JCP 134 2011 064111 The algorithm is based on the assignment of integration weights to each point in the numerical grid by evaluating the flow of the gradient using the neighboring points This algorithm is extremely efficient and robust and is strongly recommended in the case of fields on a grid The keyword is YT Another alternative for grids is the method proposed by Henkelman et al Comput Mater Sci 36 254 360 2006 J Comput Chem 28 899 908 2007 J Phys Condens Matter 21 084204 2009 which is implemented in critic2 using the keyword BADER The field that determines the basins being calculated is always the reference field see The reference field However it is in general interesting to one or more integrable properties using other scalar fields For instance we can calculate the charge inside an ELF basin the ELF would be the reference field and the electron density would be an integrable property 12 2 List of properties integrated in the attractor basins INTEGRABLE INTEGRABLE id i F FVAL GMOD LAP LAPVAL MULTIPOLE MULTIPOLES lmax i NAME name s INTEGRABLE expr s INTEG
21. is read in subsequent runs by using the same FILE syntax instead of calculating the CPs again Critic2 writes all the critical points found by AUTO to two internal lists the non equivalent list containing only those CPs not equivalent by symmetry and the complete list which con tains all the CPs in the unit cell see Input format output format and notation The most important part of the AUTO output is the final report which gives the non equivalent CP list and some other useful information Its appearance is the table has been simplified to fit the width of the page 45 x Critical point list final report non equivalent cps Topological class n b r c 2 8 1 16 1 16 2 8 Morse sum 0 n pg type position mult name f grad lap 1 Td 3 3 n 0 00 0 00 0 00 4 B 7 19E 1 0 00E 00 3 00E 15 2 Td 3 3 n 0 25 0 25 0 25 4 P 2 36E 3 0 00E 00 3 00E 15 3 C3v 3 1 b 0 09 0 59 0 59 16 b1 1 25E 1 4 43E 17 2 25E 01 4 C3v 3 1 r 0 88 0 88 0 61 16 r1 1 08E 2 1 09E 16 3 45E 02 5 Td 3 3 c 0 75 0 75 0 75 4 cl 5 63E 3 1 34E 16 2 22E 02 6 Td 3 3 c 1 00 0 00 0 50 4 c2 7 28E 3 1 32E 16 2 58E 02 The non equivalent CP list gives the type and position of all the non equivalent CPs found their associated name rank and signature and multiplicity Critic2 also provides the site symmetry pg and the values of the reference field f its gradient grad and its Lapla
22. is recommended in very large grids because its more efficient memory 74 usage 13 Non covalent interaction visualization NCIPLOT NCIPLOT ONAME root s CUTOFFS rhocut r dimcut r RHOPARAM rhoparam r RHOPARAM2 rhoparam2 r CUTPLOT rhoplot r dimplot r VOID void r RTHRES rthres r INCREMENTS x r y r z r NSTEP nx i ny i nz i ONLYNEG NOCHK CUBE x0 r y0 r z0 r xl r yl r zl r CUBE filel xyz file2 xyz MOLMOTIF FRAGMENT file xyz FRAGMENT X r y r z r in angstrom ENDFRAGMENT ENDNCIPLOT Calculates the density and reduced density gradient on a cube for the visualization of non covalent interactions The output files are e lt root gt dat a 2 column file with reduced density gradient col 2 vs density col 1 calculated at the points of a grid The density in column one is multiplied by the sign of the second eigenvalue of the density Hessian e lt root gt dens cube a cube containing the electron density times the sign of the second Hessian eigenvalue times 100 e lt root gt grad cube a cube containing the reduced density gradient RDG e lt root gt vmd the VMD script for convenient visualization of the results The root of the files can be changed using the ONAME keyword default lt root gt By default the region represented is the whole unit cell with step lengths of 0 1 bohr in each direction The step lengths or the number of points in each axis can be controlled with the keywords 75
23. is set as the center of the plot window which consists of a rectangle with sides equal to two times the longest distance from the barycenter to the nuclei The reference points for the plane in PLANE CP may translated by lattice vectors optional keyword LVEC The plot plane may contain regions that are traversed by gradient lines originating at critical points located outside the plot region If this is the case the OUTCP option allows the user to extend the plane when considering which origins to be included The sx r and sy r are scale parameters The x axis extends sx r 1 1 x in each direction where 1 x is the axis length The sy r variable works the same way Consequently the plane determined by the vectors given in PLANE acts as a clipping plane while the scaled plane determines the gradient path origins With HMAX you can set the maximum distance from a CP to the plane to be included in the plot Default 1d 4 The ORIG keyword adds a source of gradient lines to the plot Its crystallographic coordi nates are X r y r and z r atriis 1 if the point is to be treated as a ncp or ccp the up and down trajectories start from points located on a sphere centered on the origin and it is 0 if the point is to be treated as a bep or ccp a circle is built around the CP in the plane determined by two eigenvectors whose eigenvalues have equal sign The remaining eigenvector determines a unique direction up i and down i are the number of gradient
24. lattice translation 9 2 Requesting more information about the critical point list CPREPORT SHORT LONG VERYLONG SHELLS n i ESCHER CPREPORT OBJ PLY OFF MOLMOTIF CELL MOLCELL BORDER ix i iy i 12 1 CPREPORT prints additional information about the critical points to the output SHORT print the list of non equivalent critical points with crystallographic coordinates multiplicity and properties of the reference scalar field LONG the complete list of critical points in the unit cell and the connectivity in the case of bcp and rcp when the graph is calculated VERY LONG detailed information at every critical point including the derivatives of the reference field the evaluation of all other fields and the flatness SHELLS local neighbor environ ment of every critical point up to n i shells default 10 ESCHER write the crystal structure description to an octave escher script containing the critical points The OBJ keyword writes a lt root gt _cell obj file in Wavefront OBJ format This format can be viewed with view3dscene meshlab blender and many other programs Alternatively the PLY and OFF 3d graphics formats can be used The keywords have the same meaning as in WRITE MOLMOTIF completes all molecules in the unit cell using atoms from adjacent cells BORDER includes in the representation the atoms that are exactly on the cell border CELL represents the unit cell with red sticks and ix i iy i iz i tell criti
25. lines planes grids 8 1 Points POINT POINT x r y r z r ALL FIELD id i expr s 40 Calculates the value of the reference field its derivatives and related quantities at the point X r y y z r in crystallographic coordinates If ALL is used all loaded fields are evalu ated In addition all arithmetic expressions that have been registered using the POINTPROP keyword are also calculated see List of properties calculated at points POINTPROP The POINTPROP keyword combined with POINT is useful to evaluate chemical functions at arbi trary points in space If FIELD is used and followed by an integer id i then only that field is evaluated FIELD followed by an arithmetic expression calculates the value of that expression at the point 8 2 Lines LINE LINE x0 r y0 r z0 r xl r yl r zl r npts i FILE file s FIELD id i expr s GX GY GZ GMOD HXX HXY HXZ HYX HYY HYZ HZX HZY HZZ LAP Calculate a line from x0 r y0 r z0 r to x1 r yl r z1 r with npts i points By default the result is written to the standard output but it can be redirected to a file using FILE The reference field is used unless a FIELD keyword appears in which case the field id i or the expression expr s are evaluated Together with the value of the field an additional quantity is evaluated the components of the gradient GX GY GZ the norm of the gradient GMOD the components of the Hessian HXX and the Laplacian def
26. non orthogonal cells have become quite a standard and can be written by a lot of mainstream solid state programs so it is a very good option if critic2 provides no native interface to the densities of your program of choice e WIEN2K s struct files may or may not contain the symmetry operations for instance if they have been generated by the web interface but not run If symmetry is provided then critic2 will use it Otherwise critic2 will try to guess the symmetry see Symmetry options e Depending on the version VASP s POSCAR and CONTCAR and also CHG and CHG CAR may be missing the atomic symbols In that case they need to be provided by hand after the file name either using a list of atomic symbols or the location of the POTCAR Even though it is the name accepted by VASP files that have the extension POSCAR CONTCAR CHG and CHGCAR are also accepted e g nacl POSCAR Note that the pseudopotential charges are NOT read from the POTCAR 21 Any file with extension OUT will be understood to be in elk s GEOMETRY OUT format even though it may not be called GEOMETRY Regarding Quantum ESPRESSO outputs usually file scf out only the out extension is detected the block at the beginning of the run is read from Title to Cartesian axes Because this block is repeated at the end of a geometry optimization Ca final calculation at the relaxed geometry it says the final structure from a successfully completed g
27. of the reference field is integrated If the reference field is the density then it is indeed the charge Otherwise the charge in the output is only a label for the integrated field on the basin e Laplacian lap f the Laplacian of the reference field The integrated Laplacian has been traditionally used as a check of the quality of the integration because the exact integral is zero regardless of the basin because of the divergence theorem However it is difficult to obtain a zero in the Laplacian integral in critic2 because of numerical inaccuracies In fields based on a grid the numerical interpolation gives a noisy Laplacian In FPLAPW fields WIEN2k and elk the discontinuity at the muffin surface intro duce a non zero contribution to the integral The keyword CLEAR resets the list to its initial state volume charge and Laplacian Using the INTEGRABLE keyword will print a report on the list of integrable properties 12 3 Bisection INTEGRALS GAULEG ntheta i nphi i LEBEDEV nleb i CP ncp i RWINT PHASETH theta r PHASEPH phi r VERBOSE Integrate the attractor basins using bisection Ntheta i and nphi i are the number of theta polar angle and phi azimuthal angle points for the Gauss Legendre quadrature if GAU LEG is used The number of azimuthal angles depends on the actual value of the polar angle theta and is adapted according to the formula realnphi int nphi i sin theta 1 In the
28. paths to be started in the upwards and downwards direction respectively 51 The CP keyword accepts a critical point identifier from the complete CP list or the com plete atom list The number of upwards and downwards gradient paths must be given A special case is the CPALL keyword which adds as origins every critical point in the CP list on the selected plane The default number of gradient paths is 36 down for ncps and 36 up for ccps and 2 up and 2 down for beps and reps The BCPALL keyword is similar to CPALL except that only the bond critical points are included as origins If BCPALL is used the user must supply the number of gradient lines in the upwards and downwards directions In a similar way RBCPALL includes bond and ring critical points and the user must give the number of upwards and downwards gradient paths for bonds bup i bown i and rings rup i rdown i The CHECK environment allows the user to enter the crystallographic coordinates of a CP of the scalar field to add it as an origin If the point given is not a CP or if it lies out of the selected plane it is ruled out of the origin list The valid CPs in the CHECK list are identified and an adequate number of gradient paths are started according to its character for a ncp and ccp 36 upwards or downwards and for a bep or rep 2 upwards and 2 downwards The keywords F GX request critic2 to generate a plot in which the gradient paths calculated in GRDVEC are merged w
29. resulting structure with a visualization program In the case of QE critic2 tries to conform as much as possible with the QE rules for writing the CELL PARAMETERS matrix 6 Scalar fields 6 1 Loading a field LOAD Scalar field functions that associate a value to every point in real space are loaded with the LOAD keyword A number of different field formats are supported LOAD file cube 31 LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD LOAD file DEN file_DEN file CHGCAR file CHG file ELFCAR file qub file xsf file grid file clmsum file struct file RHO BADER DRHO LDOS VT VH file OUT GEOMETRY OUT file OUT GEOMETRY OUT OTHER OUT file wfn file wfx filel ion natl i atl s file2 ion COPY id i TO id2 i PROMOLECULAR PROMOLECULAR file xyz WIEN ELK PI CUBE ABINIT VASP VASPCHG QUB XSF ELKGRID file NEAREST TRILINEAR TRISPLINE EXACT APPROXIMATE RHONORM VNORM CORE NOCORE NUMERICAL ANALYTICAL TYPNUC 3 1 1 3 NORMALIZE n r AS expression s nl i n2 i n3 i SIZEOF id i GHOST AS PROMOLECULAR nl i n2 i n3 i SIZEOF id i file xyz AS CORE nl i n2 i n3 i SIZEOF id i AS LAP id i AS GRAD id i AS CLM ADD idl i id2 i SUB idl i id2 i Critic2 loads scalar fields in field slots integer identifiers that represent the field through out the run There
30. speed of the field calculation using nn i points default 10000 RUN SYSTEM command s Execute a shell command ECHO string s Write the string to the output Useful for partitioning long outputs expression s If the input is not identified as any of the keywords above then evaluate the line as an arithmetic expression Useful for simple calculations in the command line with critic2 q END Terminates the execution 85 15 Appendix 15 1 Related programs and output file formats Some programs required or just useful when working with critic2 are e gnuplot most of the output critic2 creates are text files with column organized grid data readily formatted to use with gnuplot Also in some tasks critic2 also generates the gnuplot scripts required for the representation e geomview some atomic basin plots are created in geomview s OFF and COFF format which are described below e tessel tessel is a generalized plotting program for crystal structures Critic2 provides input files for tessel mainly in FLUXPRINT Also BASIN and DBASIN files containing the information about the atomic basins are generated which are read and plotted by tessel e avogadro can be used to manipulate xyz files for nciplot The description of the output file formats in critic2 follows INT files The INT files contain a description of an IAS surface for a number of rays The rays are given by a fixed 2d angular quadrature specifi
31. the sphfactor solves this problem SPHFACTOR 1 0 70 At lower levels QTREE is reasonably fast so a trial and error selection of beta spheres is acceptable Note that the beta spheres used in QTREE have no relation to the ones reported after an AUTO calculation If the cell is periodic which means that WS_SCALE was not set the contacts between the faces of the IWST are found These contacts are used in a later step to copy the termini information between tetrahedron faces The determination of the tetrahedra contacts in a periodic integration region is de activated if the NOCONTACTS keyword is issued The opposite is the DOCONTACTS keyword By default the contacts are not calculated A grid is built for each of the IWST for which the termini of the gradient paths starting at each of the grid points will be calculated The grid is determined by subdividing the IWST gqtree_ lvl times In each subdivision step a parent tetrahedron is divided in 8 smaller tetrahedron all with the same volume V 8 by splitting each edge of the parent tetrahedron in two There are two possible ways of doing this the election being irrelevant to the performance of QTREE For a given IWST the size of the grid is given by S n n 1 n 2 6 where n 2 qtree lvl 1 the approximate scaling being as 8 qtree lvl The termini infor mation on the grid is saved to the array trm of type integer 1 with size nt S where nt is the number of IWST in fact
32. wavefunction files can be loaded by passing the wfn or wfx file to critic2 This option is normally used in combination with MOLECULE on the same file in order to ob tain the same structure from the isolated molcule The evaluation of wfn wfx densities is analytical no grids involved For aiPI inputs several ion files are necessary The ion files can be associated to atoms either by using their non equivalent atom number nat1 i or their atomic symbol at1 s The keyword PROMOLECULAR is used to load a promolecular density field same as the one in slot 0 If a finite fragment of the crystal is passed to LOAD PROMOLECULAR as an xyz file file xyz then the sum of atomic densities is built using only the atoms in that fragment Elk s STATE OUT is version dependent The following versions of elk have been tested and work with critic2 2 3 22 2 3 16 2 2 10 2 2 9 2 2 8 2 2 5 2 2 1 2 1 25 2 1 22 14 22 1 4 18 1 4 5 1 3 31 1 3 30 1 3 24 1 3 22 1 3 20 1 3 15 1 3 2 1 2 20 1 2 15 1 1 4 1 0 17 1 0 16 and 1 0 0 If your version is not supported most likely because it s newer I tend to revise the part of the code that reads elk files every aeon or so please contact me VASP fields can come in two varieties The CHGCAR and AECCAR files give the grid values in a higher precision and multiplied by the cell volume The CHGCAR can be read directly with LOAD and the AECCAR can be read with something like LOAD VASP AECCARO The o
33. 000 0 00000 0 00000 2 s3 0 597 735 5 O2 57735 y EOL ISO 3 C4 0 00000 0 00000 1 00000 4 C2 0 70711 0 70711 0 00000 5 C2 0 00000 1 00000 0 00000 6 C2 0 00000 0 00000 1 00000 7 C2 0 70711 0 70711 0 00000 8 C4 0 00000 0 00000 1 00000 9 C2 1 00000 0 00000 0 00000 10 S4 0 00000 1 00000 0 00000 11 Ss 0 70711 0 00000 0 70711 12 s3 ODIA y OOOO y Da daa 13 s3 sO DAI ULSA 7 Da 35 14 Ss 0 70711 0 00000 0 70711 15 S4 0 00000 1 00000 0 00000 16 s3 SODA S SOV S2735 de OLS 7T3S gt 17 C3 0557 139 OCS7735 9 O 5773529 18 C4 1 00000 0 00000 0 00000 19 C4 1 00000 0 00000 0 00000 20 C3 0 DABA y COLO y 0257735 21 C3 20657735 4 20257735 7 025 7735 gt 22 C2 0 00000 0 70711 0 70711 23 C2 0 00000 0 70711 0 70711 24 ES O57 735 7 OLOT y DINSA 25 i 0 00000 0 00000 0 00000 26 S 0 70711 0 70711 0 00000 27 S4 0 00000 0 00000 1 00000 28 Ss 0 00000 1 00000 0 00000 29 Ss 0 00000 0 00000 1 00000 30 s 0 70711 0 70711 0 00000 Sil S4 0 00000 0 00000 1 00000 32 S 1 00000 0 00000 0 00000 33 C3 COS 7IBS e 0 52735 9 OCS FISS 9 34 C4 0 00000 1 00000 0 00000 35 C2 0 70711 0 00000 0 70711 36 C3 O 57935 y O d7735 gt O S7735 9 37 C3 Co 1057735 A 7 O 57
