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1. 4 CO2 IN Bending of a triatomic molecule COz and costruction of the related Walsh Diagram The bending angle is a free variable which takes four different values see Directive 2 The real 2 molecule is linear with symmetry Din Dinfinite h but the symmetry descends to Coy because of the deformational coordinate In order to mantain the symmetry constant and create a Walsh Diagram it is necessary to bend slightly the molecule even in the first step Accordingly the free variable which applies to the two equivalent angles defined by the Z axis and any C O vector is equal to 90 1 in the first step TITL CO2 BENDING PAR 0 DIST 4 FV1 90 1 s 10 KEYVV EL CM NC VVF RO SYMM C2v ORIG C INT 1201 150 FV1 END 36 5 ETHYLDM IN ldealized dimerization of two ethylene molecules to generate cyclobutane The symmetry forbidness of the process is highlighted by the Walsh diagram which can be drawn after the EHC calculation The forbidden interlevel crossing Woodward Hoffmann Rules between the HOMO and the LUMO is most evident in the diagram also because the filled and empty MOs are assigned different colours TITL EthyleneaDimerization Approach of 2 C2H4 and bending of CH2 planes PAR ODIST 5 FV1 1 5 s 0 2 Fv20s 11 KEYW EL CM RO NC DI SYMM D2h ORIG DU INT 1 2 DU fv1 180 0 INT 2 1C0 7 90 0 1 INT 1 2H1 01 120 90 1 INT 1 4 DU 1 90 90 GR 1 1 4 fv2 END The example illustrates the usage of the first Fr
2. PAR 0 DIST KEYW EL WF CM RO NC RC ORIG FE 0 0 0 INT Cp 12 1 8 1800 INT Cp 112 1 8 00 0 36 FMO FKEYVV NC RO TO WF FRAG 2 1 2 2 END 12 C60PT1 IN The file contains the input for calculating the MOs of the adduct between Ceo and the metal fragment Pt PH3 2 A fragment orbital analysis analysis is also performed The overall symmetry is C but that of Ceo is Ih Since the program does not recognize the latter it is convenient to construct the Ceo within the D n pointgroup The metal atom and the phosphines bound to it have a sign follovving their symbols so that the D n molecular expansion does not apply to them Notice that for FMO analysis the first fragment is made up with 60 atoms namely only the carbon ones FCOMP line It is interesting in the CACAO session to draw a MOOP diagram relative to the overlap population between fragments MO by MO TITLE C60Pt1 KEYW EL NC SYMM D2h ORIG Du INT 90 91 DU 3 2594 148 2752 0 INT 91 11 C 1 19091 90 36 1 INT 91 12 C 1 19091 90 108 1 INT 91 13 C 1 19091 90 180 1 INT 91 14 C 1 19091 90 252 1 INT 91 15 C 1 19091 90 324 1 INT 90 92 DU 3 2574 90 31 7248 INT 92 16 C 1 19091 90 90 3 INT 92 17 C 1 19091 90 162 3 INT 92 18 C 1 19091 90 234 3 INT 92 19 C 1 19091 90 306 3 INT 92 20 C 1 19091 90 18 3 INT 90 93 DU 3 2584 58 2752 90 INT 93 21 C 1 19091 90 36 5 INT 93 22 C 1 19091 90 108 5 INT 93 23 C 1 19091 90 180 5 INT 93 24 C 1 190
3. The following limits are presently imposed a Max number of atoms 350 b Max number of orbitals 3500 c Max number of steps in the Walsh diagram 20 d Max number of free variables 50 The availability of physical memory in your PC is also a constraint not as crytical as before as the programs are not restricted anymore by the 640K limit typical of DOS The ehmo calculation uses cartesian coordinates The latter can be either given as input or can be generated by the program starting from crystallographic or internal coordinates The internal coordinates are most useful to reconstruct highly symmetrical molecules and are very helpful in fixing stereochemical rearrangements or reaction pathways Their definition is recommended The internal coordinates can be based on either a simplified Z MATRIX or a complete Z MATRIX Essentially each new atom is being defined by three preexisting atoms or points dummy atoms Figure 1 helps to understand the disposition of the four points necessary for each new atom definition In the INPUT file the latter points can be either fully explicated complete Z Matrix INTZM card or only partially explicated simplified Z Matrix INT card Figure 1 The atom with absolute number 4 A4 is being currently defined This forms a vector of the given length d4 first internal coordinate with the preceeding atom number 3 The angle at A represents the second i
4. There are two basic programs 1 Program EHC Extended H ckel Calculation This is a major revision of the original program SIMCON Cornell University with weighted Wolfsberg Helmholtz formula see R Hoffmann J Chem Phys 1963 39 1397 R Hoffmann W N Lipscomb J Chem Phys 1962 36 2179 3489 J H Ammeter H B Burgi J C Thibeault and R Hoffmann J Am Chem Soc 1978 100 3686 Initially a calculation of Cartesian coordinates from internal coordinates is performed optionally crystal coordinates can be used by providing also the CELL parameters Input cartesian coordinates are also treated as crystal ones with cell A B C 1 0 alpha beta gamma 90 Many possibilities are offered to manipolate the model either interactively or by modifying the input file at will When the model is satisfactory the actual MO calculation can be performed The program outputs the information typical of MO calculations energy levels Wavefunction coefficients Mulliken population analysis etc The length of the output can be limited by using specific keywords EL WF etc see below a complete list The program automatically determines the molecular symmetry pointgroup and each MO level is assigned the proper symmetry class In a single run it is possible to repeat the MO calculation at different molecular geometries steps by specifying in the INPUT file one or more geometrical parameters to be varied free variables In this m
