User`s manual (PDF file)
Contents
1. e Blochl projector num The number of Bl chl projectors for each L component in separable pseudopotentials If you specify 1 for Blochl projector num this means the Kleinman and Bylander KB separable pseu dopotentials local type Simple and Polynomial are available e local part vps Number of local potential in case of local type Simple local cutoff The cutoff radius of local part in case of local type Polynomial e local origin ratio Depth of local part at the origin in case of local type Polynomial Although the MBK scheme also constructs a separable form in a different way the proper selection of above the keywords is important as well You can find details for these keyword in the section Input file 6 5 How the MBK scheme is different from the others The MBK pseudopotential 6 is a norm conserving version of the Vanderbilt s ultrasoft pseudopoten tial 10 The feature allows us to take multiple states with the same angular momentum quantum number into account for construction of a separable pseudopotential Thus it is guaranteed that the MBK scheme is more accurate than the other schemes when semi core states are included in the construction of pseudopotential When the MBK scheme is used one must care the reference energy given by the fifth column in the specification by the keyword pseudo NandL Generally the energy of zero is a good starting point for further trial and error Since in the MBK sch2. FEMHF_ERI c Init_VPS c Copyright of the program package Inputtools c Log_DeriF c Make_EDPP2 c Make_EDPP3 c Make_EDPP4 c Make_EDPP c MBK c MBK_Hessian c MBK_Ozaki c mimic_omp c MPAO_RadialF c MR c Multiple_PAD c Output c PAO_RadialF c QuickSort c readfile c FEMHF_ERI h FEMHF_JKLM h Inputtools h mimic_omp h Restart c Set_Init c Simple_Mixing c TM c Total_Energy c VNLF c VP c XC4atom_PBE c XC_CA c XC_EX c XC_PBE c XC_PW91C c XC_VWN c XC_Xa c The distribution of this program package follows the practice of the GNU General Public License 23 Moreover the author Taisuke Ozaki possesses the copyright of the original version of this program package We cannot offer any guarantees in your use of this program package However when you report some program bugs we will cooperate as much as possible together with you to remove the problems Contributors T Ozaki JAIST H Kino NIMS H Kawai Kanazawa Univ M Toyoda JAIST 30 References 10 11 12 13 14 15 16 17 18 19 20 21 22 23 D M Ceperley and B J Alder Phys Rev Lett 45 566 1980 J P Perdew and A Zunger Phys Rev B 23 5048 1981 S H Vosko L Wilk and M Nusair Can J Phys 58 1200 1980 S H Vosko and L Wilk Phys Rev B 22 3812 1980 J P Perdew K Burke and M Ernzerhof Phys Rev Lett 77 3865 1996 N Troullier and J L Martine Phys
3. and Nusair is available by LDA VWN 2 AtomSpecies Give the atomic number max occupied N Give the maximum number of the principal quantum number n for occupied electrons total electron Give the total number of electrons in an atom It is also possible to give the number of electrons corresponding to not only a neutral atom but also a positive or negative charged atom However note that it becomes difficult to achieve the convergence in the SCF calculation for a negative atom there are more electrons than atomic number since wave functions tend to be delocalized or unbound spatially valence electron Give the number of electrons of valence electrons occupied electrons Give the number of electrons occupied in each orbital As seen in C inp when 1s 2s and 2p orbitals of a carbon atom are occupied by two electrons in consideration of the spin degeneracy respectively they are specified as follows lt occupied electrons 1 2 0 2 2 0 2 0 occupied electrons gt The beginning of the description must be lt occupied electrons and the last of the description must be occupied electrons gt grid xmin The radial Kohn Sham equation is solved numerically by a modified Euler type method from both a ra dial point in near the origin and a distant radial point rmax a u Here a radial point rmin near the origin is specified by the keyword grid xmin Note that there is a relation rmin a u exp grid xmin In case of
4. number of valence electrons in the pseudopotential generation local origin ratio When Polynomial is used for the keyword local type The keyword local origin ratio specifies the value of the local potential at the origin It should be noted to be Vz 0 local origin ratio x Vi ric log deri RadF calc In case of calc type VPS if you want to calculate the logarithmic derivatives of radial wave func tions for the all electron potential semilocal pseudopotentials and separable pseudopotentials then please specify ON for the keyword log deri RadF calc If not so please specify OFF The calculated logarithmic derivatives are output to the file 1d0 1d1 where means System Name you spec ified the number attached to the last of the file extension ld is the angular momentum number L In these files the first column is energy the second Do third D1 and fourth D2 columns are the logarithmic derivatives of radial wave functions for the all electron potential the semilocal non separable pseudopotential and the separable pseudopotential respectively In addition to the output of logarithmic derivatives to the files an useful quantities y and I4 are evaluated in order to discriminate the transferability of the separable pseudopotentials by log deri MaxE 3 T Do Da dE log deri MinE log deri MaxE 3 ia D D2 2dE log deri MinE Ideally the maximum transferability can be obtained w
5. K K K K K 2K 2K 140 120 100 80 rho r 60 40 Radial wave function 20 Figure 1 a Electron density of a carbon atom b Radial wave functions of a carbon atom Eeigen 21 2964361910017 Ekin 37 1873926464442 EHart 17 6249339614759 Exc 4 7271002754349 Eec 87 5097256776491 Etot Ekin EHart Exc Eec Etot 37 4244993451638 The electron density p r as a function of radius is output in a file CO aden Figure 1 a shows electron density of a carbon atom stored in C0 aden In the file CO aden the first second third columns mean log r r and the electron density in all a u respectively The order of data is also similar in the other files The radial wave functions shown in Fig 1 b are output in a file CO ao in which they are listed in order of log r r and the radial wave functions of 1 0 for n 1 For n 2 or subsequent ones radial wave functions are stored in the same order as that for n 0 However note that the ingredients are output up to l n 1 as follows n 1 log r r 1 0 n 2 log r r 1 0 1 1 3 log r r 1 0 1 1 1 2 4 Input file An input file C inp is shown below This input file has a flexible data format in which a parameter is given behind a keyword the order of keywords is arbitrary and a blank and a comment can also be described freely File Name System CurrrentDir ef default System Name co Log print Off