34. 002 58 567 575 Espinosa et al Chem Phys Lett 285 1998 170 173 for more references and an example of the application of this quantity with experimen tal electron densities vtf_kir id VTF_KIR the potential energy density calculated using gtf kir id and the local virial theorem 2g r v r 1 4 lap r in au htf kir id HTF_KIR the total energy density calculated using gtf kir id and the local virial theorem 2g r v r 1 4 lap in au gkin id GKIN the kinetic energy density G version grad rho grad rho The argument should be a wfn wfx field See Bader and Beddall J Chem Phys 1972 56 3320 Bader and Essen J Chem Phys 1984 80 1943 kkin id KKIN the kinetic energy density K version rho lap rho The argument should be a wfn wfx field 18 lag id LAG the Lagrangian density 1 4 lap rho vir id VIR the electronic potential energy density also called the virial field Keith et al Int J Quantum Chem 1996 57 183 198 he id HE the electronic energy density vir id gkin id elf id ELF the electron localization function ELF The argument should be a wfn wfx field See Becke and Edgecombe J Chem Phys 1990 92 5397 5403 The name in square brackets is a shorthand for applying the chemical function to the reference field case insensitive in the POINTPROP keyword A particular case of chemical function is xc th
35. 135 38 C2 0 70711 0 00000 0 70711 39 C4 0 00000 1 00000 0 00000 40 C3 ODIA q HO 07735 4 OLS IDO 41 S3 C HOS 7935 pa 0 AAS y FESTES 42 S4 1 00000 0 00000 0 00000 43 S4 1 00000 0 00000 0 00000 44 S3 O 57135 y ROL e OLS BO 45 53 C2 O 57935 e OLSPTSS MSI 46 S 000000 O 70711 0 70711 47 S 0 00000 0 70711 0 70711 48 S3 C 0ST T3 y DDL TID y FIIT Crystal point group Oh Number of operations point group 48 Laue class m 3m Crystal system cubic The next few lines give the number of atoms contributing to the density in the main cell the cell at the lattice origin This is the set of atoms around the main cell whose in vacuo atomic density contribution to the main cell is more than a certain threshold These atomic environments are used in certain applications of critic2 that involve quantites that break the translational symmetry of the crystal e g calculating the promolecular density at a point in space Atoms contributing density to the main cell Number of atoms 15972 A list of nearest neighbor shells for all atoms in the non equivalent list follows together with information about the nearest neighbor distance the faces of the Wigner Seitz cell these are used to calculate distances between non equivalent atoms and finally whether the input cell is orthogonal Atomic environments id atom nneig distance nneq type a Ca
36. 52 LVEC x i y i z i BRAINDEAD QUOTIENT DYNAMICAL RCP cp i 1 step r epsi r LVEC x i y i z i RCP cp i O 1 n i step r epsi r LVEC x i y i Z i BRAINDEAD QUOTIENT DYNAMICAL CCP cp i ntheta i nphi i step r epsi r LVEC x i y i z i GRAPH igraph i step r epsi r TEXT TESSEL TESS OBJ PLY OFF EVERY every i SHELLS ishl i NOSYM ENDFLUXPRINT The FLUXPRINT keyword prints three dimensional gradient paths There are several plot ting comands e POINT build a gradient path starting at point x r y r z r in cryst coordinates step r is the maximum step Cartesian coordinates for the gradient path tracing algorithm If step r gt O use it also as the initial step If step r lt O use a small step as initial 1d 3 epsi r is the gradient norm stop criterion The default values are 0 1 for step and 1e 9 for epsi The 1 1 0 field controls the direction of the path An ascending gradient path is obtained with 1 while 1 issues a descending path O 1 1 makes FLUXPRINT represent both ascending and descending paths e NCP print gradient paths starting from a small sphere centered on the nuclear CP identified by cp i this identifier comes from the complete CP list The number of points is controlled by ntheta i number of points sampling the azimuthal angle and nphi i number of points sampling the polar angle cp i specifies a ncp in the main cell up to a lattice translation The LVEC opt
37. Critic2 user s guide Author Alberto Otero de la Roza ngel Mart n Pend s V ctor Lua a Contact alberto fluor quimica uniovi es Address Departamento de Quimica Fisica y Analitica Universidad de Oviedo 33007 Oviedo Spain Contents 1 Introduction 2 Command line options usage and input overview 3 Input format output format and notation 4 Arithmetic expressions variables and functions in critic2 4l Basicusag rada A OE ARA EONS Be 42 Listof available FUMCHONS sisi Goa SRE REAR AR 4 3 Use of LIBXC in arithmetic expressions 2 0 4 4 ke ek da EROS 5 The crystal structure 5 1 Loading a crystal structure CRYSTAL MOLECULE 44 ge css a 52 Thecrystal lo sso s agoi ea bees bee ee ee ee ee ER 5 3 Symmetry Options s s ah elo ae k a ee KS See eS we RS 5 4 Atomic charge Options sss sea ee Sede OAKS SSE EOS GEESE SS 5 5 Loading multiple crystal structures excitar ense Rae Ee EEE S 5 6 Molecular SECUCHIEES lt saa smew a now EE RGR EERE Sw ARA OY 5 7 Exporting the crystal structure WRITE 225 446285 458484 ee 6 Scalar fields 6 1 Loading afield LOAD 2 5 4 4 are rss a e a ta A a 6 2 Additional options s scs idea a Ri E a 6 3 Field arithmetics croata a A ARA AA 6 4 Changing the field options after LOAD ic 4s6 844406 4 ey bees 6 5 Unloading afield curras REX ia EE oe eG Bw ROO 6 6 Whe tererence field z sss mosis arie Ga acai eee Oo oa Ye oe wae we ek 7 Usual CRYSTAL LOAD combinations 8 Simple gr
38. F List of atoms in the unit cell bohr X y Z name 0 00000000 0 00000000 0 00000000 Ca 0 00000000 5 16188142 5 16188142 Ca 5 16188142 0 00000000 5 16188142 Ca 5 16188142 5 16188142 0 00000000 Ca 2 58094071 2 58094071 2 58094071 F 2 58094071 7 74282213 7 74282213 F 7 74282213 2 58094071 7 74282213 F 7 74282213 7 74282213 2 58094071 F 7 74282213 7 74282213 7 74282213 F 7 74282213 2 58094071 2 58094071 F 8 2 58094071 7 74282213 2 58094071 F 2 58094071 2 58094071 7 74282213 F Following this information comes the cell volume in atomic units and in cubed angstrom Cell volume bohr 3 1100 30746 Cell volume ang 3 163 04874 And then the list of symmetry operations List of symmetry operations 48 Operation 1 1 000000 0 000000 0 000000 0 000000 0 000000 1 000000 0 000000 0 000000 0 000000 0 000000 1 000000 0 000000 Operation 2 0 000000 0 000000 1 000000 0 000000 1 000000 0 000000 0 000000 0 000000 0 000000 1 000000 0 000000 0 000000 Operation 48 0 000000 1 000000 0 000000 0 000000 0 000000 0 000000 1 000000 000000 1 000000 0 000000 0 000000 0 000000 Oo List of centering vectors 4 Vector 1 0 000000 0 000000 0 000000 Vector 2
39. RABLE CLEAR The list of integrable properties follows a similar strategy to field loading Loading a field LOAD and the list of properties calculated at the critical points List of properties calculated at points POINTPROP There is an internal list of the properties that will be integrated in the attraction basins which can be modified by the user using the INTEGRABLE keyword INTEGRABLE defines a new quantity to be integrated in the basins The new integrable property is related to field number id i as an integrable property This quantity can be the field value itself F its valence component if the field is core augmented FVAL the gradient norm GMOD the Laplacian LAP or the valence component of the Laplacian LAPVAL By default F is used With MULTIPOLES or MULTIPOLE the multipole moments of the field are calculated up to 1 lmax i default 5 This keyword only applies to the BADER and YT integration methods for the others it is equivalent to the field value same as F The name for the integrand can be changed using the keyword NAME In addition it is possible to define an integrable property using an expression involving more than one field exprs For instance if the spin up density is in field 1 and the spin 57 down density is in field 2 the atomic moments can be obtained using LOAD AS S1 2 REFERENCE 3 INTEGRABLE 1 2 The default integrable properties are e Volume 1 e Charge f the value
40. a hedra Useful for debugging ENVIRON SHELLS nshel i POINT x0 r y0 r z0 r Print the shells of atomic neighbors for every non equivalent atom in the cell up to nshel i shells default 10 If a point is given with the POINT keyword crystallographic coordi nates then print the atomic environment of that point instead PACKING VDW PREC prec r Compute the packing ratio assuming atomic spheres with radius equal to the nearest neighbor distance divided by 2 If VDW is used then use the van der Waals radii and allow the spheres to overlap This option is currently implemented by building a grid on the unit cell and checking whether its points are inside any atomic sphere which is not very efficient The PREC allows controlling the precision of the packing ratio calculated using the VDW keyword If PREC is used expect an error in the percent packing ratio in the order of prec r The default prec r is 0 1 IDENTIFY ANG ANGSTROM BOHR AU CRYST RECIPROCAL X r y r z r ANG ANGSTROM BOHR AU CRYST RECIPROCAL file xyz ENDIDENTIFY 79 Identify the coordinates in the input and match them against the list of atoms and critical points If a coordinate is close 1e 4 to an atom or CP the corresponding indices as well as the crystallographic coordinates are written to the output The input can come as either the coordinates of the points themselves or a filename pointing to an xyz file The default units are crystallographic
41. a scalar field They play an important role in the QTAIM theory because gradient paths of the electron density can not cross the boundary between atomic regions and as a consequence a gradient path plot is a simple way to investigate the shape and properties of a basin Gradient paths originate at maxima if the field is the density they are usually the nuclei and end at the minima the crystal voids or at infinity in case of a gas phase molecule There are two keywords for gradient path representation in critic2 GRDVEC 2D gradient paths plus a contour plot and FLUXPRINT 3D 10 2 Gradient path representations in a plane GRDVEC GRDVEC FILES ROOT ONAME rootname s PLANE x0 r yO r zO r x1l r yl r zl r x2 r y2 r 22 4 SCALE sx r sy r PLANE CP ATOM cpl i LVEC x i y i z i cp2 i LVEC x i y i z i cp3 i LVEC x i y i z i SCALE sx r sy r SIZE zx r zy r OUTCP sx r sy r HMAX hmax r ORIG x r y r z r atr i up i down i CP cp i up i down i CPALL BCPALL up i down i RBCPALL bup i bdown i rup i rdown i CHECK KLE YSL Bak ENDCHECK CONTOUR F GX GY GZ GMOD HXX HXY HXZ HYX HYY HYZ HZX HZY HZZ LAP LIN cini r cend r LOG ATAN BADER nptsu i nptsv i niso i ENDGRDVEC GRDVEC plots a plane containing all the gradient paths originating from a set of points The GRDVEC environment accepts a set of input lines in any order that control the char acteristics of the plot The syntax of GRDVEC originated fr
42. adient path on a coarse sphere around each nu cleus and reduces the sphere until all of the points are inside the basin NOCHECKBETA is used in this case An additional factor the user can define is the SPHINTFACTOR It is possible to consider the sphere where GPs terminate different from the one that is integrated If SPHINT FACTOR is defined as in SPHINTFACTOR 1 0 75 then the sphere associated to atom 1 where the integration is done has a radius which is 0 75 times that of the sphere where GP terminate The CHECKBETA and NOCHECKBETA keywords activate and deactivate the check that ensures that the beta spheres is completely contained inside the basin 62 If a beta sphere is not strictly contained in the basin QTREE detects it and stops imme diately specifically QTREE checks that every tetrahedron that is partly contained in a beta sphere has vertex termini that are all assigned to the same atom as the beta sphere owner For a new system it is always a good idea to start with a low level QTREE say level 4 to check if the default beta spheres are adequate If one of the beta spheres is too large the error message looks like An undecided tetrahedron is overlapping with a beta sphere Make beta spheres smaller for this system terms 1 1 2 1 which indicates that there is a tetrahedron that is partly contained in the sphere of the first atom terminus 1 and that has a vertex corresponding to atom 2 Modifying
43. aining the unit cell description with border see WRITE and the position of the maxima labeled as XX Note that in the output List of basins and local properties Charge refers not to the integrated electron density because critic2 doesn t know what is an electron density and what not but to the value of the integral of the reference field in its own basins which may not make much sense if you are integrating for instance the ELF or the Laplacian Loading a second field and using INTEGRABLE and the field number is the way to go in such cases Usage of the YT algorithm for grid integration is strongly recommended as it is much more efficient robust and accurate than the other alternatives combined with spline inter polation BADER is however more memory efficient than YT so it is recommended for very large grids instead 12 6 Henkelman et al method BADER The algorithm by Henkelman et al uses the BADER keyword BADER NNM NOATOMS ESCHER FIELDLIST The BADER algorithm uses the reference field to calculate the basins this field must be defined on a grid BADER assigns grid nodes to basins using the near grid method incremen tally described in Comput Mater Sci 36 254 360 2006 J Comput Chem 28 899 908 2007 and J Phys Condens Matter 21 084204 2009 Please cite these references if you use this method The output and the option keywords have the same meaning as YT Using BADER as an alternative to YT
44. all that interesting we have decided to remove that code from this version The complete CP list is the list of all CPs in the unit cell The identifiers from this list are used as input for other keywords for instance GRDVEC or FLUXPRINT as they specify a particular position in the crystal The entries are similar to the non equivalent CP list the table has been simplified x Complete CP list 46 x symbols are the non equivalent representative atoms n neg typ x Iy Iz op lvectcvec x 1 1 on 1 00 0 50 0 32 1 0 0 0 0 0 2 1 n 0 50 0 00 0 67 2 0 0 0 0 1 0 x 3 2 n 1 00 0 50 0 59 1 1 0 0 0 0 0 4 2 n 0 50 0 00 0 40 2 0 0 0 0 1 0 Lewi The columns are in order the CP identifier n the identifier for the same CP in the non equivalent CP list neq the type of CP the position in crystallographic coordinates and the symmetry operation that transforms the CP from the non equivalent CP list into the listed CP Op corresponds to one of the symmetry operations listed in the output and lvec cvec is a translation Application of the operation op to the non equivalent CP followed by the translation recovers the position of the CP in the complete list The CPs that are at exactly the same position as the corresponding CPs in the non equivalent list are listed first and marked with an x Note that for these the operation is always 1 the identity and the translation vector is always a
45. and C10 10 The latter is the default 14 6 Control commands and options ODE_MODE EULER RKCK DP step r gradeps r Select the gradient path integration algorithm Euler is plain explicit Euler RKCK Runge Kutta embedded 4 5th order method Cash Karp parametrization DP Dormand Prince 4 5th order step r is the initial step size and gradeps r is the gradient norm termination criterion for the gradient path This keyword applies to all gradient paths except those in qtree INT_RADIAL TYPE GAULEG QAGS ONG Q0AG NR nr r ABSERR aerr r RELERR rerr r ERRPROP prop i PREC delta r en eee eee ee Choose the radial integration method e g inside spheres or basins The TYPE keyword selects the qudrature method e GAULEG Gauss Legendre e QAGS quadpack s dqags general purpose extrapolation globally adaptive end point singularities All Q methods are sometimes unstable for heavy atoms and big beta spheres but this does not happen very often e QNG quadpack s dqng smooth integrand non adaptive Gauss Kronrod Patterson e QAG quadpack s dqag general purpose integrand examiner globally adaptive Gauss Kronrod The number of radial integration points if appropriate GAULEG QAG is selected with NR If the selected method is QAG the number of points may vary from nr r The allowed intervals are 7 15 10 21 15 31 20 41 25 51 30 61 Critic2 selects the appropriate interval by comparing
46. aphical representations points lines planes grids 8 1 Points POINT iaa GO a a aa a Ge oC eX 3 2 Lines LINE esca e a a be Sth ey Sa ds 8 3 Planes and contour plots PLANE 4 success aa ew a oe 8 4 Grids CUBE ca sta sisa a a SoH Ak AAA a ia 9 Finding critical points 9 1 Automatic determination of critical points AUTO 9 2 Requesting more information about the critical point list 9 3 List of properties calculated at points POINTPROP 10 Graphical representations of gradient paths IOT OVEVIEW 2 46 56 oo bo ee Se hee hee ee A Owe Ee 10 2 Gradient path representations in a plane GRDVEC 10 3 Three dimensional gradient path representations FLUXPRINT 11 Atomic basin representations 11 1 Attractor basin plots BASINPLOT xido a 11 2 Primary bundle plots BUNDLEPLOT 245 d lt 0 4 604 644 424 604 12 Integration of atomic basins IA cB mR EE EAR RR ORE BAS Oe KORE Be Be Be Sad 12 2 List of properties integrated in the attractor basins INTEGRABLE 12 3 DISCO Aaa AR Sew EH BOH IZA Qtree usina cara a a AR A A OS 12 5 Yuand Tale YT x ss ew es AA AR AI GOO 12 6 Henkelman et al method BADER 13 Non covalent interaction visualization NCIPLOT 14 Miscellaneous commands 14 1 Powder diffraction POWDER 14 2 Commands for crystallographic computation 14 3 Hirshfeld charges o sas
47. are 31 slots numbered from 0 up to 30 At the beginning of the run slot number 0 is occupied by the promolecular density which is automatically loaded right after the crystal structure is succesfully read Successive LOAD commands fill the slots in increas ing order the first LOAD will assign the new field to slot 1 the second LOAD will occupy slot 2 and so on By default the first loaded field other than the promolecular density in slot 0 becomes the reference field see The reference field The simplest usage of load is LOAD file ext The field information is read from file ext Critic2 uses the extension to decide which format should be used for the reading e cube for Gaussian cube files grid e DEN for abinit grids 32 e CHGCAR CHG or ELFCAR for vasp grids e qub for aimpac grids e xsf for xcrysden grids e grid for elk s grids this requires a patch to elk e mail to request it e RHO BADER DRHO LDOS VT and VH for siesta s grids e clmsum for WIEN2k e OUT for elk s STATE OUT e ion for aiPl ion files e win and wfx for Gaussian wavefunction files In the case of WIEN2k and elk not all the necessary information is encapsulated in the clmsum or STATE OUT for instance the muffin tin radii are missing so it is necessary to provide a second file the struct file or the GEOMETRY OUT respectively This is the case regardless of whether these same files were used in the CRYSTAL keyword Gaussian
48. at allows the user to access the external LIBXC library This is only possible if the library was linked during the compilation of critic2 See Use of LIBXC in arithmetic expressions 4 3 Use of LIBXC in arithmetic expressions If critic2 is linked to the libxc library see the README for instructions on how to do this then the xc function can be used in arithmetic expressions xc calculates the exchange and or correlation energy density for one of the functionals in the libxc library The num ber of arguments to xc depends on the type of functional invoked which is selected using an integer index The list of functionals available and their corresponding indices should be consulted in the libxc documentation The integer index that selects the functional always ap pears last in the calling sequence of xc For ease of reference the file libxc_funcs_2 0 1 txt specifying the list of functionals in version 2 0 1 of libxc is included in the doc directory The arguments to xc idx depend on the type of functional specified by the idx integer which can be e LDA xc rho idx e GGA xc rho grad idx e meta GGA xc rho grad lapl tau idx where rho is the electron density expression grad is its gradient lapl is its Laplacian and tau is the kinetic energy density Note that rho grad lalp and tau are expressions not integer indices like in the chemical functions above For instance the expression for LDA using the electron density