5. const1 expression It allows to define a series of global constants which can be used in the various FVn INT INTZM and GROUP directives The name of a constant must be not longer than 5 alphanumeric characters No numeric digit is allowed as leading character Also some words such as COS SIN TAN FVn etc are reserved and cannot be used as constants The value of the constant can be either numeric or an expression containing numeric values and or other constants already defined Expressions must be preeceded by sign The expression contains typical arithmetic operators or trigonometric functions such as or SIN COS EXP etc The square root is applied as a power with the exponent 0 5 e g the square root of 2 0 is 2 00 5 The order of the operations is sequential namely there is no jerarchy between the operations thus the usage of inclusive parentheses is highly recommended There may be more than one CONST directives max allowed 90 The program has some predefined angular constants 1 180 TET 109 4712206 TOH 54 73561 TIH 37 37736827 TOH and TIH are useful to define the orientation of the C3 axis in the Oh and Ih pointgroups respectively In fact TOH is the angle formed by the fourfold and threefold axes in Oh while TIH is the angle formed by the fivefold and the threefold axes in Ih see the sample files in the appendix Example CONST R1 1 4 Ang 119 0 R2 R1 cos Ang fv n 1 fv n 2
6. into the plane A A j A3 The sign is positive if this movement involves a righthand screw motion and negative if this movement involves a left hand motion Some confusion arises when one has to decide whether tau has a value between 0 and 90 or between 90 and 180 As a rule of the thumb consider the vector as the binding axis of a book If the book appears open as in the Figure 1 the vectors A4 Az and lie on opposite sides with respect to then tau belongs to the second quadrant Conversely if the book is closing A4 Az and A3 Ay are cis oriented tau is in the first quadrant Also to become familiar with the torsion angle definitions the new user is warmly recommended to practice by making on the paper stereochemical sketches of different molecules Assign progressive numbers to the atoms and determine all of the internal coordinates see one example below It is easy to draw with CACAO the generated structure after interrupting EHC and verify the correctness of the assignments hence go back to make the appropriate corrections To set up any reference point e g the centroid of a ring the user can define dummy atoms symbol DU and optionally a negative number Dummy atoms are automatically removed from the ehmo calculations The user can only point once to the same atom only one definition but he can point as often as needed from an existing atom to other ones This will be clearer by followin
7. the fragment may appear to possess lower symmetry than the actual one A warning message is issued by EHC As mentioned crystallographic or cartesian coordinates can be used in the input file but the usage of the internal coordinates is still warmly recommended One of the reasons is that only by using internal coordinates it is possible to construct Walsh Diagrams hence to monitor the evolution of the MOs for a certain geometric deformation or reaction coordinate In order to generate one of these pathways free variables FVn can be defined distances angles torsion angles as well as rotation and translation of rigid groups in the molecule see below and later referenced to in the internal coordinates INT or group GR lines Some of the most common molecular fragments or groups can be internally generated by the program with only one instruction line as they were single atoms e g predetermined groups such as phosphine amine cyclopentadienyl carbon monoxide phenyl etc are introduced as they were single atoms with the special symbols FO AM CP CM PH etc In order to have EHC performing a FMO analysis the keyword FMO must be specified in the input file as a single line directive following all of the atomic definitions internal cartesian or crystallographic coordinates Additional information about the composition of the fragments must follows in the subsequent lines It is also possible to have an FMO calculation by using
8. 55 s 2 SYMM C3v ORIG INTI 1 2 fv 2 180 INTN 1 3 fv100 INT Me 3 4 1 50 1100 END 15 OCTA IN This example shows how to construct an Octahedral molecule formed by a cube of Nickel atoms with the faces capped by carbon atoms It is important in order to have a correct assignement of the MO symmetries that one fourfold axis containing one C atom coincides with the Z axis The other two fourfold axes must coincide with the bisectors of the XY axes Notice that the threefold axis containing the Ni atoms is defined with the internal angular constant TOH see directive CONST TITL SYMM Oh 41 ORIG DU INT 1 2Ni 1 7 TOHO INT13C2 300 FMO FRAG 28 42 Summary of the Directives TITL Title card First compulsory line REM comment line optional used at any place IMP Import Coordinates from given file optional First group of directives in any order PAR General parameter card optional METH Computational Method optional POP Mode for populating the MOs optional CONST Definition of geometrical constants optional FVn Values of the Free Variable n at the dif optional ferent steps can also be an expression KEYW Keyword card to control the EHC output optional OVDEL Overlap deletion card optional MOOP Range of M O O P matrices printed optional SYMM Pointgroup Symbol optional Second group crystallographic or cartesian coordinates CELL Unit cell dimensions card required as first ATOM Atomic coordi
9. a file already set for a Walsh diagram i e containing free variables Indeed if the FMO instructions are present in such a file they are taken into consideration only if the keyword FMO is followed by an integer specifying the step number of the corresponding Walsh Diagram normally set to zero The FMO calculation supersedes the creation of the Walsh diagram in this case For a WALSH diagram be sure that the symmetry remains constant at all steps If at a given step the symmetry becomes higher keep it lower by introducing small deformations for the appropriate parameters usually a bond length variation of 0 01A or angular deviations of 0 1 for angle or torsion angles is sufficient 13 The program is organized to save the largest amount of printed output Notice that the elements of the Charge Matrix are printed vvith the same sign as the corresponding elements of the VVavefunction Matrix so that it is usually not necessary to print both matrices in order to determine the composition and the phase of a given MO Also the elements of the Charge matrix are normalized to 1 rather than 2 electrons so that the actual values can be derived as Charge matrix element ABS printed value 500 These magnitudes can be taken as the percent contribution of a basis set orbital atomic or fragment to a given MO The possibility of retrieving the most significant numerical quantities at any time on the screen by running CACAO greatly reduce