6. Rev B 43 1993 1991 G B Bachelet D R Hamann and M Schluter Phys Rev B 26 4199 1982 I Morrison D M Bylander and L Kleinman Phys Rev B 47 6728 1993 L Kleinman and D M Bylander Phys Rev Lett 48 1425 1982 P E Blochl Phys Rev B 41 5414 1990 D R Hamann Phys Rev B 40 2980 1989 D Vanderbilt Phys Rev B 41 7892 1990 T Ozaki and M Toyoda Comp Phys Comm 182 1245 2011 D R Bowler and M J Gillan Chem Phys Lett 325 475 2000 P Pulay Chem Phys Lett 73 393 1980 G Kresse and J Furthmeuller Phys Rev B 54 11169 1996 S G Louie S Froyen and M L Cohen Phys Rev B 26 1738 1982 T Ozaki Phys Rev B 67 155108 2003 T Ozaki and H Kino Phys Rev B 69 195113 2004 X Gonze et al Phys Rev B 41 12264 1990 D M Bylander and L Kleinman Phys Rev B 41 907 1990 D D Koelling and B N Harmon J Phys C Solid State Phys 10 3107 1977 A H MacDonald and S H Vosko J Phys C Solid State Phys 12 2977 1979 T Ozaki and M Toyoda Comp Phys Comm 182 1245 2011 J F Janak Phy Rev B 9 3985 1974 http xfree86 cygwin com http www gnu org home html 31
7. System UseRestartfile is specified as YES a restart file which contains informations of all electron calculation is used in order to skip the all electron calculation If there is no restart file a restart file is generated in case of System UseRestartfile YES System Restartfile If System UseRestartfile YES then the name specified by the keyword System Restartfile is referred to as a restart file eq type The keyword eq type specifies the type of equation For the non relativistic Kohn Sham equation please specify sch On the other hand for the scalar and fully relativistic Kohn Sham equation please specify sdirac and dirac respectively calc type The keyword specifies a calculation type The SCF calculation for all electron calculation ALL the generation of pseudopotentials VPS or the generation of pseudo atomic orbitals PAO with a confinement potential are available In addition to the three schemes ALLFEM FEMLDA and FEMHF are available for the all electron LDA and HF calculations using the finite element method FEM 11 respectively Due to a technical reason during development two specifications ALLFEM and FEMLDA are equivalent to each other xc type Approximate method LDA or GGA used for an exchange correlation energy where LDA is a form parametrized by Perdew and Zunger 1 and GGA is a form proposed by Perdew Burke and Ernzerhof 3 Also a LDA functional proposed by Vosko Wilk
8. calculations were performed using an executable file compiled with gcc Among the compiler options shown above Dnoomp and std c99 should remain unchanged when gcc is used the other parts must be property changed 2 2 Installing After downloading adpack2 2 tar gz decompress it as follows tar zxvf adpack2 2 tar gz When it is completed you can find four directories source work work FEMLDA work FEMHF un der the directory adpack2 2 The directory source contains source files and work work_FEMLDA work_FEMHF contain input files for conventional FEMLDA and FEMHF calculations respectively Then move to the directory source and change CC and LIB in makefile as explained in the subsec tion Including library After setting CC and LIB install as follows make install When the compile is completed normally then you can find the executable file adpack in the directory work To make the execution of ADPACK efficient you can change a compiler and compile options appropriate for your computational environment which can generate an optimized executable file Then it might be made by specifying CC in the makefile which exists in directory source The default for the specification of CC is as follows CC gcc Dnoomp std c99 03 I usr local include I home ozaki include However it is highly recommended to use the gnu C compiler gcc for the numerical stability since our all t
9. follows sch sch sdirac dirac eq type where sch sdirac and dirac mean the Schr dinger equation no relativistic effect a scalar rel ativistic treatment and a fully relativistic treatment of Dirac equation respectively In the scalar relativistic treatment the coupled Dirac equations are averaged with a weight of j degeneracy and solved by taking account of both the majority and minority components of radial wave function Thus the scalar relativistic treatment includes explicitly kinematic relativistic effects Darwin and mass ve locity terms and implicitly averaged spin orbit coupling no energy splitting On the other hand in the fully relativistic treatment j dependent Dirac equations are solved including both the major ity and minority components of radial wave function Thus energy splitting by spin orbit coupling are also considered In Table 1 shows eigenvalues of atomic platinum calculated by three different methods Table 1 Eigenvalues Hartree of atomic platinum calculated by the Schr dinger equation a scalar relativistic treatment and a fully relativistic treatment of Dirac equation within GGA to DFT state sch sdirac dirac j 1 1 2 j 1 1 2 ls 2612 2560 2876 3416 2868 8969 2s 434 7956 505 1706 503 1143 2p 418 0254 438 1804 419 1547 482 3721 3s 101 2589 118 6671 118 0772 3p 93 3171 99 1367 94 8406 108 7310 3d 78 3951 77 8404 76 1768 79 1659 4s 21 1326 25 4989
10. lower bound of x is always set to zero The roles of the other keywords are same as in the conventional calculations Also the database for all electron calculation performed by the FEM scheme can be found at http www openmx square org miscellaneous html The database provides calculation results and input files used for the calculations In the database it is estimated based on the virial theorem 21 that the absolute error in the total energy is less than nano Hartree and micro Hartree for the LDA and HF calculations of all elements in the periodic table respectively 28 11 Output files The list of output files is shown below The details of each file are described in each section Test calculation Generation of pseudopotential and Generation of pseudo atomic orbitals calc type A LL CO alog input file and results of SCF calculations CO ao radial wave functions in all electrons SCF calculations CO aden electron density of all electrons calc type VPS CO nsvps non separable pseudopotentials CO vps input file results of the SCF calculation and pseudopotentials in a KB separable form and partial core density PCC CO vpao radial parts of pseudo atomic orbitals for pseudopotentials CO vden valence electron density the total electron density core electron density modified core electron density for PCC CO loc local part of pseudopotentials CcO 1d0 logarithmic derivatives of wave functions 1 0 CO 1d1 logarithmic
11. optimum pseudopotentials However all electron calculation prior to the pseudopotential generation requires a considerable computational time for an atom with a large atomic number Therefore it is desirable to reduce the computa tional time that results of the all electron calculation are stored in a file and skip the all electron calculation when we regenerate pseudopotentials in different parameters To do this two keywords System UseRestartfile and System Restartfile are available The details are as follows e System UseRestartfile For an atom with a large atomic number all electron calculation requires a considerable com putational time So it is needed to reduce the computational time when optimal cutoff radii of pseudopotentials is determined in trial and error If the keyword System UseRestartfile is specified as YES a restart file which contains informations of all electron calculation is used in order to skip all electron calculation If there is no restart file a restart file is generated in case of System UseRestartfile YES e System Restartfile If System UseRestartfile YES then the name specified by the keyword System Restartfile is referred to as a restart file 23 7 Relativistic calculation 7 1 All electron calculation Relativistic effects can be included in both the scalar relativistic 18 and the fully relativistic treatment 5 19 To specify these there are three options for the keyword eq type as