49. ate transformation e CLM defines a new field as the addition id1 id2 or substraction id1 id2 of fields of the WIEN2K or elk type by using the ADD and SUB keywords respectively Note that the muffin tin radii number of plane waves etc have to be the same for both source fields 6 4 Changing the field options after LOAD The options of a given field can be changed anywhere in the input after it has been loaded using the SETFIELD keyword SETFIELD id i NEAREST TRILINEAR TRISPLINE EXACT APPROXIMATE RHONORM VNORM CORE NOCORE NUMERICAL ANALYTICAL TYPNUC 3 1 1 3 LAP NOLAP SETFIELD changes the properties of the field in slot id i The keywords have the same meaning as in the previous sections Where after the corresponding LOAD 37 6 5 Unloading a field UNLOAD id i ALL Unload the field in slot id i or all fields keyword ALL Where after LOAD 6 6 The reference field One of the loaded fields is chosen as the reference field The reference field is used as the primary field in all computations representing its basins with BASINPLOT integrations plotting etc unless otherwise specified The first field loaded becomes the reference field If no fields have been loaded then the reference is the promolecular density field 0 In order to change the reference field the REFERENCE keyword can be used REFERENCE id i Sets field number id i as reference 7 Usual CRYSTAL LOAD combinations e WIEN2k
50. ault Laplacian of the reference or the id i field 8 3 Planes and contour plots PLANE PLANE x0 r yO r z0 r x1l r yl r zl r nx i ny i PLANE ATOM ATOMS atl i at2 i at3 i SCALE sx r sy r SIZE zx r zy r nx i ny i PLANE FILE file s FIELD id i expr s F GX GY GZ GMOD HXX HXY HXZ HYX HYY HYZ HZX HZY HZZ LAP CONTOUR LOG niso i ATAN niso i BADER LIN niso i r0 r rl r Calculate the value or other properties of the reference field on a plane The results are written to a file with default name lt root gt _plane dat There are two ways to specify the geometry of the plane In the first option three points are given x0 r yO r z0 r is the origin x1 r yl r z1 r is the x end of the plane and x2 r y2 r z2 r is the y end The number of calculated points on each axis are given by nx i x axis and ny i y axis An alternative way of passing the plane geometry to critic2 is to use the ATOM or ATOMS keyword This keyword accepts three integers corresponding to the atom identifiers in the 41 atomic cell list The sx r and sy r parameters to SCALE enlarge the plot plane by sx r in the x direction and by sy r in the y direction The total length of the x or y axis can be set with SIZE in bohr SCALE and SIZE are mutually exclusive The syntax of ATOM is similar to GRDVEC The rest of the options FILE FIELD are treated in the same way Regardless of how the plane geometry is giv
51. bverse cell is used 0 0 0 1 3 2 3 2 3 and 2 3 1 3 1 3 For instance R 3 h hexagonal axes R 3 r rhombohedral axes R 3 same as R 3h For monoclinic groups when several unique axis choices where all have the same label the tokens b and c choose between the unique axis b and c respectively By default the b unique axis is used Example P 2 b unique axis b same as P 1 2 1 P 2 c unique axis c same as P 1 1 2 P 2 same as P 2 b and P 121 The space group label can also be given as a single word without spaces For instance Fm 3m is the same as F m 3 m The space group number can be used as well in which case all defaults for origin choice unique axis and hexagonal rhombohedral axes apply Example 222 is equivalent to Pn 3n Pn 3n1 and P n 3 n 1 If no SPG keyword is found in the CRYSTAL environment then an internal routine cal culates the symmetry from the atomic positions which can be deactivated using NOGUESS see Symmetry options In this case all the atoms in the cell need to be given in contrast to using SPG in which case only the asymmetric unit needs to be given There are two possible ways to input the cell parameters In the simplest approach the CELL keyword can be used to give the cell lengths and angles CELL a r b r c r alpha r beta r gamma r ANG ANGSTROM BOHR AU If the ANG or ANGSTROM keyword is used then a r b r and c r are in angstrom Other
52. c If both input and output files are present the output is redirected to file outcritic Oth erwise it is written to standard output If no file incritic is present the input is taken from standard input The extensions incritic and outcritic are not mandatory It is also valid to use critic2 lt file incritic gt file outcritic Alternatively you can use the standard input and standard output S critic2 and then enter the commands by hand In addition depending on the tasks in the incritic file auxiliary files may be generated usually with the same root as file incritic file in the example above or stdin if no input file is given The h option help prints a short help message and exits The q option quiet inhibits the initial and final messages This is useful when using critic2 in a pipe command The r option tells critic2 where to find its data files If path to critic2 is given the data files wfc dic etc should be in path to critic2 dat The input file usually contains a specification of the crystal structure using the CRYSTAL keyword For instance CRYSTAL file struct After the crystal structure is read one or more fields are loaded using the keyword LOAD LOAD file clmsum file struct Unless otherwise stated in this manual the units in critic2 are atomic units In particular distances are in bohr and the electron density is in electrons bohr After loading the relevant fields
53. c2 to represent that number of cells in each direction Essentially the OBJ file is the same as the one generated by WRITE except in that the critical points are also represented In the case of a molecular structure 47 loaded using the MOLECULE instead of the CRYSTAL keyword the MOLCELL keyword can be used to represent the molecular cell that is the region around the molecule outside which critic2 considers critical points and gradient paths to have diverged to infinity 9 3 List of properties calculated at points POINTPROP The default output for AUTO contains a list of detailed information at the critical points This is an example of how this section looks like Additional properties at the critical points Law J Critical point no 9 Crystallogrpahic coordinates 0 65183 0 90869 0 72597 Cartesian coordinates 12 89298 22 10026 33 60159 Type 3 1 Field value f 4 939109713E 03 Field value valence fval 4 939109713E 03 Gradient grad f 9 5115E 18 3 8415E 17 4 1112E 18 Gradient norm grad f 3 978845324E 17 Laplacian del2 f 1 312332087E 02 Laplacian valence del2 fval 1 312332087E 02 Hessian eigenvalues 2 11139E 03 1 48096E 03 1 67156E 02 Hessian 2 068242883E 04 5 185807347E 03 1 179735612E 03 5 185807347E 03 1 373314257E 02 4 510661176E 03 1 179735612E 03 4 510661176E 03 4 029974096E 04 For each critical point the coor
54. case of a Lebedev Laikov quadrature the number of points of the radial Gauss Legendre grid and the octahedral grid is needed The actual value of nleb i is the smallest number larger than the one given by the user included in the list 6 14 26 38 50 74 86 58 110 146 170 194 230 266 302 350 434 590 770 974 1202 1454 1730 2030 2354 2702 3074 3470 3890 4334 4802 5294 5810 By using the CP keyword a single non equivalent CP ncp i is integrated Otherwise all the CPs of the correct type found using AUTO are integrated If RWINT is present read if they exist and write the int files containing the interatomic surface limit for the rays associated to the chosen quadrature method The PHASETH and PHASEPH keywords are used to rotate the sphere quadrature for example to avoid symmetry lines Defaults ntheta i nphi i 50 nleb i 4802 SPHEREINTEGRALS GAULEG ntheta i nphi i LEBEDEV nleb i CP ncp i NR npts i RO r0 r REND rend r Integrates the volume field and Laplacian in successive spheres centered around each of the attractor CPs The same considerations for GAULEG and LEBEDEV as in the keyword above apply A total number of npts i spheres are integrated per nucleus The grid is logarithmic so that the region near the nucleus has a higher population of points The grid starts at the radius r0 r and ends at rend r If rend r lt O then the final radius is taken as half the nearest neighbor d
55. cian lap evaluated at the CPs The topological class gives the number of non equivalent ncp bep rep and ccp found The values in parentheses correspond to the total number of CPs of each class in the cell If the list is complete then the Morse sum is zero in a crystal or one in a molecule Sometimes the zero one Morse sum condition is not fulfilled which is usually caused by often unavoidable numerical shortcomings of the scalar field e In WIEN2k and elk densities there might be spurious CPs at the surface of the muffin tin where the density is discontinuous that show up in the final report list Every time a FPLAPW field is loaded every atomic muffin is checked for discontinuities and the report printed to the output e In fields defined on a grid the regions of small field i e the crystal voids are noisy which creates a lot of spurious critical points It is usual that a zero Morse sum is unobtainable in this case as multitude of CPs tend to appear clustered around the position of the real CPs The CPs where the value of the field is larger should be reliable however Using a fine grid and relatively high CPEPS and a CPRHO usually helps to eliminate the uninteresting CPs e In scalar fields with extreme variations in value e g the Laplacian of the electron density it is unlikely that AUTO will find all the core CPs A previous version of critic2 does that available upon request but since the core CPs are not
56. coordinates but they can be modified with one of the keywords that follow IDENTIFY For specific points the unit can be changed by specifying a keyword after the three coordinates The units in the xyz file are angstrom the xyz file has to have the usual syntax with the number of atoms in the first line and the title in the second line In addition critic2 provides the vertices of the cube that encompasses all the points in the list that did match an atom or CP and the same cube with a 2 bohr border The RECIPROCAL keyword is special in that points under this keyword are assumed to belong to reciprocal space Critic2 will calculate the multiplicity using the reciprocal point group operations which can be useful for determining k point weights EWALD Calculate the electrostatic energy of the lattice of point charges using Ewald s method The atomic charges are defined using the Q keyword 14 3 Hirshfeld charges HIRSHFELD Calculate the Hirshfeld charges Only for fields on a grid 14 4 Scanning Tunneling Microscope STM plots STM CURRENT curr r HEIGHT hei r TOP top r CELL CELLS nx i ny i NPTS nl i n2 1i LINE x0 r yO r xl r yl r npts i Generate an STM plot for the current system comparable to those obtained in actual STM experiments The STM keyword should be applied only to systems meeting the following requirements e The geoemtry is a slab possibly with molecules adsorbed to one or both faces e The s
57. critical points and gradient paths to have diverged to infinity The similarly popular PLY polygon file format or Stanford triangle format and OFF Geomview file formats can be used as well with the same options Quantum ESPRESSO inputs can be written using the extension scf in This conversion is especially useful in the case of low symmetry crystals e g monoclinic in a non conventional setting where the conversion from other formats such as CIF can be tricky The QE in put generation works by first determining the Bravais lattice from the symmetry opera tions Critic2 uses ibrav 0 always and writes a CELL PARAMETERS block containing the 30 crystallographic to Cartesian transformation matrix QE is particular about how this matrix should written in order for its own symmetry module to work If the crystal setting matches any of those covered in the QE manual then that particular matrix is used Otherwise critic2 uses its own internal CELL PARAMETERS matrix which may result in Quantum ESPRESSO failing to recognize the crystal symmetry A tessel input extension tess and a critic2 input using the CELL NEQ mechanism in critic can be written A VASP POSCAR or CONTCAR can be generated by using the POSCAR CONTCAR ex tension or name The list of atomic types is written to the critic2 output This list is necessary to build the corresponding POTCAR The atoms are always ordered in increasing atomic number An abinit input fi
58. d adaptive step 3rd order with 5th order error estimation The FSAL first step also last allows only 4 evaluations per step Local extrapolation 7 Runge Kutta Cash Karp embedded method adaptive step 4th order with 5th order error estimation 6 evaluations per step 8 Dormand Prince 4 5 embedded method adaptive step 4th order with 5th order error estimation 6 evaluation per step with FSAL Local extrapolation For embedded methods 4 8 the absolute error requested to the method can be set using the ODE _ABSERR keyword The default of this variable is chosen so that reason able stepsizes are kept This default is 1d 3 for Euler Heun and 1d 4 for the rest Note that it makes no sense an equivalent ODE _RELERR keyword Experimentally using a method with n more evaluations is better than reducing the step size of the lower accuracy method n times Additionally there is no upper limit to the step size I am assuming nobody is going to use ODE_ABSERR 1d2 so methods with greater accuracy 7 and 8 save evaluations by increasing stepsize to values much larger than their lower accuracy counterparts The step size of the fixed step methods 1 4 is controlled with the STEPSIZE keyword In the variable step methods 5 8 the value of STEPSIZE is used as the starting step The default QTREE_ODE_MODE is Dormand Prince 8 71 e When the integration of the base tetrahedron is finished the termini of the grid points located
59. ded if there is ever interest in parallelizing the integration over IWST e A tetrahedra stack is built and initialized only one element the base tetrahedron An iterator works on the stack performing at each step the following tasks Pop a tetrahedron from the stack The termini of the vertex of the tetrahedron are calculated if they are not already known Let us assume for now that we have a method that traces a gradient path and reliably locates the terminus for a given grid This will be treated below If all the termini of the tetrahedron correspond to the same atom its inside of the tetrahedron is painted This means that all the grid points that are in the interior or border of the tetrahedron are assigned the same color as its vertex thereby saving the tracing of the gradient paths This painting can be dangerous whenever a curved IAS crosses the face of the tetrahedron which undergoes the operation To this end a minimum level is de fined using the keyword QTREE_MINL If the subdivision level of the tetrahedron is lower or equal than QTREE_MINL the tetrahedron is not painted Note the base tetrahedron corresponds to level 0 Furthermore if all the termini correspond to the same atom and are located out side of the beta sphere region the tetrahedron is integrated and does not enter another subdivision process Once more this only happens to tetrahedra with a level of subdivision strictly greater
60. dinates Cartesian and crystallographic the type and the evaluation of the reference field and its derivatives is given However in many cases it is interesting to calculate the value of a different field or even an arithmetic expression involving other fields at those critical points For instance it is relatively common to use the kinetic energy density at the bond critical points of the electron density as a measure of bond covalency To obtain more information at the critical points of the reference field the procedure in critic2 is to register a field or an arithmetic expression involving known fields in the proper ties list accesible using the POINTPROP keyword POINTPROP name s expr s POINTPROP shorthand s POINTPROP CLEAR POINTPROP LIST The POINTPROP keyword associates the expression expr s with the name name s and register that name in a list of properties When AUTO is run or CPREPORT if the POINT 48 PROP order comes after AUTO those arithmetic expression will be applied to each of the CPs and the result printed in the output For instance if one does POINTPROP MYGTF gtf 1 POINTPROP STH log 1 2 Then the result of AUTO for the critical point above becomes Critical point no 9 Crystallogrpahic coordinates 0 65183 0 90869 0 72597 Cartesian coordinates 12 89298 22 10026 33 60159 Type 3 1 Field value f 4 939109713E 03 Field value valence fval 4 939109713E 03 G
61. e Despite its origins critic2 is not limited to QTAIM analysis Many other convenient fea tures are available such as sundry techniques related to QTAIM e g Hirshfeld charges NCI plot tools for graphical representations and crystallographic computation etc At the most basic level critic2 is also useful to perform arithmetic manipulations on fields defined in real space and to interconvert between crystal structure and field file formats Many scalar fields other than the electron density are amenable to an analysis using the same tools as in QTAIM finding the topology and integrating the attractor basins These techniques called Quantum Chemical Topology QCT by P Popelier can be applied to a variety of scalar fields including the ELF and the Laplacian of the electron density Critic2 can in principle perform all these tasks for any field provided by the user or calculated within the code Critic2 is described in Comput Phys Commun 180 2009 157 166 and Comput Phys Commun 185 2014 1007 1018 Please cite these references if you find this program useful The file THANKS contains a complete list of contributors and other programs from where parts of critic2 have been adapted 2 Command line options usage and input overview Critic2 accepts a single input file usually but not necessarily with extension incritic The command line syntax is S critic2 q h r path to critic2 file incritic file outcriti
62. e They are not more reliable or efficient than say the scheme 2 Integration scheme 6 calculates levels 4 5 and 6 using CUBPACK and the rest with subdivision up to the highest level and vertex based integration INTEG_MODE 12 12 12 1 ee 1 11 7 same as 6 but the final integration is based on the barycenter INTEG_MODE 12 12 12 1 1 1 1 let the user enter the INTEG_MODEs by hand The default integration scheme is 2 suitable for low and medium accuracy calculations 68 Border same color integration This integration applies to tetrahedra that have reached the maximum subdivision level and sit on the interface between a beta sphere and the atomic basin Some of the vertex are known to be inside the sphere and some of them are out The objective is to integrate the out of sphere part and summing it to the atomic properties while ignoring the in sphere part that has been integrated at the beginning using a sphere cubature The integration follows by assuming that the sphere radius is much larger than the tetrahedron characteristic lengths and therefore that the sphere surface can be con sidered a plane that intersects the tetrahedron The intersection points of the sphere with the tetrahedron edges are easily calculated and for the sake of simplicity in the explanation we will refer to them as the middle of the edges Note however that in the implementation these points are calculated exactly There are t