10. example shows the usage of crystallographic coordinates The latter are taken from Dapporto Ghilardi Mealli Orlandini Pacinotti Acta Cryst C40 1984 891 As a useful exercise go into the Molecular Editor select command E from the menu and optimize the symmetry Command O The molecule is idealized to C pointgroup TITL 1 8 NAPHTHYRIDINE PAR Od KEYW EL WF RO NC CELL 6 135 10 407 11 258 90 117 76 90 ATOM N 3228 4512 2064 ATOM N 2755 2680 0806 ATOM C 2250 5416 2479 ATOM C 0265 5471 2164 ATOM C 1826 4553 1354 ATOM C 2363 2626 0075 ATOM C 1284 1745 0524 ATOM C 1288 1810 0040 ATOM C 0889 3584 0836 ATOM C 1680 3586 1237 ATOM H 3313 6065 3024 ATOM H 0863 6157 2533 ATOM H 3581 4547 1143 ATOM H 4137 2603 0334 ATOM H 2165 1117 1149 ATOM H 2060 1212 0322 END 10 O2H2 IN The following example shows a cis trans isomerization of O2H2 that occurs via a torsion of the two OH groups about the O O vector This is achieved by forcing the free variable fv1 to assume opposite values fv1 and fv1 TITL Hydrogen Peroxide CIS TRANS isomerization PAR ODIST 4 FV1 0 1 s30 KEYW EL CM OP RO NC ORIG DU INT O 1 1 0 740 180 0 INT 1 2 0 740 000 1 3 1 05 110 fv1 INT H 2 41 05 110 fv1 END 39 11 FERROCEN IN To obtain the staggered conformation for ferrocene we use the torsion of the one of the internal defined group CP by 36 TITL Ferrocene
11. general discard the usage of the available symmetry information when unusual features in the drawing are observed It cannot be excluded that EHC has assigned a wrong symmetry to the given MO Report the case to the authors by supplying the INPUT file A graphic analysis of the Mulliken Population Analysis can be carried out by constructing two different types of diagrams namely those of the Reduced Charge Matrix RCM and of the Molecular Orbital Overlap Population MOOP This can be done by slecting the keys X RCM or MOOP which appear in the menu at the bottom of Interaction or Walsh Diagrams The RCM diagram displays the values of the Reduced Charge Matrix of selected atoms to each MOs within a range of energy expressed in percent The RCM Diagram is divided in three sections in the left column shows the percent contributions A of the first group of atoms to the MOs in the central the contributions B of the second group and in the right column the contributions of the remaining atoms that is equivalent to 100 A B One line is drawn for each MOs also for degenerate e g 3 parallel lines for t levels artificially splitted to show all of them On the right the real position of the MOs is reported with labels only for some of them avoiding overlapping labels Entering the X RedChg option the user has two cases depending if coming from Walsh or FMO diagrams In the case of FMO analysis it is possible to display a sp
12. in the molecule are accomodated in the appropriate number of MOs which are the lowest in energy If the energy difference between two adjacent Frontier MOs is lt 0 1 eV two or more electrons become unpaired It may happen in a Walsh Diagram that the HOMO and the LUMO become very close in energy only at a certain point In this case a change of the ground state is imposed If popul is 0 the control on the energy differences between the frontier MOs is suppressed for instance the HOMO always contains two electrons even if it is practically degenerate with the next empty level If popul is a negative integer its value is taken as the imposed number of the unpaired electrons populating as many different frontier levels Such an imposed electron distribution remains constant in a Walsh Diagram One can fix a particular MO occupation other than that definable with any of the above strategies For example one wishes to have the second LUMO occupied in order to evaluate its effects on the Mulliken Population Analysis Accordingly popul is set equal to the total number of Molecular Orbitals norb This value must be followed by norb values each one defining the number of electrons in any subsequent MO it can be 0 1 or 2 The norb values are supplied by using the adequate number of POP lines Notice the the order is from the lowest filled n 1 to the highest empty nznorb CONST optional consti val1 const2 val2 FVn 24 or
13. the INT directive TOR2z same as in the INT directive GR ngroup at1 at2 rotat transl optional Used for rotating and or translating rigid molecular fragments about a pivot axis NGROUP The number of the rigid group on which rotation and or translation is operated refer to ORIG and INT in order to see how the different atoms can be assigned to a rigid group AT1 One number from the list of the valid atoms defined in the cards ORIG INT or INTZM cards AT2 The number of a second atom from the same list AT1 and AT2 define the vector about which the rigid group must be rotated clokwise in a right handed system or translated the translation coincides with the direction from AT1 to AT2 For rotations and or translations about the cartesian axes x y z see the shortcuts below ROTAT Value deg of the given angular rotation ROT can also be a Free Variable and referred to as FVn In this case the corresponding series of ramping values must be given in a FVn card If no rotation but a translation is desidered ROT must be zero TRANSL optional Value A for the linear shift of the rigid group TRANSL can also be a Free Variable The same criteria for ROTAT do apply in this case too Note More than one rotational translational operation can be performed for the same group of atoms i e there may be more directives GR for the same group n The operations are are carried out sequentially It is also possible to defi