12. the FEM calculation a different type of grid is used See the section FEM calculation for the detail grid xmax The keyword grid xmax specifies a distant radial point rmax a u which begins to solve a Kohn Sham equation As well as grid xmin note that rmax a u exp grid xmax The selection of a suitable grid xmax is dependent on an atom For an atom with only localized electrons such as carbon and oxygen the use of about 2 5 a u is recommended as grid xmax In case of an atom such as Na Ti Fe with delocalized electrons the use of about 3 0 a u or more is recommended as grid xmax Moreover a large value for grid xmax should be used when a atom is charged negatively In case of the FEM calculation a different type of grid is used See the section FEM calculation for the detail grid num The radial coordinate r is discretized to solve the radial Kohn Sham equation by a modified Euler type method The number of division is specified by grid num The actual mesh division is done for x log r as dx grid xmax grid xmin grid num 1 rather than for r to cope with large variations near the origin of potential and wave functions In case of the FEM calculation a different type of grid is used See the section FEM calculation for the detail grid num output It is possible to change the number of grids for r in output files by the keyword grid num output although the actual calculation is performed using grid num scf maxI
13. the actual calculation is performed using grid num Usually we use 500 for it scf maxIter Set the maximum number of SCF iteration scf Mixing Type Choose a method for charge mixing Either simple GR Pulay or Pulay is available In most cases the simple mixing scheme is enough to achieve a sufficient convergence scf Min Mixing Weight Set the minimum mixing weight scf Max Mixing Weight Set the maximum mixing weight 15 11 12 13 scf Mixing History Set previous SCF steps for charge mixing in the GR Pulay or Pulay method scf Mixing StartPulay Set a SCF iteration number from which the GR Pulay or Pulay starts scf criterion Set scf criterion At least 1 0e 10 for the keyword should be chosen for a convergent calculation 16 6 Generation of pseudopotential 6 1 Example Generation of pseudopotentials is illustrated for the case of a carbon atom Please set the keyword calc type to VPS in the input file C inp and perform as follows adpack C inp When the calculation is completed normally the following eight files are newly generated in the directory work CO nsvps non separable pseudopotentials CO vps input file results of the SCF calculation and pseudopotentials in the KB or Blochl separable form and partial core density for PCC CO vpao radial parts of pseudo atomic orbitals for pseudopotentials CO vden valence electron density the total electron density core electron d
14. 25 3346 4p 17 7166 19 0862 18 0570 21 3626 4d 11 4203 11 2646 10 9124 11 5257 4f 3 0221 2 5775 2 4568 2 5821 5s 2 9387 3 7323 3 6983 5p 1 8756 2 0571 1 8911 2 43384 5d 0 2656 0 2259 0 2020 0 24966 6s 0 1507 0 2074 0 2079 7 2 Enhancement or depletion of a spin orbit coupling To study the effect of a spin orbit coupling it is possible to generate a pseudopotential with a larger or smaller spin orbit coupling compared to that in a real atom The scaling factors can be specified to each angular momentum quantum number by the following keyword 24 lt S0 factor o 1 0 1 0 5 2 2 0 S0 factor gt The beginning of the description must be lt SO factor and the last of the description must be SO factor gt The number in the first column corresponds to that in the keyword pseudo NandL and a scaling factor is given for each pseudopotential by the second column where 1 0 corresponds to the spin orbit coupling in a real atom One can control the strength of spin orbit coupling by changing the scaling factor 25 8 Generation of pseudo atomic orbitals The pseudo atomic orbitals are used in the program package OpenMX as the primitive basis orbitals The pseudo atomic orbitals are generated as follows first the SCF calculation is performed in consid eration of all electrons under a confinement potential second the pseudopotentials are generated and finally the pseudo atomic orbitals for th
15. 402 Hartree NormRD 9 7504824337909 SCF 2 Eeigen 31 2507824481920 Hartree NormRD 9 6908568790503 SCF 3 Eeigen 29 2904374089900 Hartree NormRD 6 4223342805654 SCF 4 Eeigen 24 3586103571626 Hartree NormRD 1 3490158536346 SCF 5 Eeigen 21 9965036829842 Hartree NormRD 0 1523028186916 SCF 6 Eeigen 21 5002109590127 Hartree NormRD 0 0119067469939 SCF 7 Eeigen 21 3467192266812 Hartree NormRD 0 0005718475963 SCF 8 Eeigen 21 3045977061498 Hartree NormRD 0 0000175378857 SCF 9 Eeigen 21 2984619045622 Hartree NormRD 0 0000005376916 SCF 10 Eeigen 21 2965170176425 Hartree NormRD 0 0000000125540 SCF 11 Eeigen 21 2966277103150 Hartree NormRD 0 0000000012975 SCF 12 Eeigen 21 2964361910017 Hartree NormRD 0 0000000000864 The eigenvalues and the total energy Etot are also output in C0 alog KKK K K K 2 FK K K K K K K FK FK FK FK K K K K K K K FK 2K 2K 2K FK FK FK FK K K 2K FK FK FK FK FK K FK K K K K K K gt K OK Eigenvalues Hartree in all electrons calculations BEGG AA 3K K K K K aK 2K 2K CC ACI A I A I I I ICI 3K K 21 21 21 21 K K K K K K K K K 2K 2K n l 0 9 9479219357833 n 2 l 0 0 5009865574917 n 2 1 1 0 1993096022259 KKK KK 2 2 FK K K K K K K FK FK FK FK 2 K K K K K K K 2K FK 2K FK FK FK FK K K K K FK FK FK FK FK FK K K K K K K gt K OK Energies Hartree in all electrons calculations kk k ak 3k 3k 3k 3k 3K 3K K K K K K 2K K ACACIA I I I I I 3K 3K 3K K K K KK K K K K
16. ON OFF System UseRestartfile yes NO YES default NO System Restartfile co default null Calculation type eq type sch sch sdirac dirac calc type all ALL VPS PAO xc type LDA LDA GGA Atom AtomSpecies 6 max occupied N 2 total electron 6 0 valence electron 4 0 lt occupied electrons 1 2 0 2 2 0 2 0 occupied electrons gt parameters for solving 1D differential equations grid xmin 8 0 default 7 0 rmin a u exp grid xmin grid xmax 2 8 default 2 5 rmax a u exp grid xmax grid num 2000 default 4000 grid num output 500 default 2000 SCF scf maxIter 60 scf Mixing Type simple scf Init Mixing Weight 0 10 scf Min Mixing Weight 0 001 scf Max Mixing Weight 0 800 scf Mixing History 7 scf Mixing StartPulay 9 scf criterion 1 0e 10 Pseudopotetial cutoff A U vps type T number vps 2 lt pseudo NandL 0 1 2 0 2 1 1 50 0 0 1 62 0 0 pseudo NandL gt Blochl projector num 4 local type polynomial local part vps 1 local cutoff 1 50 local origin ratio 4 00 log deri RadF calc on log deri MinE 3 0 log deri MaxE 2 0 log deri num 50 lt log deri R 0 2 2 1 2 4 log deri R gt ghost check off H H H H H H HF H H HH HF OF default 40 Simple GR Pulay default 0 300 default 0 001 default 0 800 default 5 default 6 default 1 0e 9 BHS TM default 1 which means KB form Simple Polynomial default 0 def