63. e dat The current implementation of STM has benefited from the code and the guidance kindly provided by Enrico Benassi see THANKS 81 14 5 The exchange hole dipole moment XDM model of dispersion The XDM module calculates the dispersion energy using the exchange hole dipole moment XDM model See J Chem Phys 127 154108 2007 J Chem Phys 136 174109 2012 and J Chem Phys 138 204109 2013 for more details XDM RHO irho i TAU itau i ELF ielf i PDENS ipdens i CORE icor i LAP ilap i GRAD igrad i RHOAE irhoae i XB ib i XAl al r XA2 a2 r ONLYC UPTO 6 8 10 XDM uses the electron density RHO the kinetic energy density TAU the Laplacian LAP and the gradient of the electron density GRAD to compute the exchange hole dipole moment in the Becke Roussel model B The promolecular density PDENS and the core density CORE are used to calculate a Hirshfeld partitioning of the unit cell All of these fields have to be available or are calculated when running XDM The corresponding keywords accept an integer corresponding to a previously LOADed field During the XDM run cubes for all of these fields are generated so they can be loaded in subsequent runs Note that the PDENS cube is the same as generated in NCIPLOT except for changes in size The list of requierements is e RHO the electron density By default irho i is the reference field This field is required in XDM It is also required to
64. e density is greater than rhoplot r the rdg in the grad cube file is set to 100d0 effectively eliminating the point from the isosurface plot Also the color scale represented in RDG isosurfaces ranges from rhoplot r to rhoplot r The default value is 0 05 selfcon sistent densities or 0 07 promolecular The dimplot r controls the isosurface value to be represented in VMD Default 0 5 SC or 0 3 promolecular MOLMOTIF Complete the molecules that lie across unit cell faces by using atoms in the neighboring cells ONLYNEG Represent only the points where the second eigenvalue of the Hessian is negative 76 NOCHK Do not read or write the checkpoint file VOID void r Represent only the points where the promolecular density is lower than void r FRAGMENT file xyz FRAGMENT K P yr Z in angstrom ENDFRAGMENT In the current version of NCIplot it is possible to define molecular fragments in order to focus on some part of the crystal or some particular interaction This is done by using the FRAGMENT environments Each FRAGMENT block defines one fragment and only the intermolecular interactions between fragments are represented hence you need at least two blocks The atomic positions in Cartesian coordinates the units are angstrom of the atoms in the fragment appear inside To obtain the list of atoms the recommended procedure is to write an xyz file using the WRITE keyword then cutting it into pieces using for
65. e expensive because it involves a sum over neighboring atoms In those cases it is recommended to calculate the promolecular density once for a certain grid then use the checkpoint file e Some programs most notably VMD have problems dealing with non orthogonal cells There s little critic2 can do about this as the cube files on output are correctly writ ten Using FRAGMENT or CUBE in critic2 so that a orthogonal piece of the crystal is represented may help 14 Miscellaneous commands 14 1 Powder diffraction POWDER POWDER TH2INI t2i r TH2END t2e r L LAMBDA l r FPOL fpol r NPTS npts i SIGMA sigma r ROOT root s Generate the powder diffraction pattern for the current crystal structure Consider only the 2 theta range going from t2i r default 5 degrees to t2e r def 90 The wavelength of the incident radiation is given by l r in angstrom The polarization of the x ray radiation affects the treatment of the resulting intensities The default is fpol r 0 corresponding to unpolarized light For synchrotron radiation use fpol r 0 95 npts i is the number of points in the generated spectrum Gaussian broadening is used on the observed peaks with width parameter sigma r def 0 05 By default two files are generated lt root gt _xrd dat containing the 2 theta versus intensity data and lt root gt _xrd gnu the gnuplot script to plot it The name of these files can be changed using the ROOT keyword 14 2 Commands
66. e parts of critic2 that require derivatives or interpolation at points outside of the grid are called If only grid based algorithms e g YT BADER NCIPLOT with default NSTEP then no additional memory is used Applies to grids Default TRISPLINE CORE NOCORE The electron density from a pseudopotential plane waves calculation given on a grid only represents valence electrons In order to get an approximation to the all electron density it can be augmented by summing the corresponding core contributions to the electron density at the atomic sites The ZPSP values are used to determine how many electrons are added by each core NOCORE deactivates this behavior i e critic2 will use only the valence density from the external grid file Applies to grids it can be activated for any other field using CORE but that would not make much sense Default CORE Note that for most grid fields read with LOAD the pseu dopotential charges ZPSP are not set so even if CORE is active by default in practice no core augmentation is done because critic2 does not know how many core electrons to add Hence the effective behavior is not to core augment despite CORE being active The excep tion to this are the grid fields loaded from an abinit DEN file from which the pseudopotential charges ZPSP are automatically extracted and set EXACT APPROXIMATE The calculation of the electron density in aiPI fields is relatively expensive Using the AP
67. ed in the first line of the file The successive lines are the r_ias in the precise order needed Only for internal use of CRITIC BASIN files The surface of an atomic basin is approximated in critic2 by a polyhedron with vertices on the rays on which the zero flux surface has been determined This surface named basin from now on is approximately described as a number of polygonal facets each being a ordered list of vertices Let us consider in addition several scalar properties evaluated on the vertices of the surface We can select any of this properties to create a color map of the scalar property on the basin surface This files can only be used to analyze those surfaces that are monovalued in spherical coordinates i e surfaces that have one and only one value of the radial coordinate for every angular point The structure of the BASIN files is 86 e Rec 0 comment Comment lines starting with may appear anywhere e Rec 1 nvert nface nedge Number of vertices faces and edges of the polyhedron e Rec 2 npropty Number of properties scalars or scalar components that will be given for each point e Rec 3 propname i i 1 npropty Alphanumerical label for each property Blank characters one or more separate the properties Notice that vectors are given as three separate components etc e Rec 4i i 0 nvert 1 x i y i z i propG i j 1 npropty For each vertex the Cartesian coordina
68. edron they are discarded and not checked This is the default except in the grid module 3 qtree gradient This method behaves much like the full gradient but when ever the gradient path steps near a grid point it is projected to it When a pro jection occurs the grid point is pushed into a stack At the end of the gradient path when the terminus is known all the grid points in the stack are popped and assigned the terminus The projection regions are spheres located around each grid point whose radius is controlled by the QTREEFAC keyword The radius of these spheres is minlen 2 qtreelvl qtreefac where minlen is the smallest edge length of the full set of IWST and qtreelvl is the maximum subdivision level Note that QTREEFAC equals 1 is the maximum value allowed and corresponds to touching spheres along at least one tetrahedron edge By default QTREEFAC is 2 that is a compromise value Lower levels of QTREEFAC tend to give errors when assigning the grid points that lie on the IAS of two atoms although only there With higher levels the time saving is gone and qtree gradient reduces to full gradient Additionally the projection can be started only after a certain number of initial steps The MPSTEP keyword controls this value and defaults to 0 1 2 3 these correspond to the same as their positive values but each gradient path terminus is compared to their full gradient version using
69. efined and utilized in any expression Variable names must start with a letter and be composed only of letters numbers and the underscore char acter Also they can not have the same name as a known constant pi e eps or a function regardless of case Variables in expressions are case sensitive To use a variable first you need to assign it For instance a 20 10 ar ET 1 a 7 1 o 5 2857142857143 By using the q command line option critic2 can be used as a simple calculator echo l erf SRANDOM 100000 critic2 q 1 2578249310340 When used in combination with other keywords arithmetic expressions must be enclosed in either double quotes single quotes or parentheses or they must form a single word i e no spaces For instance this is valid critic2 input 15 a 0 12 NEQ 1 3 2 3 1 4 a Be but this is not NEQ 1 3 2 3 1 4 Be Arithmetic expressions can contain e Operators or modulo e Functions see List of available functions e Constants pi e and eps the machine precision e Variables defined by the user as above Parentheses can be used and the usual rules of associativity and precedence apply In some cases arithmetic expressions can be applied to transform a scalar field Scalar fields are denoted with a dollar sign followed by an optional identifier and the field number The latter corresponds to the order in which the field was loaded
70. el s Note all CRYSTAL keywords can be replaced by MOLECULE and viceversa with the effect discussed below The first part of every critic2 input usually specifies the crystal structure Critic2 can read a large number of crystal structue formats In the simplest usage critic2 reads one of the popular crystal structure file formats like for instance a cif file This is done by using CRYSTAL file s The extension of file s is used to determine the appropriate reading format At present critic2 understands cif files extension cif Gaussian cube files cube WIEN2k s struct files struct abinit density files _ DEN elk s GEOMETRY OUT the OUT extension is used re gardless of whether the file name is GEOMETRY OUT or not Quantum ESPRESSO s pw x output out Quantum ESPRESSO s pw x input in VASP s POSCAR CONTCAR CHGCAR ELFCAR and CHG siesta s STRUCT_IN input and STRUCT_OUT generated by the calcu lation molecular xyz files and Gaussian s wfn and wfx files Some relevant format specific comments e Gaussian cube files are assumed to represent a periodic system even though they come from a molecular calculation This is not a limitation provided the emcompassing cell is large enough and in actuality critic2 is prepared to handle the particular case of a gas phase molecule by using the MOLECULE keyword instead of CRYSTAL See section Molecular structures Despite their name cube files may represent
71. en there are a number of additional options that control the behavior of PLANE The name of the output file can be changed with FILE Using FIELD one of the loaded fields id i or an expression exprs can be evaluated In addition to the field value a second property can be evaluated the field again F its derivatives Gx its second derivatives Hxx the gradient norm GMOD or the Laplacian LAP The keyword CONTOUR writes a contour map representation of the plane two contour line files iso and neg iso and a gnuplot script gnu The isovalue distribution can be logarithmic LOG with niso i contours arctangent ATAN with niso i contours the original aimpac distribution BADER 1 2 4 8 x10 3 2 1 0 1 and linear LIN niso i contours from r0 r to r1 r The field property selected with F GX is used for the contour plot The GRDVEC keyword see Gradient path representations in a plane GRDVEC performs the same functions as PLANE with the CONTOUR option and more like for instance tracing gradient paths in the plane but it is a little more complex to use 8 4 Grids CUBE CUBE x0 r y0 r z0 r x1l r yl r zl r nx i ny i nz ilbpp r CUBE CELL nx i ny i nz ilbpp r CUBE GRID CUBE FILE file s FIELD id i expr s F GX GY GZ GMOD HXX HXY HXZ HYY HYZ HZZ LAP The CUBE keyword writes a three dimensional grid in Gaussian cube or VASP CHGCAR formats The limits of the grid can be se
72. eometry optimization will be read However if the optimization crashed then the first structure is read Quantum ESPRESSO PW inputs can also be read usually file scf in but only the in extension is detected A gas phase molecule can be input using an xyz file or a Gaussian wfn wfx file These file formats can be read using the CRYSTAL keyword but MOLECULE will make critic2 select the appropriate default options for molecules in a supercell The input molecule is enclosed in a parallelepiped that is larger default 3 bohr in all directions than the minimal parallelepiped encompassing the molecule If the CUBIC or CUBE key word is given then a cubic supercell is used The width of the vacumm around the molecule can be changed with the optional border r argument in bohr The molecule is automatically translated to the center of the cube See the section below Molecular structures for more details CIF files are read using the ciftbx library by Sydney R Hall If the CIF file provides the symmetry operations they are read The specific data block to read from a multi block cif file can be specified with the optional argument datablock s For instance to read the data_shelx block use datablock s shelx If datablock s is not present then the first block is read If none of the file formats above is available the crystal structure can be specified by hand This is done using the CRYSTAL environment For instance the input fo
73. g one or more SEED keywords When a SEED keyword is used the default seeding strategy is forgotten by critic2 and manual control of the seeding is used instead Several SEED keywords can be used at the same time each one specifying a single seeding action that is determined by the keyword immediately after SEED This keyword can be e WS a recursive subdivision of the Wigner Seitz cell to level depth i keyword DEPTH default 1 The WS cell can be displaced and centered somewhere in the unit cell using XO cryst coord default origin and scaled down to a radius of rad r bohr keyword RADIUS default not used e OH a sphere of radius rad r keyword RADIUS mandatory is built around x0 r yO r zO r keyword XO cryst coord mandatory On the surface of that sphere points are set according to a recursive subdivision algorithm that starts from a single octahedron and uses depth r recursion levels keyword DEPTH default 1 This is the same proce dure as the TRIANG keyword in BASINPLOT Each resulting point on the sphere surface determines a single ray along which nr r seeds are uniformly distributed keyword NR mandatory from XO to the surface of the sphere e SPHERE a sphere of radius rad r keyword RADIUS mandatory is built around x0 r yO r z0 r keyword XO cryst coord mandatory On the surface of that sphere points are uniformly distributed with a placement algorithm that uses nphi i points in the azimuthal ang
74. han QTREE MINL The integrated properties are to be assigned to a single atom so the only problem with inner integration is to obtain an accurate value of these integrals In the current implementation of QTREE several integration methods are possible and are controlled by the INTEG_MODE keyword The possible values of INTEG_MODE are 66 11 use the information of the density Laplacian and properties at the vertex of the tetrahedron to integrate The integral is approximated by a quadrature of four terms each corresponding to a volume that is 1 4 of the volume of the tetrahedron and multiplied by the value of the properties at the vertex This integration method is useful if only charge or charge and Laplacian are being integrated because the information gained during the gradient path tracing and saved in the fgr and lapgr arrays is used Nevertheless it is not very accurate for large tetrahedra 12 use the CUBPACK routines CUBPACK provides an adaptive tetrahedron inte gration method based on recursive subdivision exactly the same as QTREE by the way and an integration rule with 43 nodes degree 8 that is equivalent to the DCUTET library by Bernsten et al The integration rule is fully symmetric under the Th group operations The error estimation is compared to the error requested by the user that is controlled using the CUB_ABS absolute error CUB_REL rela tive error and CUB_MPTS maximum number of function evaluations
75. he critic2 keywords atoms can be selected by their atomic symbol at s in the syntax definitions in which case the keyword applies to all atoms with the same atomic number unless otherwise stated Atoms can also be selected by an integer identifier from the non equivalent atom list nat i in the definitions in those cases in which symmetry makes it irrelevant which of the symmetry equivalent atoms in the cell are used In the example above nat i 1 is Ca and nat i 2 is F For example the non equivalent atom identifier can be used to instruct critic2 to calculate the atomic population in the Ca basin Because all Ca are equivalent by symmetry it is not necessary to specify which Ca atom we want In the cases in which symmetry can not be used for instance if we want to represent the basin of an atom at a particular location then critic2 reads an integer identifier from the complete atom list at i in the following In the example above at i 1 represents the Ca at 0 0 0 at i 2 is the Ca at 0 5 0 5 0 and so on In exact parallel to the atomic lists critic2 also maintains a list of non equivalent critical points CP and a complete or cell list of critical points found for the current reference scalar field The CPs in the non equivalent list reproduce all the CPs in the complete list by symmetry In the keyword definitions the same rules for atoms apply to the CP identifiers ncp i for non equivalent CPs and cp i for comple