14. to Fragment 1 the subsequent NF2 atoms to Fragment 2 etc If the molecule is constructed by using the directive SYMM i e by exploiting the symmetry of the pointgroup the automatically assigned numbers of the symmetry generated atoms are unknown at the time when the input files is built In this case the user can complete the input file at a later stage First he discards any FCOMP directive but he runs EHC with the option mole gt EH name mol He checks from the molecular drawings the correctness of the model and collects the proper atomic numbers to be inserted in the FCOMP line after returning to the editor An example of the usage of such the directive FCOMP is provided in the INPUT file ETHYLEN IN see below FDEF charge keyword 1 optional Enter as many directives as the number of fragments NFR This directives are mainly used to control the numerical output in the MO calculation for the fragments If only a standard output is required they may be omitted since it is possible to specify the fragmental charges also in FRAG card CHARGE Charge assigned to the fragment this value supersedes that given in FRAG card KEYWORDS for selecting the OUTPUT same as in KEYW card EN This card is the last instruction optional 34 INPUT FILE selected examples Copies of the INPUT files illustrated belovv are found in the directory FILES subdirectory of MOAN supplied with the programs 1 N2 IN Molecular nit
15. 0 Nickel bisphosphine ethylene ROP 1 n r Ev averaged 1_bonds ROP 1 075 1 075 MO range 16 25 Eu 1 scale integration for IMOOP 16 6b1 7 7 4 integral of MOOP 11 H 1 5 thick y 17061 for HOMO 13 2 fag 13032 22 bal unsplitted 15 A 15 23 5a1 splitted for MOOP gt 250 antibonding bonding 40 60 MOs energy FMO1 21 0 5 15 30 50 75 100 percent groups OV POPs for FMOs x100 lt 111 29 33 4 Liman D NICKEL BISPHOSPHINE ETHYLENE lt 101 302 13 lt 91337 3 131 31 3 1 T E cev 420 37 634 63 AE 70 214 96 C2v C2v tor ee lt 171 30 6 2 charges 609 000 509 lt 111 349 13 lt 101 352 13 4 10 6a1 4 16 6b1 7 4 2 2b1 9 4 11 4 71 11 4 1 4 17 5b1 18 8 1 as 4 190662 13 J100 125a 20 741 30 5 1 Baas Biss 38 15 2b2 31 2af iz 1 85a 22 1 2 15 199 Sb 226 25 2 2 el MO 16 1 E 6 167 MO 17 5 1 E 11 969 MO 18 8a1 12 052 Ly niman Ly niman niman LUMO HOMO 1 22 THE STRUCTURE OF THE INPUT FILE in DETAILS Selected INPUT files are at the end of this document and in the subdirectory FILES The examination of a few examples will help the user to understand the philosophy for creating the INPUT Here follovvs the description of the INP
16. 91 90 252 5 INT 93 25 C 1 19091 90 324 5 INT 90 1 PT 5 4300 180 0 INT 1 2FO 2 25 128 8 0 40 INT 1 3FO 2 25 128 8 180 FMO FKEYVV RO EL OP FRAG 2 60 FCOMP END 13 CAMBR IN This File shows how to import a structure from the Cambridge Structural Database The File in question is fosf2 dat also supplied in the directory Files and contains all of the structures of trimetallic clusters with three phosphido bridges You can select one of them interactively by its refcode if the structure consists of cations anions etc only the opportune residue may be selected Then the model can be simplified and the symmetry optimized within the molecular editor Upon the SAVE option the file CAMBR IN will contain the cartesian coordinates This input file can be opportunely manipulated to make Interaction FMO or Walsh Diagrams select atoms as groups which can be rotated or translated with the directive GR TITL cambridge IMP CSD C MOAN Files FOSF2 DAT END 14 NMEI2SU IN This file shows how to prepare the data for a bidimensional surface 7x7 to be used with plotting programs such as MATLAB The case in question is relative to the adduct between amine and iodine and the independent elongation of the N I and 141 bonds is performed see the usage of FVn and FV n free variables TITL N CH3 3 I2 PES for the independent elongation of N I and l I distances PAR Dist 7 fv12 1s 2 fv2 2
17. TAU magnitude can be referenced to the n Free Variable FVn The actual value is that relative to the current step being calculated If FVn is preceeded by a negative sign the sign of corresponding free variable given in the Fvn line is inverted TOR2 cannot be a free variable In the definition of the special fragments CP or BZ the DIST value refers to the dummy atom at the center of the ring being defined Also any DIST ALPHA TAU magnitude can be defined as an expression preceeded by the sign However the expression must contain in this case only constants and not free variables In general all the free variables defined vary synchronously However in order to generate a bidimensional grid of steps one or more free variables can be varied independently from the others This is simply done by referring to the n free variable with a negative n Thus if the number os teps is 5 ipoint 5 in the PAR directive and five Fv lines have been given the first 3 free variables can be varied independently from the last 2 by referring to them as FV1 FV2 FV3 FV 4 and FV 5 In this manner the free variables 4 and 5 assume all of their possible values five for any given combination of the first three free variables Hence the EHMO calculation is repeated 5x5 25 times In this case the EHC output must be inspectioned directly as CACAO is not able to process the corresponding binary output and no graphics can be produced Walsh Di
18. The User Manual of C A C A O Computer Aided Composition of Atomic Orbitals A Package of Programs for Molecular Orbital Analysis PC Beta Version 5 0 1998 CARLO MEALLI and DAVIDE M PROSERPIO with major contribution of ANDREA IENCO Original Reference Journal of Chemical Education 1990 67 399 402 Symmetry routines written by Klaus Linn 1991 Walsh Diagram Legend and other revisions Jos A Lopez 1992 Consulence and contributions Angelo Sironi 1992 4 Free Format routines originally provided by Luis Farrugia 1994 3D Surface data generation Enrique P rez Carreno 1997 Modified EHT ASED Calzaferri Piero Macchi 1997 Molecule Symmetrization Routines Provided kindly by Tullio Pilati and Alessandra Forni 1997 program SIMMOL J App Cryst 1998 in press The package is created and distributed from Istituto per lo Studio della Stereochimica ed Energetica dei Composti di Coordinazione ISSECC C N R Via J Nardi 39 50132 Florence Italy Tel 39 55 2346653 243990 FAX 2478366 e mail mealli cacao issecc fi cnr it Present address of D M P Dipartimento di Chimica Strutturale e Streochimica Inorganica Universita di Milano Via Venezian 21 20133 Milano Italy Tel 39 2 70635120 FAX 39 2 70635288 e mail davide csmtbo mi cnr it For any problem please report to the authors with a copy of the input file Your help and suggestions will be appreciated Whatsnew The package mantai