17. Please make sure that only OpenMX Ver 3 4 or later accepts the pseudopotentials and the basis functions for the virtual atoms Also it is noted that basis functions for the pseudopotential of the virtual atom must be generated for the virtual atom with the same fractional nuclear charge since the atomic charge density stored in pao is used to make the neutral atom potential in OpenMX 27 10 Finite element method FEM calculation A highly accurate finite element method FEM 20 is available for all electron calculations within LDA by Vosko Wilk and Nusair 2 and the Hartree Fock scheme In the calculations spherical charge distribution and spherical potential are assumed for the Schr dinger equation The FEM calculation is not supported for the Dirac equation The following keywords are especially relevant for the FEM calculation calc type ALLFEM FEMLDA and FEMHF are available for the all electron LDA and HF calculations using the finite element method FEM 11 respectively Note that due to a technical reason during development two specifications ALLFEM and FEMLDA are equivalent to each other grid xmax In the FEM calculation the grid is generated at regular intervals on a coordinate x where the relation between the radial coordinate r and x is given by r x The keyword grid xmax specifies the upper bound of x in this case Note that the definition of x is different from the conventional calculations in ADPACK The
18. User s manual of ADPACK Ver 2 2 Taisuke Ozaki Japan Advanced Institute of Science and Technology JAIST 1 1 Asahidai Nomi Ishikawa 923 1292 Japan Contributors T Ozaki JAIST H Kino NIMS H Kawai Kanazawa Univ M Toyoda JAIST September 28 2011 Contents 1 About ADPACK 2 Installation Qo Imcludine library el A A igh A A A th Se a 2 2 Stalling sia a y A ee eo Bote oa OOS 3 Test calculation 4 Input file 5 All electron calculation 6 Generation of pseudopotential Gl Example osa Bee Bee eo ee ge aa et WP Sok Ae Ee ee Rok eee a ee G22 COUO TALIS a o at Scie rt Secchi Seca E Ae e A nl Sere de Bees 6 3 Pseudopotentials for unbound states ooo aa a ee 6 4 Separable form Livia dos a ee i Ba a es ce Bed Se a a 6 5 How the MBK scheme is different from the others 2 6 6 Logarithmic derivative of wave function 0 0 0000 eee ee ee 6 7 Ghost States o ae gh te A as A ee oy Bete oleae PPS 6 8 Partial core COrrectiOn 2 Ack a eH de te Siete ke a ee e ad BA 6 9 Restart 4 wk A woe ak Wh Oe ee A a ee ee ls la 7 Relativistic calculation TI Allelectron calculation 4 22 a eon eon Be So bak a a ee eae ta 7 2 Enhancement or depletion of a spin orbit coupling 2 8 Generation of pseudo atomic orbitals 9 Virtual atom with fractional nuclear charge 10 Finite element method FEM calculation 11 Output files 12 Templates of the input files 13 Database of optimized
19. VPS and PAO 14 Others 15 17 17 19 20 20 21 21 22 23 23 24 24 24 26 27 28 29 29 29 30 1 About ADPACK ADPACK Atomic Density functional program PACKage is a program package for atomic density functional calculations in which either Schr dinger or Dirac equation under a spherical atomic poten tial is numerically solved within a local density approximation LDA 1 2 or a generalized gradient approximation GGA 3 to the exchange correlation energy The distribution of this program pack age and the source codes follow the practice of the GNU General Public License GPL 23 The program package can be freely downloadable from http www openmx square org Features of ADPACK Ver 2 2 are summarized as follows All electron calculation by the Schr dinger or Dirac equation LDA and GGA treatment to exchange correlation energy All electron LDA and Hartree Fock calculations by a finite element method FEM for the Schr dinger equation Pseudopotential generation by the Troullier and Martine TM 4 and Bachelet Hamann and Schluter BHS 5 and Morrison Bylander and Kleinman MBK 6 schemes Pseudopotential generation for unbound states by Hamann s scheme 9 Kleinman and Bylander KB separable pseudopotential 7 Separable pseudopotential with Bl chl multiple projectors 8 e Partial core correction to exchange correlation energy 14 Logarithmic derivatives of wave function
20. account for the calculation For example scf Mixing History is specified to be 3 and the SCF step is 6th Then the output electron density at 5 4 and 3 SCF steps are taken into account to construct an optimum input electron density scf Mixing StartPulay The SCF step which starts the GR Pulay or Pulay method is specified by the keyword scf Mixing StartPulay The simple mixing method is employed in SCF steps before starting GR Pulay or Pulay method scf criterion 10 The keyword scf criterion specifies a convergence criterion for the SCF calculation The SCF iteration is terminated when a condition NormRD lt scf criterion is satisfied where a norm of the deviation be Pinp r a Pout r r adr tween the input and output electron densities NormRD is defined by 47 Tmin Specific keywords fo calc type VPS PAO vps type When VPS is chosen for the keyword calc type the keyword vps type specifies a generation method of pseudopotentials Either BHS 5 TM 4 or MBK 6 is available number vps Give the total number of pseudopotentials that you want to generate pseudo NandL The keyword pseudo NandL specifies a set of a principal quantum number N and an angular mo mentum quantum number L of pseudopotentials corresponding to the number of potentials specified by the keyword number vps For example if number vps is chosen to be 2 for a carbon atom and the pseudopotentials for 2s and 2p orbitals are gene
21. andL O 2 0 1 50 0 0 1 2 1 1 62 0 0 pseudo NandL gt The first number specifies a serial number beginning from zero which is used in the specification of the keyword local part vps In the second or third columns a principal number and an angu lar momentum quantum number are given The fourth column provides a cutoff radius a u for the generation of pseudopotentials Although an optimum cutoff radius is determined so that the generated pseudopotentials has a smooth shape without distinct kinks and a lot of nodes however the selection includes somewhat an empirical factor The fifth column provides an energy at which each pseudopotential is generated However if the state is occupied non zero occupation then the eigenenergy is used instead of the value given by the fifth column The energy given by the fifth 19 column is used for only a state with zero occupation Regardless of the occupation number the fifth column has to be provided It is also possible to take into account semicore states in the generation of pseudopotentials For example if you want to include 3s and 3p states as semicore states in a sodium atom the specification is as follows lt pseudo NandL 0 3 0 1 8 0 0 1 3 1 2 3 0 0 2 4 0 1 8 0 0 3 4 1 2 3 0 0 pseudo NandL gt In this case a pseudopotential is generated for the lowest state in each angular momentum quantum number in the BHS 5 and TM 4 schemes On the other hand the MBK scheme 6 takes multip