76. here the indicated file is used instead to perform the lookup The path can be absolute or relative to the execution directory 5 3 Symmetry options Critic2 has two symmetry modules spg and guess Spg accepts a label for instance P m 3 m and builds the symmetry from it guess reads the unit cell description lengths angles and the complete list of atoms in the cell and calculates all the symmetry operations Depending on the type of CRYSTAL input the symmetry behavior defaults to e cif uses the symmetry operations inside the file symmetry equiv pos as xyz or space group symop_ operation xyz labels e cube guess e struct internal symmetry operations if present Otherwise guess e vasp guess e abinit internal information in the DEN file e elk guess e espresso guess e cell cartesian neq spg if used Otherwise guess The treatment of symmetry in critic2 can be controlled using the GUESS NOGUESS be fore CRYSTAL and CLEARSYM after CRYSTAL keywords GUESS NOGUESS Activates GUESS or deactivates NOGUESS the use of guess They must be used before crystal to be effective The default is GUESS CLEARSYM Clear all symmetry operations that is use space group P 1 It must be used after CRYS TAL to be effective 26 5 4 Atomic charge options The Q or QAT and ZPSP keywords can be used to change the atomic charge and pseudopo tential charge after CRYSTAL Q QAT ZPSP nat1l ilatl s q
77. his face is nv nv 3 in the triangular tesselations and 4 in the quadrilateral ones For each vertex in this face the number of order in the previous vertex list Remember that vertices are numbered from 0 to nvert 1 OFF and COFF files The OFF COFF files can be viewed and printed with geomview The structure is 16 Rec 0 comment Comment lines starting with may appear anywhere Rec 1 file type Either OFF or COFF keyword Rec 2 nvert nface nedge Number of vertices faces and edges of the polyhedron Rec 3 x i y i z r gG b alpha i i O nvert 1 Cartesian coordinates x y z of the vertices In the case of COFF files additional in formation is given regarding the RGB color associated to the vertex and the degree of transparency alpha of the surface at this position Rec 4j j 0 nface 1 nv ivert k j k 1 nv The number of vertices of this face is nv nv 3 in the triangular tesselations and 4 in the quadrilateral ones For each vertex in this face the number of order in the previous vertex list Remember that vertices are numbered from 0 to nvert 1 Copyright notice Critic2 including its documentation is distrubted under the GNU General Public License Please see COPYING in the root directory of the critic2 distrubtion for details 88
78. hree possible cases One vertex is outside three inside The tetrahedron formed by the vertex that is outside and the three middle points of the edges that stem for it form a tetrahedron by itself that is integrated and added to the atom properties Three vertex are outside one inside The difference between the whole tetrahe dron integration and the small tetrahedron inside the sphere is added to the atom properties The small tetrahedron is formed by the vertex that is inside the sphere and the three edges connected to it Two vertex are inside two outside The region outside of the sphere is a triangular prism that is split in three tetrahedra and integrated Note that the INTEG_MODE of the maximum subdivision level qtree_lvl applies to all the sub integrations of the border same color integration Border diff color integration As in the case of border same color integration this method only applies to tetrahedra which are at their maximum subdivision level In this case the termini of the vertex corresponding to at least two different atoms In the current implementation of QTREE the tetrahedron is integrated as a whole Then the properties are equitatively assigned to each of the termini atoms For instance if the termini are 1 1 1 3 the properties of the tetrahedron are integrated then 3 4 of them assigned to atom 1 and 1 4 to atom 3 In the literature this problem has been addressed alth
79. instance avogadro and then placing the resulting atom lists in FRAGMENT environments Alternatively the fragment can be read from an xyz file There are three options that control the behavior of the fragments RTHRES RHOPARAM and RHOPARAM2 RTHRES rthres r When fragments are used the density and rdg grids are reduced to a piece encompassing the fragments with a border of rthres r bohr default 2 0 RHOPARAM rhoparam r Consider only the points where none of the fragments contributes more than rhoparam r times the total promolecular density default 0 95 RHOPARAM2 rhoparam2 r Consider only the points where the sum of the density of all fragments is more than rhoparam2 r times the total promolecular density default 0 75 Note that the fragments need not include all atoms in the crystal Some advice regarding the execution of NCIPLOT e If the density is given on a grid it is usually much faster and the result is much better if core augmentation ZPSP is not used The reason is that if the core augmentation 77 is not present the reduced density gradient and the Hessian components can be cal culated by Fourier transform which is smoother and it is not necessary to sum over neighboring atoms The NCI regions are in the interstitial where the density is mostly correct anyway and the plots are only qualitative e Likewise any option that activates the calculation of the promolecular density VOID or FRAGMENT is going to b
80. ional options Regardless of the types of fields in the expression passed to LOAD AS a grid field can be enforced by explicitly specifying the size of the grid either by giving the number of points in 36 each direction n1 i n2 i n3 i or by adopting the size of another grid SIZEOF the mold grid has field id i If grid fields appear in the expression but you want a ghost field then use the GHOST keyword The PROMOLECULAR option to LOAD AS allows the creation of a grid out of the pro molecular density with number of points n1 i n2 i n3 i or the size of grid field number id i if the SIZEOF keyword is used Similarly CORE creates a grid using only the core densities as specified by the ZPSPs of the atoms If a fragment of the crystal is passed as an xyz file to any of those keywords then only the atoms in the fragment contribute to the sum of atomic or core densities The LAP GRAD and CLM keywords of LOAD AS apply only to specific types of fields e GRAD only applies to grid fields It defines a new grid as the norm of the gradient of the grid field with index id i e LAP applies to grid WIEN2K and elk fields In all cases the keyword creates a field of the same type containing the Laplacian of the field with index id i Ifid iis a grid the Laplacian is calculated by Fourier transform If it is a WIEN2k or elk field the Laplacian is calculated analytically both inside the muffin tins and in the interstitial using the appropri
81. ional keyword allows the user to enter a lattice vector to displace the represented ncp gradient paths from their position given in the complete cp list written by AUTO e BCP print gradient paths starting at the vicinity of a bond CP identified by cp i If the gradient path is ascending 1 in the fourth field the unique bond path associated to the bcp is represented If 1 is given instead the IAS associated to the bcp is sampled starting from a small circle surrounding the bcp with n i points on it With a O value both tasks are performed The three keywords BRAINDEAD QUOTIENT and DYNAMICAL establish the method employed in generating the starting angular grid With BRAINDEAD critic2 uses a uniform angular grid Using QUOTIENT the uniform grid is remapped by x 11 12 where 11 and 12 are the two negative eigenvalues at the bcp This way the points get 53 accumulated around the bcp with lowest eigenvalue highest if absolute value is taken DYNAMICAL uses a linearized model of the interatomic surface and predicts the initial angles critic2 has to take in order to generate a uniform distribution of points a given distance away This distance is calculated as 90 of the distance to the nearest ccp found in a coarse exploration of the IAS omega limits Unfortunately this algorithm works only in cases where the bcp has significant but not too large ellipticty Also there is no gain in using this method in cases where the number of ccps
82. is different than 4 By default BRAINDEAD is used H1 is experimental RCP print gradient paths starting at the neighbourhood of a ring CP The situation is analogous to that of the beps CCP print gradient paths starting at the vicinity of a cage CP Again the situation is symmetric to the ncp case GRAPH represent the complete graph in the unit cell This means All the bond paths for which both ncps and the bcp lay inside the main unit cell All the ring paths for which both ccps and the rcp lay inside the main unit cell The critical points on the boundary of the main cell are also represented The igraph i value represents the quantity of information that is to be printed It is a sum of values each representing an element to plot 1 print ring paths associated to the reps 2 print bond paths associated to the bcps These options are only available if an AUTO task was carried out with the option SET GRAPH Several parameters of FLUXPRINT can be changed using the options keyword The format of the output file can be controlled with the following keywords TEXT plain text file TESS or TESSEL tessel OBJ Wavefront obj PLY ply format and OFF Geomview s off The EVERY keyword makes critic2 write only one in every every i points for each gradient path Finally the SHELLS keyword applies only to graph and graphcp It represents the number of unit cell shells where the graph is going to be p
83. istance for each atom times abs rend r Default npts i 100 In GAULEG ntheta i 20 and nphi i 20 In LEBEDEV nquad i 770 r0 1d 3 rend rnn 2 for each CP id i O all attractors 12 4 Qtree QTREE MINL minl i GRADIENT_MODE gmode i QTREE ODE MODE omode i STEPSIZE step r ODE_ABSERR abserr r INTEG_ MODE level i imode i INTEG_ SCHEME ischeme i KEASTNUM k i PLOT_MODE plmode i PROP_MODE prmode i MPSTEP inistep i QTREEFAC f r CUB_ABS abs r CUB_REL rel r CUB_MPTS mpts i AUTOSPH 1 2 SPHFACTOR ncp i fac rlat s fac r 59 SPHINTFACTOR atom i fac r DOCONTACTS NOCONTACTS ACTIVE atom i INACTIVE atom i WS_ORIGIN x r y r z r WS_SCALE scale r WS_EPS_VOL eps_vol r NOWS KILLEXT NOKILLEXT CHECKBETA NOCHECKBETA PLOTSTICKS NOPLOTSTICKS COLOR _ALLOCATE 0 1 SETSPH LVL lvl i VCUTOFF vcutoff r QTREE maxlevel i plevel i The QTREE integration method is a new algorithm capable of calculating the QTAIM atomic properties in a more efficient way than the bisection approach QTREE is specific to solid state problems and is based on a hierarchical subdivision of the irreducible part of the WS cell employing a tetrahedral grid The integration region is selected so as to maximize the use of symmetry and partitioned into tetrahedra These tetrahedra enter a recursive subdivision process in which each of them is divided in 8 at each level up to a level given by the user the maxlevel i indicated after
84. ith a contour plot in the spirit of PLANE CONTOUR see Planes and contour plots PLANE This contour map corresponds to the reference scalar field if F is used to its Laplacian LAP etc In a way analogous to CONTOUR the contour lines may be calculated using a linear spacing between isocurves on a remapped scalar field If LOG is given log f and log abs f are used while for ATAN the function is 2 pi atan f The BADER keyword corresponds to a fixed set of iso values 1 2 4 8 x10 3 2 1 0 1 LEVEL selects a linear set of contour values from cini r to cend r The number of points on each axis of the grid and the number of contour lines can be optionally given with nptsu i nptsv i and niso i By default they are 100 100 and 100 Note that GRDVEC is able to handle non orthogonal axis If the two plane axis determined in the PLANE keyword are non orthogonal the final graph will correctly reflect the actual appearance of the plane by conserving the original angle between the x and y axis Also note that at most 2 gradient lines may be traced from bcps and reps either upwards or downwards Thus for example BCPALL 2 2 is equivalent to BCPALL 2 100 or BCPALL 100 100 10 3 Three dimensional gradient path representations FLUX PRINT FLUXPRINT POINT 1 1 0 x r y r z r step r epsi r NCP cp i ntheta i nphi i step r epsi r LVEC x i y i z i BCP cp i 1 step r epsi r LVEC x i y i z i BCP cp i 0 1 n i step r epsi r
85. keywords If CUB_MPTS is exceeded an error message is output but the QTREE integration continues Note that no matter how low the error requirements are the CUBPACK integration spends at least 43 function evaluations per tetrahedron so it is quite expensive if compared to other integration modes This should be reserved for large tetrahedra see below or for really accurate calculations 1 10 use a non adaptive rule from the KEAST library Keast et al 1986 the number corresponding to x 1 order 1 degree 0 x 2 order 4 degree 1 3 order 5 degree 2 4 order 10 degree 3 5 order 11 degree 4 6 order 14 degree 4 7 order 15 degree 5 8 order 24 degree 6 9 order 31 degree 7 10 order 45 degree 8 In particular the first KEAST rule uses the barycenter of the tetrahedron XK XA XA XX XX o The syntax of the INTEG_MODE keyword is INTEG_MODE lvl i mode i where mode i is one of the modes above and lvl i is the level for which it applies This means that if a tetrahedron of a given level is to be integrated the value of IN TEG_MODE level is checked to decide on the method 67 A last INTEG_MODE value is possible 1 do not integrate and force the tetrahedron into the subdivision process This value of INTEG_MODE can be combined with a positive value at higher levels amounting to a recursive integration in the style of CUBPACK Of cour
86. keywords are used to perform the required tasks For instance AUTO automatic determination of critical points INTEGRALS atomic integration NCIPLOT non covalent interaction index plots etc A concise description of the critic2 keyword syntax is given in the syntax txt file If you are already familiar with this program that file will probably be more useful to you than this guide 3 Input format output format and notation The input for critic2 is free format and case insensitive Lines preceded by are treated as comments The input syntax is keyword oriented The first word in a non blank input line is the main keyword and determines one task that critic2 is required to perform In the remainder of this manual these main keywords and their usage are described Keywords are written in CAPS and sometimes in color if they are within a code block Input variables are denoted using a suffix to indicate their type a real number r an integer i or a string s Almost anywhere that a number is expected it is possible to use an arithmetic expression see the Arithmetic expressions variables and functions in critic2 section If an arithmetic expression is required quotes expr s are used When several alternative keywords are possible the or symbol is used Square brackets denote optional keywords and curly braces are used for grouping Some of the sections in the rest of this manual contain an additional o
87. l Calculated from the above unless given The usual way of running XDM for the first time is CRYSTAL rho cube ZPSPC406H1 LOAD rho cube LOAD elf cube XDM elf 2 This generates several cube files root tau cube root pdens cube root core cube root lap cube root grad cube and root b cube Subsequent runs can circumvent the calculation of B PDENS and CORE by doing CRYSTAL rho cube ZPSPC406Hm1 LOAD rho cube LOAD root b cube LOAD root pdens cube LOAD root core cube XDM XB 2 PDENS 3 CORE 4 Note that passing RHO 1 is not necessary because rho cube is the first field loaded hence the reference and assumed by default to be the density by XDM Again the ZPSP of all atoms are needed for an XDM calculation Also only closed shell non spinpolarized systems can be calculated for now During the calculation cubes for almost all the properties above are generated so they can be reused in future calculations The other options are XA1 al r The value of the al damping parameter adimensional Default 0 6836 PW86PBE parametrization for QE XA2 a2 r The value of the al damping parameter in angstrom Default 1 5045 PW86PBE parametrization for QE ONLYC 83 Calculate the dispersion coefficients but not the dispersion energy forces and stress By default they are calculated UPTO 6 8 10 Only calculate the contributions to the energy coming from the C6 term 6 from the C6 and C8 terms 8 and from C6 C8
88. l r nat2 ilat2 s q2 r Changes the atomic charge Q QAT or the pseudopotential atomic number ZPSP of the non equivalent atom il i i2 i or the atom type atl s at2 s Real numbers for the charges are acceptable but they are internally converted to integers See the discussion above Loading a crystal structure CRYSTAL MOLECULE for an explanation on the behavior of Q and ZPSP NOCORE Clears the ZPSP values of all atoms 5 5 Loading multiple crystal structures Critic2 can only work with one crystal structure at a given time However more than one crystal can be loaded in the same run simply by giving a new CRYSTAL or MOLECULE keyword When the second and subsequent CRYSTAL keywords are read critic2 clears all the information for the previous crystal structure including the structural data cell parameters and atomic positions as well as all the fields that had been loaded all the critical point information and the atomic and core density grids Effectively critic2 behaves as if starting a new run except in that the variables and global options are carried over To clear the variables and set the global options to their default values use the RESET keyword RESET 5 6 Molecular structures Critic2 can be used to analyze scalar fields in isolated molecules as well as in crystals This behavior is activated by using the MOLECULE keyword to load the structure instead of the usual CRYSTAL The MOLECULE keyword is mo
89. lab and the corresponding vacuum are perpendicular to one of the crystallographic axes a b or c The two angles related to the perpendicular axis must be right For instance a typical situation is one where a and b form a hexagonal cell in the plane and c is perpendicular to the slab The angles related to c alpha and beta both are 90 degrees 80 e The slab has two faces one with vacuum above and one below Only the face with vacuum above it will be used e The STM plot calculation uses the reference field For results consistent with the Tersoff Hamann approximation the reference field should be the local density of states LDOS in the following at the Fermi level that is the density generated by the Kohn Sham states close to Ef This field can be obtained easily from common condensed matter electronic structure programs For instance in QE one would use plot num 3 or 5 in pp x There are two modes of operation in the STM keyword In the default mode CURRENT the plot gives the height in angstrom for which the LDOS equals curr r a u units default 1d 3 This corresponds to the constant current mode in STM experiments The other mode is HEIGHT in which the LDOS at a constant height over the surface is plotted This is the constant height mode in STM experiments The hei r option to HEIGHT is the fractional co ordinate along the perpendicular axis of the plot plane By default critic2 uses the fractional coordinate cor