19. UT file line by line referred to as directives or cards Each directive is characterized by a keyvvord follovved by the parameters vvhich can be given in Free Format separated either by spaces or commas It is important to follovv the order of the directives as they are given in the summary below Only REM INT INTZM and GR directives can be freely mixed up The alphanumeric input is not case sensitivel DIRECTIVES see a summary at the bottom of the file Note that those parameters given in curly parentheses are optional and may be omitted vvhile those given in square parentheses 1 are required even if only equal to zero If a directive is always required even though the rest of the line is blank this is indicated A required space is indicated by the character TITL always needed Any 72 alphanumeric characters A second Title line is expected if a star appears as the last character of the first TITL line usually col 77 Although concisely use the TITL line to write the contents of the input file This whole piece of information can be retrieved when making a choice of the dataset in a CACAO session thus allowing you to remember the details of a particular calculation This becomes important after the generation of many datasets since the memonics associated to a DOS filename are insufficient only 8 characters Notice in addition that only the initial 32 characters of the title are reported as the heade
20. agram or 3D drawings By manipulating the EHC output file NAME OUT selected magnitudes can be extracted e g Total Energies and passed to specific applications to generate two dimensional surfaces INTZM at n1 symb at n2 dist at n3 alpha at n4 tau ngroup tor2 Definition of internal coordinates of atom at n1 according to the full Z Matrix notation The required definition of the three vectors implies a reference to three general atoms which have already been defined Notice that the INT directive implies in which any atom e g at n2 has two fixed generators at n3 and at n4 respectively The structure of this directive is common 30 to other quantomechanical programs and can be exported to construct their inputs e g Gaussian AT N1 number of the atom being currently defined A4 in Figure 1 SYMB same as in the INT lines AT N2 number of a previously defined atom A3 in Figure 1 that is taken as the generator of AT N DIST Length in A of the vector AT N 1 AT N AT N3 number of any previously defined atom A2 in Figure 1 necessary to define the angle alpha see below ALPHA Bond angle defined by the vectors AT N3 AT N2 and AT N2 AT N1 AT N4 number of any previously defined atom A1 in Figure 1 necessary to define the torsion angle tau see belovv TAU Torsion angle defined by the three vectors AT N1 AT N2 AT N2 AT N3 and AT N3 AT N4 NGROUP same as in
21. an coordinates For cartesian coordinates a b c 1 alpha beta gamma 90 The latter may not be explicitated thus a line with the single keyword CELL implies the specification of Cartesian coordinates 27 ATOM nat symb x y z required SYMB Atomic Symbol In general the details specified below for the ORIG directive do apply However in this case the symbol of one or two characters can be followed without any interrupting blank by the atom number in order to allow the transfer of the data from any existing crystallographic dataset If SYMBz a card defining the STOs Slater Type Orbitals for the given atom must follow the whole series of the Internal Coordinates Otherwise the predefined STOs in the file PARAM DAT are used X Y Z Cartesian or Crystallographic Coordinates Tips if crystallographic coordinates are used the molecule is translated with the center of mass in the origin SYMB may also follow the x y z coordinates kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk If CELL and ATOM directives have been used skip the next series of cards kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Internal Coordinates ORIG symb fx y z ngroup required SYMB Symbol of the atom in the origin This may be a Real or Dummy atom DU If SYMB a card defining the STOs Slater Type Orbital for the given atom m
22. and internal coordinates ATOM INT or INTZM directives is allowed Added flexibility in the construction of the input file is provided by the Constants and Free Variables lines The constants CONST allow to define only once some repetitive parameters The Free Variables FVn necessary to construct Walsh Diagrams are more flexible than before The complete series of variables can be defined with the starting value and its increment or it can be the result of an expression which depends on other free variables and which is evaluated at the run time Some modified algorithms speed up the ehmo calculations and even very large molecules depending on the amount of memory available the present version can now process molecules with up to 400 atoms and 3500 orbitals can be analyzed fast enough with pentium processors The second part of the package program CACAO permits the visual analysis of the ehmo results The improved quality of the graphic window is evidentiated by menus which simplify the different operations and the switching among Walsh Diagram Interaction Diagrams and 3D drawings of the MOs Concerning the latter the best view is now easily fixed by interactive molecular rotations Through the menu most structural information may be retrieved as well as all of the quantities generated by the ehmo calculation including the Mulliken analysis Important parts of the latter can be now analyzed via new graphic capabilities such as the pl
23. anner the program builds up the necessary information to make a WALSH diagram later drawn by CACAO Otherwise it is possible to specify in the INPUT file two fragments in which the molecule is ideally separated so that the program can perform a Fragment Orbital Analysis FMO This means that separate MO calculations are performed for the molecule itself and for the single fragments Eventually information is obtained about the contribution of the fragment molecular orbitals FMO basis set to the main MOs themselves The information can be used later by CACAO to construct an Interaction diagram between the sets of FMOs This type of analysis is very powerful to focus on the formation of specific chemical bond s within the molecule Notice that although the EHC allows the definition of more than two fragments and it calculates the composition of the MOs in terms of these multiple basis sets the graphic routines of CACAO work only when two fragments are selected 2 Program CACAO Computer Aided Composition of Atomic Orbitals The program is interactive and reads the information in the files NAME COR cartesian coordinates ascil and NAME BIN binary created by previous EHC runs Multiple Dataset can be processed at one time The program can produce the follovving graphics a Walsh diagrams or Interaction diagrams b three dimensional drawings of several MOs for one molecular geometry c One MO at different geometries i e at diffe