22. ault smallest_cutoff_vps default 3 0 ON OFF default 3 0 Hartree default 2 0 Hartree default 50 ON OFF Core electron density for partial core correction pcc ratio origin rho_core origin rho_core ip pcc ratio rho_core rho_V charge pcc calc on pcc ratio 0 25 pcc ratio origin 5 00 Pseudo atomic orbitals maxL pao num pao 5 ON OFF default 1 0 default 6 0 default 2 default 7 radial cutoff pao 5 0 default 5 0 Bohr height of wall 20000 0 default 4000 0 Hartree rising edge 0 2 default 0 5 Bohr ri rc rising edge search LowerE 3 000 default 3 000 Hartree search UpperE 20 000 default 20 000 Hartree num of partition 300 default 300 matching point ratio 0 67 default 0 67 The specification of each keyword is as follows Common keywords for calc type ALL VPS PAO System CurrrentDir The directory that files are output System Name The file name of output files Log print The informations during the calculation are output to the standard output Specify Log print ON when outputting or Log print OFF when non outputting This keyword is used for developers System UseRestartfile For an atom with a large atomic number all electron calculation requires a considerable computational time So it is needed to reduce the computational time when optimal cutoff radii of pseudopotentials are determined in a trial and error If the keyword
23. ctions of j l 1 2 and j l 1 2 are evaluated respectively ghost check In case of calc type VPS if you want to check whether there are ghost states for the generated separable pseudopotentials please specify ON for the keyword ghost check If not so please specify OFF for the keyword The calculation result appears on the standard output your display charge pcc calc A charge density used for a partial core correction PCC to the exchange correlation functional 14 is calculated by turning charge pcc calc on pcc ratio The keyword pcc ratio is a parameter in the calculation of a partial core electron density The core electron density is approximated using a fourth order polynomial below the cutoff radius pe at which the ratio p py between the core electron density pe and the valence electron density py becomes pcc ratio pcc ratio origin The keyword pcc ratio origin is a parameter in the calculation of a partial core electron density The core electron density is approximated using a fourth order polynomial so that the core electron at the origin satisfies a relation p 0 pcc ratio originxX pe Tpec Specific keywords for calc type PAO 13 maxL pao The pseudo atomic orbitals are generated up to an angular momentum quantum number maxL pao num pao The number of pseudo atomic orbitals generated with the same angular momentum quantum number radial cutoff pao The keyword radial cutoff pao specifi
24. derivatives of wave functions 1 1 calc type PAO CO pao radial parts of pseudo atomic orbitals under a confinement potential In these output files two files CO vps and C0 pao could be the input files for OpenMX When these two files are used in OpenMX please copy CO vps to directory openmx DFT_DATA VPS and copy CO pao to directory openmx DFT_DATA PAO respectively 12 Templates of the input files There are templates of the input files of several atoms which can be used for your purpose The directories work work_FEMLDA work FEMHF contain those for conventional FEMLDA and FEMHF calculations respectively 13 Database of optimized VPS and PAO A database Ver 2011 for the optimized pseudopotentials VPS and pseudo atomic orbitals PAO is provided in the OpenMX web site These data can be used for OpenMX calculations as it is 29 14 Others Program The program package is written in the C language including one makefile makefile five header files adpack h and 65 routines addfunc c FEMHF_JKLM c adpack c FEMLDA_A11_Electron c A11_Electron c Find_LESP c A11_ElectronFEM c Frho_V c A11_ElectronFEM_T c Gauss_Legendre c BHS c Gauss_LEQ c Calc_Vlocal c Generate_VNL c Core c ghost c Density c GR_Pulay c Density_PCC c GVPS1 c Density_V c GVPS2 c DMF_Func c Hamming_1 c Empty_VPS c Hamming_0 c E_NL c Hartree c FEM_A11_Electron c HokanF c FEMHF_A11_Electron c Initial_Density c
25. e CO loc in order of log r r and the local part Figure 2 b shows the local part of the pseudopotentials C0 ld The logarithmic derivatives of radial wave functions are output in the file CO 1d where means the angular momentum quantum number The data are stored in order of energy and the logarithmic derivatives of radial wave functions under the all electron potential semi local pseudopotential and fully separable pseudopotential 18 o IN Valence electron Partial core density Electron density a u o N Figure 3 Valence electron and partial core densities of a carbon atom In the generation of pseudopotentials it is possible to choose either the BHS type the TM type or the MBK type In the template file C inp the TM type is chosen as the generation scheme In practice the choice of a suitable cutoff radius in the pseudopotential generation is made by trial and error so that the shape of the generated pseudopotentials can be smooth Also it is required to carefully check whether appropriate results are obtained or not for physical quantities that you want to calculate when density functional calculations are performed for molecules and solids using the generated pseudopotentials In addition to this a proper choice of valence states have be checked by a series of benchmark calculations 6 2 Cutoff radius Cutoff radii of pseudopotentials are specified by the following keyword lt pseudo N
26. e confinement pseudopotentials are evaluated numerically up to a required excited state In this section the generation of the pseudo atomic orbitals is illustrated In the file C inp please set the keyword calc type to PAO and run the executable file adpack as follows adpack C inp When the run is completed normally then you find a file CO pao in the directory work In this file CO pao the valence electron density and the radial parts of the pseudo atomic orbitals are output For your adversaria the contents of the input file and the results of all electron SCF calculation are also included They are stored in order of log r r and the valence electron density and in order of log r r and the radial part 1 the radial part 2 in the flexible date format respectively In Fig 4 the confinement potential and the pseudo atomic orbitals for the s orbital are shown From Fig 4 we see that the pseudo atomic orbitals are localized due to the confinement potential and the number of nodes increases as the eigenvalue increases The confinement potential is made by modifying the core potential as follows for r lt r1 3 Veorelr D bnr for r lt r lt Te 1 n 0 h for re lt r where bo bi ba and b3 are determined so that the values and the derivatives are continuous at both r and re Considering that there are relations re radial cutoff pao r re rising edge and h height of wall we find that the tunn