90. ld number two a 1 2 to calculate the same grid Expressions involving fields can also be used in LOAD and in other keywords POINT LINE INTEGRABLE etc The value of a variable can be cleared using the CLEAR keyword CLEAR varl s var2 s CLEAR ALL This keyword deletes the variables varl s var2 s etc or all the variables ALL At any moment the internal list of variables can be printed to the output using the keyword LIST LIST 4 2 List of available functions Arithmetic expressions can use any of the functions in the critic2 function library These functions include the usual mathematical functions like exp or sin but also functions that are meant to be applied to scalar fields of a certain type e g the Thomas Fermi kinetic energy density gtf It is very important to distinguish whether a function expects a numerical argument e g sin x an integer field identifier e g gtf id The list of arithmetic functions is abs exp sqrt floor ceil ceiling round log log10 sin asin cos acos tan atan atan2 sinh cosh erf erfc min max All these functions apply to numbers or other arithmetic expressions and their behavior is the usual For instance sin 2 pi max 1 0 and atan2 yx are all valid expressions The following chemical functions accept one or more integer field identifiers as their arguments Their purpose is to provide shorthands to build fields from other fields using physically relevant
91. le keyword NPHI mandatory and ntheta i points in the polar angle keyword NTHETA mandatory Each resulting point on the sphere surface determines a single ray along which nr r seeds are uniformly distributed keyword NR mandatory from XO to the surface of the sphere e PAIR seeds are placed on the interatomic lines for all atom pairs at a distance less than dist r bohr keyword DIST default 15 The number of seeds per line is n i keyword NPTS default 1 44 e TRIPLET seeds are placed at the barycenter of every atomic triplet in which the three atoms are at a distance from each other less than dist r keyword DIST default 15 e LINE place n i seeds keyword NPTS default 1 along a line between x0 r yO r z0 r keyword XO cryst coords default origin and x1 r y1 r z1 r keyword X1 cryst coords mandatory e POINT place a single seed at x0 r yO r z0 r keyword XO cryst coords mandatory Multiple SEED keywords can be given in the same AUTO command For instance AUTO SEED PAIR SEED WS SEED POINT 1 4 1 4 1 4 executes three seeding actions a search between all atoms pairs 1 seed per pair a recursive subdivision of the WS cell one level and a single seed at 0 25 0 25 0 25 The seed placement can be visualized using the optional VERBOSE keyword that writes an OBJ file lt root gt _seeds obj containing the unit cell and all the seed positions The AUTO search can be restricted to a porti
92. le containing the input structure can be written by using the abin ex tension An elk input template can be written using the elk extension A simple cif file no symmetry is generated if the cif extension is used The octave script file extension m contains the crystal structure in octave format and is prepared to be read using escher visit gatsby ucmerced edu for more information A simple GULP template input file containing the structure and EEM as the first line can be written using the gin extension If the DREIDING keyword is used critic2 will attempt to find the atom types in the DREIDING force field No resonant atoms are detected For file names with an extension lammps critic2 writes a simple LAMMPS data file containing one unit cell length units are angstrom Only orthogonal cells are supported for now Both the GULP and the LAMMPS outputs are experimental so please exercise care and double check the templates Two types of siesta inputs can be generated The fdf extension writes a template for a proper functional siesta input template containing the crystal structure The STRUCT_IN extension writes a files that can be read using the MD UseStructFile option To make critic2 try to reduce the current cell to the primitive cell before writing the template file use the PRIMITIVE keyword The code that does this is still not very well polished particularly for the more exotic centering types so I recommend you check your
93. loaded in field number 1 would be xc 1 1 xc 1 9 19 because idx 1 is Slater s exchange and idx 9 is Perdew Zunger correlation PBE a GGA would be xc 1 2 101 xc 1 2 130 Here 101 is PBE exchange and 130 is PBE correlation Field 1 contains the electron density and 2 is its gradient which can be determined using for instance LOAD AS GRAD 1 5 The crystal structure 5 1 Loading a crystal structure CRYSTAL MOLECULE CRYSTAL file cif datablock s CRYSTAL file cube CRYSTAL file struct CRYSTAL file POSCAR atl s at2 s POTCAR CRYSTAL file CONTCAR atl s at2 s POTCAR CRYSTAL file CHGCAR atl s at2 s POTCAR CRYSTAL file CHG file ELFCAR atl s at2 s POTCAR CRYSTAL file_DEN CRYSTAL file OUT e g elk s GEOMETRY OUT CRYSTAL file out e g ESPRESSO s file scf out PW output CRYSTAL file in e g ESPRESSO s file scf in PW input CRYSTAL file STRUCT_IN CRYSTAL file STRUCT_OUT MOLECULE file xyz border r CUBIC CUBE MOLECULE file wfn border r CUBIC CUBE MOLECULE file wfx border r CUBIC CUBE CRYSTAL SPG spg s CELL a r b r c r alpha r beta r gamma r CARTESIAN scal r comment BOHR AU ANGSTROM ANG xlr yl r zl r RL V2 22 7 x3r Y3nr 23 r ENDCARTESIAN END NEQ x r y r z r at s ZPSP zpsp i Q q i 20 ANG ANGSTROM BOHR AU CENTER CENTRE x r y r z r ENDCRYSTAL ENDMOLECULE END CRYSTAL LIBRARY lab
94. longing to a particular basin is calculated by evaluating the trajectory flow to neighboring points 73 The YT algorithm is described in J Chem Phys 134 2011 064111 which should be consulted for further details Please cite this reference if you use this keyword in your work The located maxima are identified by default with the closest nucleus If non nuclear maxima are expected use the NNM keyword to assign only maxima that are only within 1 bohr of the closest atom The NOATOMS option is appropriate for scalar fields where the maxima are not expected to be at the atomic positions or at least not all of them If NOATOMS is used all the maxima found are given as NNM This is useful for fields such as the ELF the Laplacian With the ESCHER keyword it is possible to write a m octave script containing the geom etry that can be interpreted by escher run by the escherplot m file in the src subdirectory With FIELDLIST critic2 writes a list of all the maxima found and the value of all integrable fields at those points Not all the properties defined by the INTEGRABLE keyword are integrated Only the subset of those properties that are grids have F or FVAL as the integrand and are congruent with the reference grid are considered This limitation can be circumvented by using LOAD AS In addition no core is used even if the CORE keyword is active The volume is always integrated A xyz file lt root gt _yt xyz is always written cont
95. lotted Thus 0 represents the main unit cell 1 the main unit cell and its 26 neighbours and so on By default SHELLS adopts the 1 value which is equivalent to 0 for the graph keyword and means that the partial graph generated in graphcp is not expanded through symmetry NOSYM do not use symmetry operations Using this keyword the complete list of CPs in the unit cell is written together with the identity matrix as the only operation in the space group 54 11 Atomic basin representations 11 1 Attractor basin plots BASINPLOT BASINPLOT CUBE lvl i TRIANG lvl i SPHERE ntheta i nphi i OFF OBJ PLY BASIN DBASIN npts i PHASE phtheta r phphi r CP cp i PREC delta r VERBOS MAP id i expr Plot the attraction basin of the CP cp i from the complete list if CP is not given all the non equivalent attractors are used The rays on which the bisection is carried out are deter mined by the method chosen With CUBE a cube is selected as the starting polyhedron and recursively subdivided lvl i times The final convex polyhedron is placed on the attractor and the zero flux surface limit for the rays is determined TRIANG follows the same process starting from an octahedron SPHERE stands for a direct triangulation of the unit sphere There are nphi r parallels The equatorial circles contain exponentially more points than the polar Ntheta i thus represents a seed The total number of points is given by the fo
96. ntegration If the tetrahedron has termini corresponding to different atoms its properties are integrated and split into contribution to atoms according to the number of termini each atom has These tetrahedra are located on the IAS and require a third class of integration border diff color integration A tetrahedron that has not been integrated continues to the subdivision step In this step 8 new tetrahedra are pushed into the stack To this end the edges of the parent tetrahedron are split in two Note that by construction the newly generated points correspond to grid points also The subdivision scheme is x XK XA XA XX XX 1 1 2 1 3 1 4 2 1 2 2 3 2 4 3 1 3 2 3 3 4 4 1 4 2 4 3 4 2 3 1 2 1 3 1 4 1 4 1 2 2 3 2 4 1 4 1 3 2 3 3 4 2 3 1 4 2 4 3 4 where a represents a vertex of the parent tetrahedron and a b the midpoint of both vertex Each of the 8 child tetrahedra enclose the same volume equal to V 8 l where is the subdivision level and V is the volume of the base tetrahedron The 4 last subdivisions can be chosen in yet another way but this is not relevant to the results of QTREE When the stack is empty the work on the base tetrahedron is finished Inner integration The inner integration applies to tetrahedra that are completely con tained in the non beta sphere region of a basin It can apply to a tetrahedron of any level as long as it is greater t
97. of cells used in each direction is given by ix i iy i and iz i default 1 1 1 For the purpose of its graphical representation it is sometimes interesting to include atoms which are almost exactly at the edge of the cell For instance when doing CRYSTAL SPG f m 3 m CELL 5 64 5 64 5 64 90 90 90 ANG NEQ 0 0 0 na NEQ 1 2 1 2 1 2 c ENDCRYSTAL 29 WRITE nacl xyz Critic2 will correctly generate a list of 4 Na and 4 Cl atoms representing 1 8th of the conventional cell because the atoms at 1 0 0 1 1 2 0 etc are repetitions of the atoms in the main cell However this does not look good when the unit cell is represented graphically because many of the atoms in the cubic cell are missing By using BORDER these atoms are included The keyword MOLMOTIF is used in molecular crystals All atoms in the requested cells are written to the xyz file Then the molecules that lie across the cell boundary are completed using atoms from the neighboring cells In order to do this a connectivity criterion is used two atoms are bonded if their distance is less than 1 5 times their sum of covalent radii The BURST keyword is similar to MOLMOTIF in that the molecular crystal structure is par titioned into individual molecules which are then completed using the atoms from neighbor ing cells However in contrast to MOLMOTIF each of those molecular fragments is written to a separate file The SPHERE keyword writes all atoms inside
98. om and is similar to Bader s AIMPAC suite of programs 50 By using the FILES keyword equivalently ROOT or ONAME the user sets the root name of the output files containing the information for the plot default lt root gt These files include e lt root gt grd gradient path data e lt root gt dat values of the field on thea plane e lt root gt iso lt root gt neg iso positive and negative contour lines e lt root gt gnu gnuplot script file that generates the merged gradient contour plot e lt root gt label gnu gnuplot script file loaded in lt root gt gnu containing the information for the position of the CPs in the plot plane In the standard syntax PLANE specifies the plane for the plot using three points x0 is the origin x1 the end of the x axis and x2 the end of the y axis all in crystallographic coordinates The SCALE option allows the user to extend the plane relative to the reference points The x and y axis of the rectangle are scaled using the sx r and sy r values There is another possibility the PLANE CP keyword or the equivalent syntax PLANE ATOM accepts three atoms or critical points from the complete CP or atom list The first atom or CP is taken as reference and the other two are replicated by symmetry until critic2 finds the equivalent position that is nearest to the first The three points found this way hopefully determine a plane The barycenter of the points is calculated and
99. on of the unit cell using the CLIP keyword The CLIP keyword specifies a periodic region of real space Only the seeds inside that re gion are used and only the CPs found inside that region are accepted although symmetry can replicate the CPs and send them outside the CLIP region use CLEARSYM or NOGUESS to deactivate symmetry if necessary see Symmetry options There are two possible region shapes in CLIP a parallelepiped CUBE and a sphere SPHERE The parallelepiped is speci fied by giving its initial x0 and final x1 points in crystallographic coordiantes The sphere requires a center x0 in cryst coords and a radius in bohr A number of additional optional keywords control the behavior of AUTO GRADEPS is the gradient norm threshold for the optimization if a CP is found with gradient norm less than GRADEPS default 1e 12 then it is accepted as CP If DRY dry run is used then the seeding is done but the actual CP search is skipped This is useful to examine the seed placement in combination with VERBOSE and also to print the current list of CPs at zero computational cost for intsance after a CHECK run CPRHO and CPEPS control the minimium field value that a CP needs to have to be ac cepted and the minimum distance between CPs to consider them equivalent respectively Because finding the CPs can be an expensive task in large low symmetry crystals the CP list can be saved to a file using the FILE keyword The file cps file
100. only irreducible in the local symmetry of the origin not by the full set of space group operations The IWS is the region that is to be integrated in later steps of QTREE We will refer to single IWS tetrahedra as IWST It is possible through the WS_ORIGIN keyword to shift the origin of the WS cell away from the 0 0 0 position Using the procedure above the number and shape of IWST changes depending on the origin chosen Trivially a general position will make the IWS exactly equal to the WS Also for large systems the user can choose to shrink the size of the original WS cell in order to integrate a smaller region using the WS_SCALE keyword most likely in combination with WS ORIGIN to move the region around If a value is given to WS_SCALE say rws then all the vectors connecting the origin of the WS cell with the vertex are shrunk by a factor rws therefore decreasing the volume by a factor rws 3 The IWS is calculated using the smaller WS cell and integrated in the same way Note that this integration region is non periodic it does not fill the volume of the solid and it does not integrate to the total number of electrons per cell e Non overlapping spheres are chosen centered on each of the atoms of the cell the so called beta spheres Atoms equivalent by symmetry share the same beta sphere radius say beta_i for atom i The beta sphere takes two roles in QTREE The atomic properties are integrated inside the beta s
101. otif perhaps extended with some of atoms in the neighboring cell The simplest way of doing this is by writing an xyz file CRYSTAL myfile_DEN WRITE myfile xyz MOLMOTIF The MOLMOTIF keyword writes all atoms in the unit cell and completes the molecules by using the atoms in the neighboring cells A covalent radii criterion is used to determine whether two atoms are bonded or not The full syntax of the WRITE keyword is WRITE file xyz g jf SPHERE rad r x0 r y0 r z0 r CUBE side r x0 r y0 r z0 r BORDER MOLMOTIF BURST ix i iy i iz i WRITE file obj ply off SPHERE rad r x0 r y0 r z0 r CUBE side r x0 r y0 r z0 r BORDER MOLMOTIF BURST CELL MOLCELL ix i iy i iz il WRITE file scf in PRIMITIVE WRITE file tess WRITE file incritic WRITE file POSCAR file CONTCAR PRIMITIVE WRITE file abin PRIMITIVE WRITE file elk PRIMITIVE WRITE file cif WRITE file m WRITE file gin DREIDING WRITE file lammps WRITE file fdf WRITE file STRUCT_IN At present a number of formats can be written by critic2 although it is easy to add more to this list and it is likely to increase in the future As in CRYSTAL the type of file is detected by the extension xyz in tess incritic etc In the first WRITE command above an xyz file containing a finite piece of the crystal is generated Alternatively if the gjf extension is used a template for a Gaussian input file is written The number
102. ough in cubes not in tetrahedra by using a Monte Carlo integration inside the region This requires tracing a gradient path for each of the random points to achieve a overall accuracy that scales as sqrt N where N is the number of nodes However I feel that if this type of approach is to be used then it is better to continue subdividing the tetrahedron in a way that is equivalent to going to a higher QTREE level that scales as N 69 e Gradient path tracing The gradient path start always at grid points and are traced using one of three methods controlled by the GRADIENT_MODE keyword that can assume the following values 1 full gradient This method is ODE integration as it is meant to be The integration is carried out ignoring the grid information As was explained before the gradient path is terminated whenever it enters a beta sphere region 2 color gradient At each point of the gradient path the neighboring grid points are checked If all of them correspond to the same atom then the terminus of the gradient path is assigned to that atom In a tetrahedral mesh the meaning of neighboring grid points is not as clear as in a cubic mesh For a given point x the neighbors are calculated by first converting x to convex coordinates that range from 0 to 2 l restricted tox_1 x_2 x_3 lt 2 The neighboring points are AI T x2 O AS APS L If any of these neighbors are not valid points in the tetrah
103. pheres using a 2d cubature The cubature can be a product of two 1d Gauss Legendre quadratures or a Lebedev quadrature of the sphere Both methods and the number of nodes can be selected using the INT_SPHEREQUAD keywords explained below The radial quadrature can be any of the available in critic and is controlled by the INT RADQUAD options The default values however are usually fine integrating the beta spheres in a matter of seconds with a precision that is orders of magnitude better than the overall QTREE performance This beta sphere integration removes the error of the finite elements integration of a region where the integrated scalar fields present the steeper variations in value By removing the high error regions from the grid integration the accuracy of QTREE is enhanced In particular this increase in precision outweighs the loss by creating an additional interface between the grid and the sphere The space inside the beta sphere of an atom is assumed to be inside the basin of that atom The terminus of any gradient path that reaches the interior of the beta 61 sphere i is assumed to be the atom i It is known that most of the steps in the integration of the gradient of the electron density are spent in the close vicinity of the terminus Therefore this modification saves precious function evaluations The default beta sphere radius is set to 0 80 times half the nearest neighbor distance Both i and ii above assume