24. couple of atoms could be selected even at non bonding distance if interested in particular weak interaction The diagram reports a partial list of the selected bonds 1 the number of averaged bonds 2 the averaged value of the Reduced Overlap Population for the same bond s for the given occupation 3 The ROP value is also proportional to the lenght of the integral at the HOMO see figure The diagram is divided in two parts On the left the values of MOOP are displayed with the scale at the bottom starting from the central 0 line On the left of the line are the red antibonding contribution and on the right the green bonding ones to each MOs The right part report the integral value of the MOOP IMOOP defined IMOOP MO n MOOP MO n IMOOP MO n 1 or in a more general way with LOMO Lowest Occupied MO IMOOP MO n gt MOOP MO i LOMO It follows immediately that for neHOMO IMOOP HOMO ROP Because the IMOOP grows faster than MOOP the scale of IMOOP is half than for MOOP but the user can also fix the scale as option to be able to compare with different plots for different bonds Incidentally after a FMO calculation a special MOOP diagram can be constructed which allows to evaluate how much each MO contributes to build up the total overlap population between the two fragments For people familiar with solid state calculation the MOOP diagram is equivalent to the COOP plots with integral 2
25. ct of the different atomic STO parameters on the MOs In the FVn directive all of the IPOINT values can be explicitly provided or as an alternative only the initial value is reported followed by the keyword Step or simply the character S and by the actual increment Finally the different values can be calculated at the run time by an explicit expression to which the same rules outlined in the directive CONST apply must be preceeded by the sign In this case the expression depends on previously defined Free Variables as well as on predefined constants In the FVn lines if n is negative e g FV 2 the corresponding free variable is varied independently from all of the others This is an useful way of constructing bidimensional surfaces of the order IPOINTxIPOINT read the section relative to CACAO in order to learn how to exploit this information TIP if one set of free variables remains constant from a certain point on use the alphabetic character s following the first group of values namely the increment after the last specified value is 0 E g FV8 110 0 100 0 90 0 s the angular parameter referenced as Free Variable 8 remains constantly equal to 90 0 from the third up to the last step IPOINT KEYW keyword 1 optional used to control the output of the matrices in EHC calculations Choose one or more of the following two character words in any order Di distances WF wavefunctions OV overlap matrix OP over
26. d antibonding MOs Since the pairs of the FMOs which are involved in significant direct interactions are shown at the right side of the Interaction Diagram itself CACAO does greatly simplify the exploration of the chemical bonding in the Molecule Also the atomic coordinates the geometric information the reduced overlap population ROP between two atoms etc can be retrieved under the Menu 3 If the current dataset is relative to a Walsh Diagram one can select the step of interest by entering the corresponding number as a negative value and make all of the possible inquires about it Moreover useful tables relative to the variations of a given magnitude for all of the steps e g ROP or atomic 15 charge are automatically generated by entering one tvvo or three atom numbers separated by commas At any moment the user can svvitch back to the drawings to investigate additional features hence he can move again to the retrieval of associated numeric quantities The above procedure can be repeated for different datasets as well as it is possible to switch between many Interaction Walsh and MO drawings Recall that the files opened at any moment are those relative to the picture on the screen This means that the subsequent new pictures or numerical quantities to be recalled refer to that particular dataset Any previously drawn picture can be recalled by its number made negative e g 3 recalls the third drawing If the picture in questi
27. e pathway can be easily examined and buttons 37 6 PSTOOL IN Piano Stool Complex This example illustrate the usage of PREDEFINED groups 4 carbon monoxide CM and 1 cyclopentadienyl CP Also the possibility of changing the atoms parameters with respect to the standard ones contained in the File PARAM DAT is pointed out In this case the atomic symbol Mo is replaced by a in the corresponding Internal Coordinate Definition line INT This means that a STO line is expected TITL piano stool PAR 1 DIST KEYW EL CM RO NC ORIG 0 0 INT CM 1 2 2 0 70 0 INT CM 1 4 2 0 70 90 INT CM 1 6 2 0 70 180 INT CM 1 8 2 0 70 270 INT Cp 1 10 1 8 180 0 90 STO MO 6 5 1 96 8 34 5 1 92 5 24 4 4 54 10 5 6097 1 9 6097 END 7 NIOLEF IN Nickel bis phosphine ethylene A study of the rotation of ethylene to check the presence of an energy barrier The example again exploits the rotation of a rigid body or GROUP Notice the definitions of the phosphines as predefined groups a single line TITL Nickel bisphosphine ethylene PAR ODIST 4 FV1 0 1 30 60 89 9 KEYVV EL CM NC RO ORIG NI 0 0 0 INT fo 12 2 2 90 130 INT fo 16 2 2 90 230 INT DU 1 1 1 7 90 0 INT C 1 10 7 90 270 1 INT C 111 7 90 90 1 INT H 10112 1 01 120 90 1 INT H 10 13 1 01 120 270 1 INT H11 14 1 01 120 90 1 INT H 11 15 GR 1 1 1 fv END 01 120 270 1 1 10 38 9 NAPHT IN 1 8 naphthyridine The