27. eling of wave function for the confinement wall becomes small as height of wall increases Also it is possible to control the shape of the rising edge around the wall by changing rising edge If you use a huge value for height of wall then you might meet a case that the calculation is not completed normally since the computational instability appears often In such a case the numerical instability may be avoided by enlarging the keywords rising edge and num grid As for the keyword rising edge please refer the section Input file The file pao created here can be an input file of the program package OpenMX 26 4 0F oh 2 D 20k D S T 5 0 0f S 2 L a o ES 3 2 0 E D S L 1 0 lt 4 0 0 1 2 3 4 5 Figure 5 Confinement potential and radial parts of pseudo atomic orbitals of a carbon atoms 9 Virtual atom with fractional nuclear charge It is possible to generate pseudopotentials and basis functions for a virtual atom with fractional nuclear charge The relevant keywords in ADPACK are given by AtomSpecies 6 2 total electron 6 2 valence electron 4 2 lt occupied electrons 1 2 0 2 2 0 2 2 occupied electrons gt The above example is for a virtual atom on the way of carbon and nitrogen atoms By just controlling the above keywords you can easily generate pseudopotentials and basis functions for virtual atoms When you use those in OpenMX as input data no specification by keywords is required
28. eme the number of pro jectors in the separable form is determined by the number of states with the same angular momentum quantum number the number of projectors can be different from each other depending on the choice of valence states Also it should be noted that even if the MBK scheme is employed by the keyword vps type the TM scheme is employed for angular momentum quantum number with only one state and the number of projectors is determined by the keyword Blochl projector num for the separable pseudopotential with the angular momentum quantum number 6 6 Logarithmic derivative of wave function To check the transferability of generated pseudopotentials a useful measure is to compare logarithmic derivatives of wave functions 16 If the logarithmic derivative of pseudopotential is comparable to that by the all electron calculation through a wide range of energy then the pseudopotential would possess a good transferability In Fig 4 shows the logarithmic derivatives in a carbon atom indicating a good transferability of the pseudopotential The keywords concerned to the calculations of the logarithmic derivative are as follows 21 6 All electron 7 6 E p state All electron Semi local Semi local Fully separable Fully separable Logarithmic derivatives o 1 1 i i 1 i 1 A 1 1 1 2 2 1 0 1 2 Energy Hartree l N l ot Figure 4 Logarithmic derivativ
29. ensity modified core electron density for PCC CO loc local part of pseudopotentials C0 1d0 logarithmic derivatives of wave functions 1 0 CO 1d1 logarithmic derivatives of wave functions 1 1 C0 1d2 logarithmic derivatives of wave functions 1 2 CO nsvps In a file CO nsvps the pseudopotentials in a non separable form are output in which they are listed in order of log r r the pseudopotential 0 and the pseudopotential 1 where the number referred to specify the pseudopotential corresponds to the number given for the first column in the specification of the keyword pseudo NandL in the input file All the units employed are in atomic unit Figure 2 shows the pseudopotentials of a carbon atom stored in the file CO nsvps CO vps In a file CO vps the pseudopotentials in a separable form are output in which they are listed in order of log r r the local part of the pseudopotential and the non local part of the pseudopotential Also the input file and the results of the SCF calculation are added in this file for your adversaria The file is output in the flexible data format since the file vps is used for the input file to the program package OpenMX In Fig 2 b shows the separable pseudopotentials of a carbon atom In case of charge pcc calc ON then the file also includes the partial core density for PCC 14 The format is the same as that of the pseudopotential and they are listed in order of log r r and the par
30. es a cutoff radius r a u for the pseudo atomic orbitals height of wall The keyword height of wall specifies a height Hartree of confinement wall rising edge The keyword rising edge controls a shape of rising edge of the confinement wall Note that there is a relation rj r rising edge See also the section Generation of pseudo atomic orbitals search LowerE The keyword search LowerE gives the lower bound of energy for searching eigenenergies of pseudo atomic orbitals search UpperE The keyword search UpperE gives the upper bound of energy for searching eigenenergies of pseudo atomic orbitals num of partition The keyword num of partition gives the number of energy partitioning ranging from the search LowerE to the search UpperE First the eigenstates of pseudo atomic orbitals are roughly explored for the energy ranges partitioned by the keyword num of partition Then the eigenstates are refined in the energy range with a correct number of nodes matching point ratio The keyword matching point ratio gives a matching point to connect two wave functions solved from the origin and the distant It should be noted that the matching grid number is given by match ing point ratio x grid num 14 5 All electron calculation In this section keywords for the all electron calculation are explained These keywords discussed here are important for all calculations including the generation of pseudopotentials and p
31. es of radial wave functions under the all electron potential semi local pseudopotential and fully separable pseudopotential of a carbon atoms e log deri RadF calc When the logarithmic derivatives are calculated then ON otherwise OFF e log deri MinE The lower bound of energy Hartree used in the calculation of logarithmic derivatives of radial wave functions e log deri MaxE The upper bound of energy Hartree used in the calculation of logarithmic derivatives of radial wave functions e log deri R Radius at which the logarithmic derivatives of radial wave functions are evaluated You can find details for these keyword in the section Input file In case of log deri RadF calc 0N calculated logarithmic derivatives are output in files 1d where is the file name that you specified by the keyword System Name and is the angular momentum number If the fully relativistic calculation is performed as eq type dirac the file name is l1d _ where runs 0 to 1 corresponding to j l 1 2 and j l 1 2 respectively 6 7 Ghost states The fully separable form of pseudopotential would possess artificial ghost states 17 which is one of serious problems in the separable form while multiple projectors proposed by Bl chl 8 is highly effective to avoid the existence of ghost states To check it a keyword ghost check is provided 22 Although the keyword is useful to find the ghost states however it should be noted t