104. planes grids For instance if rhoup cube and rhodn cube are the spin up and spin down densities it is possible to get the total density and the spin density using LOAD rhoup cube LOAD rhodn cube LOAD AS 1 2 LOAD AS 1 2 The spin up density is loaded as field 1 rhodn cube is field 2 field 3 is defined as the sum of both and field 4 is the spin density which can for instance be graphically represented or integrated in the atomic basins to get the atomic magnetic moments see INTEGRABLE in Integration of atomic basins The list of arithmetic operations that can be performed on fields is quite large see Arith metic expressions variables and functions in critic2 If no additional keywords are present between LOAD AS and the arithmetic expression like LAP GRAD or CLM see below then two types of fields can be loaded If the arithmetic expression involves at least one grid the resulting field will be a grid with the same number of points If more than one grid appears in the expression then the new grid size is the maximum of the number of points in every dimension If the expression contains no grid fields then the resulting field is what critic2 calls a ghost field A ghost field is just an arithmetic expression that is parsed and processed every time the field is evaluated The analyitcal derivatives for a ghost field are naturally not available so the NUMERICAL option is the default for this kind of field see Addit
105. ptions subsection These provide some independent keywords that control the behavior of critic2 and are meant to be used either before or after the keywords in the section in which they appear For instance NOGUESS can be used before CRYSTAL to deactivate the automatic calculation of the crystal symmetry NOGUESS CRYSTAL benzene cif Hence NOGUESS appears in this manual as an additional option to CRYSTAL The critic2 output is mostly self explanatory although there are a number of key concepts that need to be understood The crystal structure in critic2 is represented by two lists of atoms The non equivalent atom list contains the atoms in the asymmetric unit that is the minimal list of atoms that generate all the atomic positions in the crystal by symmetry The cell atom list equivalently called the complete atom list contains all atoms in the current unit cell The non equivalent atom list reproduces the complete atom list by applying all symmetry operations except lattice translations known to critic2 For instance an input for the conventional cell of the fluorite CaF2 crystal is CRYSTAL SPG f m 3 m CELL 5 463 5 463 5 463 90 90 90 ANG NEO 0 0 0 ca NEQ 1 4 1 4 1 4 ENDCRYSTAL The non equivalent atom list contains Ca at 0 0 0 with multiplicity 4 and F at 1 4 1 4 1 4 with multiplicity 8 The cell atom list contains 4 Ca atoms at 0 0 0 1 2 1 2 0 etc and 8 F atoms at 1 4 1 4 1 4 3 4 1 4 1 4 etc Note that c
106. r magnesium oxide rocksalt structure would be CRYSTAL SPG F m 3 m CELL 4 213 4 213 4 213 90 90 90 ANG NEQ 0 0 0 Mg NEQ 1 2 1 2 1 2 0 ENDCRYSTAL There are several relevant keywords in the CRYSTAL environment A particular space group can be used with the SPG keyword in which case only the atoms in the asymmetric unit need to be given 22 SPG spg s The SPG keyword builds the complete set of symmetry operations in the crystal from the space group label alone The space group names known to critic2 correspond to those given in the International Tables for Crystallography vol A in the Hermann Mauguin notation Each element in the label is separated by one or more blanks and the input is case insensitive Examples of values for spg s are F m 3 m P b a 2 P 1 n 1 P 63 m c without the quotes If two origin choices are possible then an additional token 1 or 2 can be appended to the space group label to choose between them If no origin choice is specified origin 1 is used by default note that in most electronic structure programs origin 2 is default however For example F d d d 1 F d d d with origin choice 1 F d d d 2 same group with origin choice 2 F d d d same as origin 1 For R space groups hexagonal and rhombohedral axes are possible These can be specified by an h or r token after the space group label If no h or r is given hexagonal axes are used For the hexagonal the o
107. r of NEQs that are necessary Otherwise the complete list of atoms in the cell has to be given and the symmetry guess will reduce it to the non equivalent atoms list The coor dinates x r y r z r are crystallographic fractional coordinates unless the ANG ANGSTROM or BOHR AU keywords are used Usage of Cartesian coordinates requires a previous CELL or CARTESIAN in order to convert the atomic positions to crystallographic The atomic symbol is at s and the atomic number is detected from the symbol essentially from the beginning of it so atoms like C11 or baxx2 are valid Deuterium D is detected as hydrogen In addition to the atomic position and identity the atomic charge Q and pseudopotential charge ZPSP can be given The former is used to calculate the point charge electrostatic energy using Ewald s method see Commands for crystallographic computation and if Q is positive to build the promolecular density using the corresponding cation instead of the neutral atom The role of ZPSP is to augment the fields defined on a grid a procedure called core augmentation ZPSP is the pseudopotential atomic number that is the atomic number of the atom minus the number of electrons represented by the pseudopotential For instance ZPSP 2 for Ba The normal use of critic2 with grids involves loading the valence density or pseudo density that sometimes needs to be augmented to recover an electron density that has maxima at the nuclear positions
108. radient grad f 9 5115E 18 3 8415E 17 4 1112E 18 Gradient norm grad f 3 978845324E 17 Laplacian del2 f 1 312332087E 02 Laplacian valence del2 fval 1 312332087E 02 Hessian eigenvalues 2 11139E 03 1 48096E 03 1 67156E 02 Hessian 2 068242883E 04 5 185807347E 03 1 179735612E 03 5 185807347E 03 1 373314257E 02 4 510661176E 03 1 179735612E 03 4 510661176E 03 4 029974096E 04 mygt gt 0 4 112914774E 04 sth log 0 2 1 062114037E 01 The properties in the list are calculated at the end The properties list is also used in other parts of critic2 notably in the output of POINT Points POINT Any arithmetic expression can be used in POINTPROP but it is common to use on of the chemical functions from the critic2 function library List of available functions The shorthand names for the chemical functions can also be used to apply those functions to the reference field For instance POINTPROP GTF activates the calculation of the Thomas Fermi kinetic energy density gtf function on the reference field POINTPROP can only be used with arithmetic expressions involving known fields The keyword CLEAR deletes all the properties in the list The list of properties can be accesed at any time using POINTPROP LIST 49 10 Graphical representations of gradient paths 10 1 Overview Gradient paths are the solution of the differential equation x grad f x where f is
109. responding to the last atom before the vacuum The CURRENT plot shows the distance in angstrom with respect to a point that also corresponds to the last atom before the vacuum In the case of a surface with adsorbed molecules on it this is not very useful usually one wants to refer this value to the top of the slab surface The TOP keyword allows changing this value top r is the fractional coordinate along the perpendicular axis that will be used as reference for the CURRENT plot The CELL or CELLS keyword controls the number of unit cells plotted in each in plane crystallographic direction default 1 1 The number of points plotted in each in plane unit cell is given by the NPTS keyword n1 i and n2 i By default critic2 uses 51x51 points or if the reference field is a grid the number of grid points in each of those directions If a grid is used letting critic2 use the grid geometry is strongly recommended because it is more time efficient and accurate On output two files will be written The lt root gt _stm dat file contains the 2D data for the STM signal on the selected plane The lt root gt _stm gnu file is an example script that generates a plot similar to those found in the literature The LINE keyword makes critic2 plot a line instead of a plane The line goes from x0 y0 to x1 y1 in fractional coordinates for the in plane crystallographic axes npts i points along the line are calculated The output file is lt root gt _stm_lin
110. ritic2 uses the input cell as given it does not convert the input to the primitive cell which would be rhombohedral in this case The output for the fluorite example is similar to the following First the header with some information about the system the version the commit number and the location of the relevant library and density files E2 analysis of real space scalar fields 1996 2013 A Otero de la Roza Distributed under GNU GPL Bugs requests and rants in solids A Martin Pendas V Luana v 3 see COPYING for details alberto fluor quimica uniovi es If you find this software useful please cite Comput Phys Commun 185 2014 1007 1018 Comput Phys Commun 180 2009 157 166 CL TEMEZ compile ho commit 8758a50 st Linux xxxx compile date Thu May 21 19 54 25 MDT 2015 using 77 ifort g 90 ifort g FR fopenmp g CU C traceback fpe0 debug fpp check all check noarg_temp_created 00 ldflags debug yes compiled dat usr local share critic2 datadir home alberto git critic2 dat dic file home alberto git critic2 dat cif_core dic was found CR I C2 201575 25 Ai 13 06 26 273 After the CRYSTAL keyword is read critic2 first lists the basic information about the crys tal starting with the cell parameters and the number of atoms in the crystal motif x Input crystal data
111. rmula 2 nphi 2 ntheta 1 2 The output keyword selects the output format for the basin plot OFF OBJ PLY BASIN and DBASIN Note that DBASIN files also contain information about scalar fields measured along the basin rays The initial polyhedron may be rotated an angular phase phtheta r and phphi r to avoid high symmetry lines The naming scheme of the output files is lt root gt cp ext where root is the general root of the run the name of the input file up to the first dot unless changed by the ROOT keyword cp is the complete CP list id of the attractor and ext is the appropriate extension off basin or dbasin The precision of the bisection is delta r set using the PREC keyword VERBOSE gives more information in the output about the bisection process If a 3d model format is used OFF OBJ PLY the MAP keyword can be utilized to col ormap a given field given by number id i or field containing expression expr onto the surface The color scale limits are the minimum and the maximum value of the field or ex pression on all the points of the surface The mapping function is the same as in gnuplot r sqrt x g x 3 b sin 360 x with x from O to 1 Default TRIANG method Ivl i 3 ntheta i nphi i 5 OBJ output phtheta r Od0 phphi r 0d0 all the non equivalent attractors found in AUTO 11 2 Primary bundle plots BUNDLEPLOT BUNDLEPLOT x r y r z r 55 CUBE lvl i TRIANG lvl i SPHERE ntheta i nphi i
112. rystallographic coordinates of all atoms by x r y r and z r The typical scenario for this keyword is the calculation of promolecular densities from an xyz file in order to displace the molecule to the center of the periodic cell by using CENTER 0 5 0 5 0 5 Note that it is not a good idea to use this keyword with for instance a cube file input since the field and the geometry are going to be out of sync Also note that molecules read from xyz wfn and wfx files are automatically centered by 1 2 1 2 1 2 5 2 The crystal library A library of simple crystal structures is provided with critic2 and can be accessed using the CRYSTAL LIBRARY keyword like this CRYSTAL LIBRARY NaCl Critic2 tries to find the NaCl label case insensitive in an internal library file that is distributed with the code and usually located in dat crystal lib relative to the source of the distribution The relevant library entry in this case reads STRUCTURE B1 rock_salt rocksalt Nacl CRYSTAL SPG f m 3 m CELL 5 6402 5 6402 5 6402 90 90 90 ANG NEQ 0 0 0 0 0 0 na NEQ 0 5 0 5 0 5 cl ENDCRYSTAL 25 ENDSTRUCTURE Note the four aliases B1 rock _salt rocksalt and NaCl that are defined for the same crystal structure The syntax in the CRYSTAL environment is exactly the same as above The user can define their own library of crystal structures either by modifying the crystal lib directly or by using the LIBRARY keyword LIBRARY path to library w
113. se 1 is not an acceptable value for the last level qtree lvl As setting these INTEG_MODE by hand could be confusing QTREE provides some more or less well tested sets of INTEG_MODE values which we will call integration schemes An integration scheme conveys a full set of INTEG_MODEs that span from the lowest to the highest level of subdivision Integration schemes are selected using the INTEG_SCHEME keyword that can assume the following values O do not integrate only calculate volume and plot see below This is equivalent to setting PROP_MODE to 0 1 subdivide each tetrahedron up to the highest level and then integrate using the vertex information This is most useful if PROP_ MODE is 1 only charge and vol ume or 2 charge volume and Laplacian because the information of the gradient path tracing fgr and lapgr arrays are used INTEG_MODE 1 1 111 2 2 1 QTREE_MINL qtree lvl 2 subdivide each tetrahedron up to the highest level and then integrate using the barycenter INTEG_MODE 1 1 1 1 3 barycentric integration at all levels of subdivision Less accurate but faster than 2 INTEG_MODE 11 11 4 one of the Keast rules given by the KEASTNUM keyword is used at all levels If KEASTNUM is n INTEG MODE nn nn 5 CUBPACK at all levels Reserve this one for special occasions INTEG_MODE 12 12 12 12 6 this scheme and the next are poor attempts at trying an adaptive integration schem
114. st often used when loading an xyz or a Gaus sian wfn wfx file Because critic2 works under periodic boundary conditions it does the analysis of molec ular structures in the xyz wfn wfx format by placing translating the input molecule to the center of a supercell large enough to encompass it The structures loaded from a format dif ferent from xyz wfn wfx are not translated The amount of border around the molecule can be controlled see border r in The crystal structure section above as well as the shape of 27 the supercell CUBIC CUBE Provided the size of the vacuum is large enough the analysis can be carried out without problems The use of MOLECULE instead of CRYSTAL changes some of the default behavior in critic2 Namely e The symmetry module is automatically deactivated All molecular structures are run in the P1 space group e The default CP search seeding strategy is modified see Finding critical points In a crystal a recursive subdivision of a symmetry reduced portion of the Wigner Seitz cell is used SEED WS with DEPTH 1 In a molecule the default is to seed at the center of every interatomic line between atom pairs less than 15 bohr apart SEED PAIR e In addition to the supercell a second smaller cell is defined the molecular cell that can be represented using the MOLCELL keyword in WRITE Exporting the crystal struc ture WRITE or CPREPORT Finding critical points The molecular cell is only used in molec
115. t in three ways By giving the end points x0 r y0 r z0 r and x1 r y1 r z1 r in crystallographic coordinates it is possible to build a grid from an orthogonal fragment of the crystal The CELL keyword calculates a grid spanning the entire unit cell which may or may not be orthogonal depending on the crystal structure GRID has the same effect as CELL regarding the output grid geometry The number of points in the grid can also be controlled in several ways If the cube limits are given explicitly or using CELL then the number of points in each axis can be indicated by giving three integers nx i ny i and nz i corresponding to the number of points in the x y and z axis respectively If a single number bpp r is found then the number of points is the length of the axis divided by bpp r that is bpp is the number of bohrs per point hence the name The GRID keyword can be used to write a field defined on a grid directly to a cube file This is useful when combined with the LOAD keyword to read manipulate and then 42 save grids to an external file If GRID is used both the geometry of the grid and the number of points are adopted from the corresponding field Independently on how the grid is set up several options control the behavior of CUBE FILE sets the name of the output file default lt root gt cube If the extension of file s is not cube then critic2 uses the vasp style CHGCAR format for the output FIELD sets the field slo
116. t number to be used Alternatively an arithmetic expression that combines the existing fields can be used Finally a derivative of the scalar field gradient Hessian Laplacian can be selected instead of the value of the field itself F to build the grid 9 Finding critical points 9 1 Automatic determination of critical points AUTO AUTO GRADEPS eps r CPRHO rho r CPEPS eps r FILE file s VERBOSE DRY AUTO CLIP CUBE x0 r y0 r z0 r xl r yl r zl r AUTO CLIP SPHERE x0 r y0 r z0 r rad r AUTO SEED SEED AUTO SEED WS DEPTH depth i X0 x0 r y0 r z0 r RADIUS rad r AUTO SEED OH DEPTH depth i XO x0 r yO r z0 r RADIUS rad r NR nr r AUTO SEED SPHERE X0 x0 r y0 r z0 r RADIUS rad r NTHETA ntheta i NPHI nphi i NR nr r AUTO SEED PAIR DIST dist r NPTS n i AUTO SEED TRIPLET DIST dist r AUTO SEED LINE X0 x0 r y0 r z0 r X1 x0 r y0 r z0 r NPTS n i AUTO SEED POINT XO x0 r yO r z0 r The search for the critical points CP of a scalar field the points where the gradient of the field vanishes is a basic task in QTAIM In critic2 this search is almost always conducted using the automatic CP localization algorithm via the AUTO keyword The automatic search for critical points has two steps seeding and searching In the seed ing step a collection of points are selected in the unit cell that span the crystal or molecular space where CPs are likely to appear In
117. te list CPs Since the atoms are always critical points the non equivalent complete atom list is a subset of the non equivalent complete CP list Critic2 makes sure that the integer identifier for all atoms in atomic lists is the same as the identifier for the same atom in the CP list Hence in the example above cp i 2 can be used to select the critical point associated to Ca 0 5 0 5 0 in the complete CP list because at i 2 is that atom in the complete atom list Some additional notation particularities that will be used in the rest of the manual e By scalar field or field we mean a numerical or analytical representation of a function that associates a scalar value to every point in space Most of the time this function is the electron density for which special techniques are provided for instance core augmentation in the case of valence densities see ZPSP below However critic2 can deal with any arbitrary field the ELF the Laplacian e The promolecular density is the scalar field built by using the sum of the in vacuo atomic densities This object comes up in a number of contexts For instance NCIPLOT and HIRSHFELD or in the calculation of the deformation density the real electron density minus the promolecular density The promolecular density does not require any input from the user other than the crystal structure and is always available using field identifier 0 e We denote by lt root gt the root of the input file