28. eated as well Strike either the P or the S option for printing that appears in the line at the bottom of each drawing Printing is performed by the routines PRINTGL located in the directory PRINTGL at the same level as MOAN PRINTGL is shareware which can be redistributed in its original form please contact the PRINTGL distributors to fulfill their requirements A command file PL BAT resident in MOAN is the interface between CACAO and PRINTGL PL is automatically activated during an interactive CACAO session as indicated above The commands in the PL BAT file can be modified for usage with specific printers follow the instructions in the PRINTGL package The drawings produced by CACAO can be also printed or reused in other applications wordprocessor Coreldraw etc after the end of the interactive session In fact the relative HPGL files namely CACAOx HGL and or MOANx HGL or PLUTO HGL stay in the directory MOAN till the next CACAO session 4 Complete the reading of this document and learn to make new INPUT files by using your favoured EDITOR Store the nevv file in a nevv subdirectory of MOAN e g MYDIR with the extension IN e g NAME IN Then try a calculation After the ehmo calculation has been completed there are in MYDIR two new files NAME COR and NAME BIN respectively The former contains the generated cartesian coordinates and the latter all the numerical information needed to run CACAO MAIN FEATURES OF THE PACKAGE
29. ecial RCM diagram with column A and B defined as the RCM contribution of the two fragments In this case the third column is empty because column A and B selected already all the atoms For a Walsh case the user must provide the step to be analyze After that the user is asked to input the number corresponding to the atoms contributing to the two columns If only one atom is selected for column A and or B the RCM line is multicolored to shows the single AOs contributions to each MOs the colour code for each AO is on the plot 1 in figure below For people familiar with solid state calculation the RCM diagram is parallel to the projected Density Of State DOS 18 Nickel bisphosphine ethylene MO range 16 25 f s px py pz dx2 y2 dz2 dz dyz J Mlist of atoms selectedi t1 C11 residual contribution l 1661 7 RCM of C10 C11 RCM of residual atoms 7 B 100 A B 1 thick o gt 175 for HOMO 13 13 42 2268 unsplitted ai ce A ee 15 23 5a splitted percent za percent d i percent du MOs energy 19 The MOOP diagram displays the overlap population contribution to selected bonds interactions for each MOs vvithin a range of energy together vvith the integral value of the MOOP First the user select the interactions to be analyzed i e the one or more bond to be averaged in the MOOP plot bonds equivalent for symmetry should be averaged Any
30. ee Variable FV1 vvhich reduces the separation between two approaching C2H4 molecules The initial distance between the dummy in the origin and that at the C C midpoint 2 is 1 5A 3 0A between the two molecules At the last step the separation between the C HA molecules is 1 40 A and all of the four C C bonds are equivalent Namely the newly formed C C bonds have become equal to the C C bonds in the two separated ethylene molecules which remain constant all of the times Although this may seem somewhat unrealistic it is a good idea with EHMO calculations to mantain bond distances as fixed as possible along a given pathway The variation of the Reduced Overlap population when the relative interatomic distance remains fixed is a good indicator whether the bond itself wants to be elongated or not This is a valuable chemical information that would be biased and misinterpreted if the bond itself is forced to vary This example illustrates another useful feature namely the Group rotation and or translation by using a GR card Along the pathway the four CH2 planes reorient themselves relative to the original C C bonds up to 45 Actually any group is rotated about an axis passing through the carbon atom and perpendicular to the C4 plane the dummy atom 4 is defined to the purpose The free variable FV2 determines step by step the amount of pinning back of the four CH2 planes As soon as the EHC program starts option MOL the steps along th
31. egenarate or almost degenerate are artificially shifted downward to avoid overlap Optionally the downward shift of the levels is prevented so that a more realistic picture of the level distribution is shown although many details are lost In the Walsh diagram an option allows to revert the original order of the steps For example if the free variable for the generation of the diagram is the progressive elongation of a certain bond from the left to the right it may be possible to interpret the diagram in terms of the formation of the same bond from two separate fragments The inversion of the steps is trivial but it result conceptually cleaner The total energy is optionally plotted in the Walsh diagram as a dashed red line One can choose whether to report the latter on an absolute scale 1div 1eV or on a relative scale In the latter case default the intervals on the ordinate which are meant to represent the energy scale of the single MOs in eV units are used as a reference for the total energy However each divison now corresponds to an amount of energy that is reported in the legend at the bottom together with the minimum and maximum total energies In the Walsh Diagrams the filled levels are green while the empty ones are yellow Singly populated levels have also a different color As new nice 16 feature vvhen the electron population changes along the pathvvay so it does the colour of the corresponding MO This may happen
32. en MO as in the Hoffmann type sketches the AOs are artificially contracted by a factor of 1 5 default Usually the contraction avoids the overlap between in phase atomic orbitals of adjacent atoms With very diffuse orbitals a larger contraction coefficient should be selected to reach this goal Otherwise to visualize the real MOs and not their artifacts the user restores the contraction coefficient to its natural value of 1 To improve the quality of a drawing at expenses of computing time adjust the finess of the grid The grid finess code ranges between 1 and 9 the latter corresponding to the coarsest grid DEF code 6 The code is accompanied by a key letter which specifies the drawing mode i e the spatial relation between the viewer and the molecule as well as the density of the countour lines The valid key letters are suggested by the program for example the letter X allows to draw only the MO envelopes and it is the fastest way to obtain a draft of the MO drawing In order to speed up the drawing of the given MO select only the atoms whose atomic orbital contributions has to be highlighted Thus the Atom Selection Code is assigned to a given atom only if its atomic orbitals provide a significant contribution to the MO coefficients gt gt 0 or if such contribution is to be evidentiated The codes 1 or 2 neglect any possible contribution of the given atom in constructing the MO drawing for example the atom is not very