32. est calculations were performed using an executable file compiled with gcc Among the compiler options shown above Dnoomp and std c99 should remain unchanged when gcc is used the other parts must be property changed 3 Test calculation If the installation is completed normally move to the directory work and then you can perform the program adpack using an input file C inp as follows adpack C inp The test input file C inp is for performing the SCF calculation of a carbon atom The calculation is performed in only several seconds by a 2 4 GHz Xeon machine although it is dependent on a computer When the calculation is completed normally three files C0 alog C0 ao and C0 aden are output to the directory work CO alog is the log file of the calculation which includes the contents of an input file the convergence history in SCF steps and the total energy decomposed to the contributions A part of the file CO alog is shown below It is found that the convergence is achieved by 12 SCF steps for the eigenvalues energy of a Kohn Sham equation Eeigen and the norm of the difference between the input and output densities KKK K K K FK FK K K K K K K FK FK FK FK FK K K K K K K FK 2g 2K FK FK FK FK K K K K K FK FK FK FK FK FK K K K K K K gt K OK SCF history in all electrons calculations Kk ak ak AA AA 3K K K K K K K 2K CCA ACI I I A II I IK 3K K K K 21 21 K K K K K K K K A K SCF 1 Eeigen 31 1432610521
33. hat a complete check to detect the ghost states is difficult 6 8 Partial core correction The contribution to electron density from core electrons is ignored in the evaluation of exchange correlation energy in the pseudopotential method although there is an non linearity of exchange correlation energy with respect to electron density Thus a partial core correction would be important in order to take account of the non linearity A partial core charge for the partial core correction can be constructed by the following keywords e charge pcc calc When a partial core charge is calculated ON otherwise OFF pcc ratio The keyword pcc ratio is a parameter in the calculation of a partial core electron density The core electron density is approximated using a fourth order polynomial below the cutoff radius Tpcc at which the ratio pe py between the core electron density pe and the valence electron density py becomes pcc ratio pcc ratio origin The keyword pcc ratio origin is a parameter in the calculation of a partial core electron density The core electron density is approximated using a fourth order polynomial so that the core electron at the origin satisfies a relation p 0 pcc ratio origin x p Tpec Note that a precipitous partial core charge would cause numerical instabilities Thus a modest core charge is better from a numerical point of view 6 9 Restart As discussed above a trial and error is needed to generate
34. hen Jp and J are zero So it is desirable to make pseudopotentials with small J and J ly and J are output on the standard output your display log deri MinE In case of calc type VPS and log deri RadF calc ON the keyword log deri MinE gives the lower bound of energy Hartree used in the calculation of logarithmic derivatives of radial wave functions log deri MaxE In case of calc type VPS and log deri RadF calc 0N the keyword log deri MaxE gives the upper 12 bound of energy Hartree used in the calculation of logarithmic derivatives of radial wave functions log deri R In case of calc type VPS and log deri RadF calc 0N the keyword log deri R gives the radius a u at which the logarithmic derivatives of radial wave functions are evaluated If eq type sch or eq type sdirac the keyword log deri R is specifid for each angular momentum number L as follows lt log deri R o 2 2 1 2 4 log deri R gt The beginning of the description must be lt log deri R and the last of the description must be log deri R gt The first column is the angular momentum number L and the second column is the radius at which the logarithmic derivatives of radial wave functions are evaluated If eq type dirac the third column is needed as follows lt log deri R 0 2 01 9 1 2 0 2 1 log deri R gt where the second and third column give the radii at which the logarithmic derivatives of radial wave fun
35. le states with the same angular momentum into account in the construction of pseudopotential The treatment significantly increases the transferability of pseudopotential So in most cases the MBK scheme is the best choice in ADPACK Ver 2 2 6 3 Pseudopotentials for unbound states It is possible to generate pseudopotentials for unbound states with for any higher L component by Hamann s scheme 9 For example although no electron is occupied for the 3d state in the input file C inp the cutoff radius for the 3d state can be specified as follows number vps 3 lt pseudo NandL O 2 0 1 50 0 0 1 2 1 1 62 0 0 2 3 2 1 00 0 0 pseudo NandL gt The pseudopotential generation of the 3d state will be generated with the cutoff radius and then the reference energy is 0 0 a u A principal number and an angular momentum quantum number for the unbound state should be given as the state above occupied states but with the smallest principal number 6 4 Separable form Norm conserving pseudopotentials generated by the BHS and TM schemes are written in a semi local form which is based on a projection by the spherical harmonic function In the application of pseudopotentials to molecules and bulks the semi local form is rewritten by a fully separable form proposed by Kleinman and Bylander KB 7 or Bl chl 8 to reduce the computational effort Then the following keywords are important for transferability of the separable form 20
36. rated then specify in the following way lt pseudo NandL O 2 0 1 3 0 0 1 2 1 1 3 0 0 pseudo NandL gt The first column specifies a serial number beginning from zero which is used in the specification of the keyword local part vps In the second or third columns a principal number and an angular momen tum quantum number are given The fourth column provides a cutoff radius a u for the generation of pseudopotentials Although an optimum cutoff radius is determined so that the generated pseu dopotential has a smooth shape without distinct kinks and a lot of nodes however the choice is made in a somewhat empirical way The fifth column provides an energy at which each pseudopotential is generated However if the state is occupied non zero occupation then the eigenenergy is used instead of the value given by the fifth column The energy given by the fifth column is used for only a state with zero occupation Regardless of the occupation number the fifth column has to be provided The beginning of the description must be lt pseudo NandL and the last of the description must be pseudo NandL gt Blochl projector num The keyword Blochl projector num specifies the number of projectors for each L component in sep arable pseudopotentials If you specify 1 for Blochl projector num this means the Kleinman and Bylander KB separable pseudopotential As the number of Blochl projector num increases the sep arable pseudopotential converges