118. tegrated apart from the volume see above The termini of inactive atoms are all assigned to a common unknown value the same value as the one assigned when a gradient path is killed in non periodic cells see KILLEXT above If the number of inactive atoms is large the painting of unknown termini becomes more frequent and applies to more atoms thus saving time even in the termini localization step The ACTIVE and INACTIVE keywords are used INACTIVE 2 deactivate integration of atom 2 INACTIVE 0 deactivate all atoms ACTIVE 1 activate atom 1 By default all atoms are active QTREE is described in J Comput Chem 32 2010 291 305 Please cite this reference if you use this keyword in your work 12 5 Yu and Trinkle YT YT NNM NOATOMS ESCHER FIELDLIST The Yu Trinkle YT algorithm uses the reference field to calculate the attraction basins The reference field must be defined on a grid Hence it won t work directly with wien2k elk or aiPI densities but those can be transformed into a grid by appropriate use of the LOAD keyword The algorithm proceeds by running over grid nodes in decreasing order of density If a point has no neighboring points with higher density then it s a local maximum If it does but all of them belong to the same basin then it belongs to the interior of that basin as well Otherwise it is sitting on top of the interatomic surface The actual fraction of a grid point on a IAS be
119. tes and the values of all the properties given for this point e Rec 5j j 0 nface 1 nv ivert k j k 1 nv The number of vertices of this face is nv nv 3 in the triangular tesselations and 4 in the quadrilateral ones For each vertex in this face the number of order in the previous vertex list Remember that vertices are numbered from 0 to nvert 1 DBASIN files The DBASIN files contain the description of the basin of a point and the value of a scalar property inside the basin e g the electron density Those data are used to plot the surfaces of constant value of the scalar property A regular grid of NPOINT points is defined along each ray from the origin excluded to the limit of the basin for this ray The scalar property is computed in these points Notice that the grid is in principle different for each ray The structure of a DBASIN file is e Rec 0 comment Comment lines starting with may appear anywhere e Rec 1 nvert nface nedge Number of vertices faces and edges of the polyhedron e Rec 2 npoint xnuc ynuc znuc rhonuc Number of sampled points along each ray Cartesian x y z position of the nucleus Electron density at the nucleus 87 Rec 3i i 0 nvert 1 x i y i z i rhoG i j 1 npoint For each vertex the Cartesian coordinates and the values of the electron density at the grid points Rec 4j j 0 nface 1 nv ivert k j k 1 nv The number of vertices of t
120. than QTREE_MINL As we did with the gradient path tracing let us suppose that we have at our disposal a method that calculates the integral of the selected properties over one of these tetrahedra We will refer to this methods as an inner integration method because the value of the properties will be assigned to only one atom On the contrary if all the termini are located inside the beta sphere region the tetrahedron does not subdivide but the properties are not integrated because this region corresponds to the sphere integration addressed in point 2 If the tetrahedron is in the border of a beta sphere it is divided further If the tetrahedron is at subdivision level equal to qtree lvl then it does not sub divide it is integrated and the properties are assigned to the atoms There are several possibilities depending of the nature of its vertex termini 65 x If all the termini correspond to the same atom and the tetrahedron is com pletely inside or outside of this atom s sphere it corresponds to a case in 6 3 If it is completely inside an atom basin but on the border of a beta sphere remember that being on the border of a beta sphere implies that it is inside the basin the part of the tetrahedron that is outside of the sphere is integrated and assigned to the atom Another integration method is required for this essentially different from the inner integration We will refer to this one as border same color i
121. that the beta sphere is completely contained inside the basin of the atom This may turn out not to be true for the default beta sphere radius specially for cations in ionic systems In these cases the keyword SPHFACTOR is used Its syntax is SPHFACTOR 1 0 70 Make b_1 0 70 rNN2 1 atom type 1 SPHFACTOR 0 0 60 Make b_i 0 60 rNN2 i for all atoms SPHFACTOR Si 0 60 Make b_i 0 60 for all Si atoms If SPHFACTOR lt 0 use the scheme by Rodriguez et al to determine the beta sphere radii JCC 30 2009 1082 1092 a collection of points around the atom are selected and the angle between the gradient and the radial direction is determined If all the angles are lt 45 degrees the sphere is accepted In solids this strategy yields usually spheres that too large In the case that any atomic SPHFACTOR is zero the default value for all atoms then a pre computation at a lower level is done to ensure that all beta spheres lie within the desired basins There are two methods for this that can be chosen using AUTOSPH default method number 2 Method number one involves a reduced version of QTREE The pre computation usually takes no longer than some minutes and usually only few seconds and the spheres are guaranteed to be inside the basins The keyword SETSPH LVL controls the level of the pre computation that must not be higher than 7 The default value is 6 or maxi whichever is smaller The second method default traces gr
122. the QTREE keyword default 6 Every tetrahedron vertex is assigned to a non equivalent atom in the unit cell by tracing a gradient path Finally the tetrahedra are integrated and the properties assigned to the corresponding atoms The space near the atoms is integrated using a beta sphere a method that proves more accurate despite generating a second interface in the atomic basin In the simplest approach qtree can be executed using OTREE maxlevel i where maxlevel i is the level of subdivision The optional plevel i value corresponds to the pre splitting level of the tetrahedra The initial tetrahedra list is split into smaller tetrahedra plevel i times This can be useful in cases where a very high accuracy and therefore a very high level is required but there is not enough memory available to advance to higher maxlevel i However using plevel i incurs in a overhead because the painting procedure is not as efficient when smaller tetrahedra are used Note parallelization might not work with older versions of ifort The newer versions of gfortran do work with parallel qtree 60 The steps of the algorithm are e The WS cell is constructed and split into tetrahedra all of which have in common at least the origin Then the site symmetry of the origin is calculated and the tetrahedra that are unique under the operations of this group are found This is what we call the irreducible Wigner Seitz cell IWS Note however that it is
123. the best available ODE integration method Information about the results of the comparison is output to stdout and a tess file is generated difftermxx tess where xx is the subdivision level containing the position of the points where both termini differ 70 If the integration region is not periodic then methods color and qtree are not defined There are two possible options controlled by the KILLEXT and NOKILLEXT keywords If KILLEXT is active the default behavior the gradient path tracing is killed whenever it leaves the integration region independently of the GRADIENT_MODE being used The terminus is then assigned to an unknown state and the tetrahedra it generates are not integrated If NOKILLEXT is active the gradient path is continued as a full gradient until the terminus is found The default is KILLEXT because if the integration region is not periodic the integral over atoms that are partially contained in it is most likely not meaningful to the user The ODE integration method can be chosen using the QTREE ODE MODE keyword that can assume the following values 1 Euler method fixed step 1st order 2 Heun method fixed step 2nd order 3 Kutta method fixed step 3rd order 4 Runge Kutta method fixed step 4th order 5 Euler Heun embedded method adaptive step 1st order with 2nd order error estimation 2 evaluations per step 6 Bogacki Shampine embedded metho
124. the given nr r to the lower limits of these intervals ABSERR is the requested absolute error for QUADPACK integrators RELERR is the re quested relative error for QUADPACK integrators ERRPROP controls the property for which the error is estimated If prop i corresponds to one of the integrable properties then REL ERR and ABSERR apply only to it The selected property guides the adaptive integration 84 procedure If prop i does not represent one of the integrable properties the maximum of the absolute value of the properties vector is used Note the option where max abs prop is used is unstable Some spheres usually associated to heavy atoms may integrate to non sense depending on the optimization levels of the compiler Therefore I have disabled it by default In the case of basin integrations PREC controls the precision in the determination of the interatomic surface Default GAULEG nr r 50 aerr r 1d0 rerr r 1d 12 The default errprop is the field value for fields on a grid and the Laplacian for the rest ROOT root s Change the lt root gt The root is used as prefix for most of the auxiliary files written by critic2 SUM id i MAX id i MIN id i MEAN id i COUNT id i eps r Using the field on a grid id i calculate the sum of the node values SUM the maximum value MAX the minimum MIN the average MEAN or count the number of elements that are greater than eps r COUNT BENCHMARK nn i Benchmark the
125. the search step a Newton Raphson algorithm is launched at each of the seeds in order to find nearby critical points The default seeding behavior in critic2 depends on whether the geometry under study is a crystal loaded with the CRYSTAL keyword or a molecule MOLECULE keyword e In a crystal AUTO calculates the Wigner Seitz WS cell and its irreducible part the smallest piece that reproduces the WS cell by symmetry Once the irreducible WS 43 IWS cell is found seed points are chosen by subdividing the edges faces and interior of the tetrahedra that the IWS comprises up to a certain subdivision level the DEPTH e In a molecule a single seed is planted at the midpoint between every atom pair less than 15 bohr apart In addition AUTO provides multiple seeding strategies that can be combined by the user using the SEED keyword These include searches between pairs of atoms PAIR atomic triplets TRIPLET uniform seeding in a sphere SPHERE a recursive subdivision of an octahedron OH and seeding along lines LINE and at points POINT The seed list built using these seeding actions is pruned to remove duplicates Optionally a portion of the unit cell can be selected to restrict the search in real space using the CLIP keyword Once the seed list is built Newton Raphson is applied at each of the seeds on the list making full use of shared memory parallelization and crystal symmetry The default seeding can be changed usin
126. ther format is the CHG that is also used for the ELFCAR containing the values of the ELF function In this case the grid values are given with less precision and they may or may not be multiplied by the cell volume depending on the VASP version Both can be loaded with 33 LOAD CHG LOAD ELFCAR But if you have a file in this format that does not conform to those names you can use the VASPCHG keyword LOAD VASPCHG STRANGE_CHG_FILE_NAME chg The CHGCAR files are relatively safe to use but CHGs data points may or may not be multiplied by the unit cell volume and you have to tell critic2 which one it is If you have a CHG file that is multiplied by the volume then you can force critic2 to load it in the same way as a CHGCAR with LOAD VASP CHG I have never seen an ELFCAR that is multiplied by the volume it would not make much sense anyway so the default for ELFCAR files is to assume this Using a patched version of elk it is possible to generate other files OTHER OUT contain ing the spherical harmonics plane waves representation of other fields such as the elf and the Coulomb potential See the tools elk mod directory for the patch source files When the OTHER OUT e g ELF OUT file is used then that field is loaded instead of the density 1 In some cases the extension of the file to be loaded may be different from the one that critic2 expects For instance WIEN2k creates files with extensions other than clmsum for
127. tractors are usually nuclei and the basins are the atomic regions In this case the integrated properties are atomic properties e g atomic charges volumes moments etc The attractor basins are defined by a zero flux condition of the electron density gradient no gradient paths cross the boundary between attractor regions This makes the basins local to each attractor but their definition yields a relatively complex algorithmic problem The simplest way of integrating an attractor basin is bisection A number of points dis tributed in a small sphere around the atom are chosen each of them determining a ray On each ray a process of bisection is started A point belongs to the basin if the gradient path traced upwards ends up at the position of the attractor we are considering If the end point is a different attractor then the point is not in the basin By using bisection it is possible to determine the basin limit called the interatomic surface IAS The bisection algorithm is implemented in critic2 and can be accessed with the INTEGRALS keyword An algorithm has been proposed based on the recursive subdivision of the irreducible Wigner Seitz IWS cell called qtree In qtree the smallest symmetry irreducible portion of space is considered and a tetrahedral mesh of points is superimposed on it The gradient path 56 is traced from all those points and the points are assigned to different atoms the points are colored The final
128. trons 152 Number of valence electrons Number of core electrons 0 152 Reading new promolecular density grids Read density file home alberto git critic2 dat ca_pbe wfc Log grid r axe bx x with a 1 2394E 04 b 2 0000E 03 Num grid points 5855 rmax bohr 15 0633965 Integrated charge 19 9999732987 El conf 18 2 25 2 2P 6 3S 2 3P 6 4S 2 Read density file home alberto git critic2 dat f__pbe wfc Log grid r axe bx x with a 2 7542E 04 b 2 0000E 03 Num grid points 5161 rmax bohr 8 3542920 Integrated charge 8 9999953160 El conf 1S8 2 2S 2 2P 5 Reading new core density grids Finally the just built promolecular density is made available to the user through identifier number 0 and it is set as reference A list of the current integrable properties is also given This is the list of properties that would be integrated in the attraction basins if the user runs INTEGRALS or any of the other integration methods x Field number 0 is now REFERENCE Integrable properties list Id Type Field Name 1 V O Volume 2 fval O Charge 3 lval O Lap The execution finishes with a report of the warnings found and the timestamp It is always a good idea to check for warnings in the output CR I C2 ended succesfully CR H C2 2015 5 25 13306732168 13 0 WARNI NGS 0 COMMENTS In most of t
129. ules loaded from a xyz wfn wfx file The region outside the molecular cell is assumed to belong to the vacuum Any CPs found outside the molecular cell are dis carded and all downwards gradient paths that exit the molecular cell are assumed to have diverged to infinity In the unusual case in which you want to analyze a molecular structure not coming from a xyz wfn wfx critic2 will not automatically translate or set up a molecular cell In this case you can use the MOLCELL keyword to set it up MOLCELL border r The MOLCELL keyword calculates the smallest parallelepiped encompassing the molecu lar motif and then adds a border to it in order to build the molecular cell The default border is 3 bohr but can be controlled by passing an additional numerical argument Note that using this keyword only makes sense if the molecule is placed close to the center of the cell and if there is a sizable amount of vacuum between the molecule and the cell edges In order to use MOLCELL the input structure needs to be read using the MOLECULE keyword and the cell needs to be orthogonal 5 7 Exporting the crystal structure WRITE Critic2 can be used as a converter between different crystal structure file formats For in stance if we are given a cif file that needs to be converted to a QE input we use CRYSTAL myfile cif WRITE myfile scf in 28 Sometimes it is also useful to create a finite representation of the crystal by taking the crystal m
130. which is important for certain applications for instance plotting While this procedure is not satisfactory from the theoretical point of view in practice the valence regions are mostly unaffected Of course core augmentation needs 24 to be deactivated if the field is not the electron density or if the grid already contains the core contributions and it is usually a better option to use the full all electron density from the electronic structure code if it is able to reconstruct it The value of ZPSP can be found easily in a VASP calculation by grepping ZVAL in the POTCAR file In Quantum ESPRESSO this information is in the UPF file the number of valence electrons The ZPSP and Q values are not set when the structure is read from a file except in the case of abinit files The standalone versions of ZPSP and Q can be used outside the CRYSTAL environment see below The MOLECULE keyword can be used as an alternative to CRYSTAL to deal with molecular grids and wavefunctions Also cube files calculated with Gaussian e g with cubegen can be used in critic2 The program will assume periodic boundary conditions but topologies graphical representations and computations with cubes can be performed nevertheless see the Molecular structures section below When using a molecule as input for instance from an xyz file using the ANGSTROM keyword the CENTER keyword can be useful CENTER CENTRE x r y r z r CENTER displaces the c
131. wise cell parameters are in bohr by default the keyword BOHR or AU can be used but it is redundant Using the CELL keyword lets critic2 decide on the crystallographic to Cartesian transformation matrix which is not unique critic2 always uses the Cholesky decomposition of the metric tensor for consistency Alternatively one could input this matrix using the CARTESIAN keyword CARTESIAN scal r 23 comment BOHR AU ANGSTROM ANG ALO NL Ze xX2 Y1 y2 r z22 Yr XL YD ZE ENDCARTESIAN END CARTESIAN reads the Cartesian coordinates of the cell vectors in some arbitrary orthonor mal reference frame Each row corresponds to a vector hence the metric tensor is G R R where R is the matrix above and is the transpose and the coordinate transformation is cryst cart R If scal r is given all vectors are scaled by that factor The input units can be controlled with the BOHR AU and ANG ANGSTROM keywords default bohr The CARTESIAN keyword is particularly useful for inputs based on Quantum ESPRESSO results since the matrix corresponds exactly to the CELL PARAMETERS matrix and scal r can be set to celldm 1 The NEQ keyword can be used to specify the atomic positions NEO x r y r z r at s ZPSP zpsp i Q q i ANG ANGSTROM BOHR AU NEQ adds one atom to the crystal If symmetry was given via SPG then only the non equivalent atom list needs to be given as in the MgO example above which decreases the numbe

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