37. s 16 Detection of ghost states in separable pseudopotentials 17 e Scalar relativistic treatment 18 Fully relativistic treatment with spin orbit coupling 6 19 Generation of pseudo atomic orbitals under a confinement potential 15 e Analysis of wave functions Analysis of electron density e Database of pseudopotentials and pseudo atomic orbitals The norm conserving pseudopotentials and pseudo atomic orbitals generated by ADPACK could be input data to OpenMX a program package of performing density functional calculations for molecules and solids It is expected that ADPACK is executable on a standard unix like environment such as unix linux and cygwin 22 since the code is written in a standard C language A database of pseudopotentials and pseudo atomic orbitals is also found in the above website 2 Installation 2 1 Including library ADPACK uses one library package LAPACK http www netlib org which must be linked during the compilation Instead of LAPACK an alternative library such as ATLAS MKL and ACML can be used as well To link an library CC and LIB in makefile stored in the directory source have to be property changed depending on your computational environment The default setting for CC and LIB are cC LIB gcc Dnoomp std c99 03 I usr local include I home ozaki include L home ozaki lib latlas_p4 static We strongly recommend for users to use the gnu C compiler gcc since our all test
38. seudoatomic basis functions since both the generations of pseudopotentials and pseudo atomic orbitals are based on the all electron calculation The list of keywords and some comment for the all electron calculation are as follows 10 xc type Choose GGA LDA or LDA VWN total electron Give the total number of electrons It is also possible to give the number of electrons corre sponding to not only a neutral atom but also a positive or negative charged atom grid xmin Set grid xmin min a u exp grid xmin where fmin is the minimum radius from which radial differential equations are solved toward a distant An appropriate value for grid xmin is 7 0 from H to Kr and 10 0 for heavier atoms grid xmax Set grid xmin Tmax a u exp grid xmax where rmax is the maximum radius from which radial differential equations are solved toward the origin An appropriate value for grid xmin is 2 5 to 4 0 but could depend on whether there are delocalized states or not grid num Set the number of grids to solve radial differential equations A larger number of grids gives a higher degree of accuracy while the computational time increases An appropriate value for grid num is 3000 to 12000 For heavier atoms the use of a larger number of grids is better to achieve a reliable calculation grid num output It is possible to change the number of grids for r in output files by the keyword grid num output although
39. ter The maximum number of SCF iterations is specified by the keyword scf maxlter The SCF loop is terminated at the number specified by scf maxlter even if the convergence criterion is not satisfied scf Mixing Type A mixing method of generating an input electron density at the next SCF step is specified by keyword scf Mixing Type Three schemes are available Simple GR Pulay and Pulay which are the simple mixing method GR Pulay method Guaranteed Reduction Pulay method 12 and the Pulay method 13 respectively The simple mixing method used here is modified to accelerate the convergence by referring to a convergence history So the use of the simple mixing method is recommended because of its robustness scf Init Mixing Weight The keyword scf Mixing Weight gives an initial mixing weight used by all the mixing methods in ADPACK The valid range is 0 lt scf Mixing Weight lt 1 scf Min Mixing Weight The keyword scf Init Mixing Weight gives the lower limit of a mixing weight in the simple mixing method scf Max Mixing Weight The keyword scf Max Mixing Weight gives the upper limit of a mixing weight in the simple mixing method scf Mixing History In the GR Pulay and Pulay methods the input electron density at the next SCF step is calculated by making use of the output electron densities in the several previous SCF steps The keyword scf Mixing History specifies the number of previous SCF steps which are taken into
40. the semilocal non separable pseudopotential We recommend you to use 2 or 3 for Blochl projector num in order to increase the transferability of the separable pseudopo tential We guess that you might consider the increase of computational efforts due to the increasing projectors However the matrix elements for the non local part are evaluated outside the SCF loop Therefore the computational demand for a larger number of projectors is quite small 11 local type The keyword local type specifies a way for generating the local part of pseudopotentials Simple means that a l component of pseudopotential specified by the keyword local part vps is used as the local part Polynomial means that the local part for the inside of a cutoff radius is generated using a polynomial and that the outer part is proportional to 1 r At the cutoff radius the two parts are connected so that up to third derivatives are continuous local part vps When Simple for the keyword local type is used the keyword local part vps specifies the local potential used in the generation of factorized pseudopotentials In this specification please choose the number of the first column in the specification of the keyword pseudo NandL local cutoff When Polynomial is used for the keyword local type the cutoff radius rie a u at which a poly nomial local part is connected to N r is specified by the keyword local cutoff where Ny is the
41. tial core density The data of the partial core density is also used as the input date of OpenMX In Fig 3 the partial core density is shown together with the valence electron density stored in the file CO vden CO vpao The pseudo atomic orbitals corresponding to the pseudopotentials are output in a file CO vpao The format of the output is the same as that of CO nsvps Figure 2 a shows the pseudo atomic orbitals and the pseudopotentials 17 T T T T T T T T T T 6 o 6 JU 0 4 Of Local D ly g Non local s 5 2 a y Non local p T 710 45 8 lt 5 g 0 S Cc lt o S _o o a 03 SB 5 O 4 O p J o o D A s component 7 g oa p component 1 0 4 N 2 O 40 LL Figure 2 a Radial parts of the pseudo atomic orbitals and the corresponding norm conserving pseudopotentials b Norm conserving pseudopotentials in a separable form CO0 vden The electron density for the valence electron is stored in a file CO vden In case of charge pcc calc OFF the data are output in order of log r T Pv Pt Pes Anr py ATT pr Arr pe In case of charge pcc calc ON the data are output in order of log r r Pv Pt Des Doce Anr py ATT pt Anr pc ATT Ppcc where py Valence electron density pt Total electron density Pc Core electron density Ppce Modified core electron density for PCC C0 loc The local part of separable pseudopotentials is output in the fil
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