33. enzene eta 6 PH phenyl eta 1 In all of these cases the number of the being defined AT N refers to the first real atom of the fragment Be sure to account for the total atoms of the fragment when defining the atom that immediatly follows the predefined fragment For example after the definition of a CP group that follows atom N the number of atoms is increased by 10 so the next atom is numbered N 10 1 see the sample file PSTOOL IN The character must be appended to SYMB if the atom in question is to be excluded by the automatic expansion of the molecule imposed by the presence of the directive SYMM e g P AT N 1 number of a previously defined atom A3 in Figure 1 that is taken as the generator of AT N AT N number of the atom being currently defined A4 in Figure 1 Each atom with progressive number N2 is defined starting from a previously defined atom N1 In the simplified Z Matrix the program must refer to the atom from which N1 was generated say N3 and also to that generating N3 see Figure 1 and the relative comments In order to define the first atom departing from that in the origin the unit vector Z of a right handed cartesian system must be referred to as the immediately preceeding vector Moreover as the second vector needed for the definition of the definition of the dihedral angle the unit vector X is used see the Figures at p 6 The number of the atom is a part of its labelling a
34. ether vvith additional next cards no FMO analysis is performed if STEP 0 In this manner the required manipulation of the INPUT files in passing from Walsh to Interaction Diagrams and viceversa is minimum FKEYW keywords 1 optional These keyword help to select the output of the FMO calculation Choose one at least or more of the following two character words in any order Di distances MW wavefunctions AO basis set FW Fragment wavefunctions AO basis set WF wavefunctions FMO basis set OV overlap matrix between atomic orbitals TO transformed overlap between FMOs OP overlap population between FMOs CM charge matrix EL energy levels RO reduced overlap matrix for fragments RC Reduced Charge Matrix HM Huckel Matrix EM Energy Matrix RE Reduced energy Matrix EP Energy Partitioning RP Reduced Energy Partitioning If this FKEYW line is not present the output is limited to the overlap population and reduced overlap matrices for fragments The Fragment Charges and the FMO occupations are ALWAYS typed Inportant Tip the calculated Molecular Charge which is the last piece of information printed by the FMO part of EHC must be equal to the charge value CHA provided by the user in the directive PAR card The calculation is most likely WRONG if such a match is not observed Please recheck the geometry of the molecule in the input file and if the problem persists notify it to the authors including a copy of your inp
35. fv n ipoint optional or fv n 1 Step increment or expression Definition of the free variables allow to construct a Walsh Diagram mono dimensional array or prepare data for drawing three dimensional surfaces In this case use other packages such as MatLab after a reorganization of the data performed interactively with CACAO For constructing surfaces the free variables are distinguished by plus or minus numbers e g FV1 FV 2 FV3 FV 4 indicate that the variables 1 and 3 are to be varied asynchronously with respect to 2 and 4 As indicated the syntax for these directives has three different modes In the first one all of the values aassumed from the variable n up to the final point ipoint is specifcally written down IN the second mode the user specifies the initial value the keyword STEP or S and the increment Finally the user can write an expression depending on constants and on previously defined variables Any FVn line max 20 fixes the actual value assumed by the n variable at each one of the IPOINTs specified in the PAR directive FVn can be referenced in any INT or INTZM or GROUP directives where symbolically it represents a geometric magnitude distance angle 25 torsion group rotation or translation As a special case FVn can appear also in a STO directive to represent an atomic parameter orbital coefficient or Hi In this manner a special Walsh Diagram be constructed to follovv the effe
36. g the next example relative to the ideal complex PtL3 Etylene 11 Z A H 4 H ce c 2 H 7 H 5 0 L 9 X bs L 10 Figure 2 The first atom Pt 1 in the input file defines the origin and it is fixed by providing its cartesian x y and z coordinates line 1 in the box below Notice that the origin can be a dummy atom in some cases The first two atoms departing from the origin require the usage of two predefined vectors to make explicit the alpha and tau angles lines 2 3 These directions are the cartesian Z pointing toward negative Z values arrow a in the Figure2 and the X axes arrow b in the order For example if we choose an angle alpha of 180 the dummy atom DU 1 is on the Z axis in positive direction and the torsion angle is undefined 0 Now we define C 2 by fixing the angle M DU C at 90 This is not sufficient as also a torsion angle tau is needed C 2 lies in the X Z plane for both the tau values of 0 and 180 If C 2 has to eclipse the X direction the the torsion angle is 0 closed book Obviously the second carbon atom C 3 on the opposite side with respect to C 2 has tau 180 open book The hydrogen atoms linked to C 2 are defined by the three previously defined atoms e C 2 DU and M in descending order The user does not have to waist much time in defininig the tau angles for H 4 and H 5 as if one is 90 the other must be 90 o
37. he programs have been fully tested with DOS versions 6 x and full screen DOS shells of Windows 95 98 NT 1 Install the package see message txt The location of the executables is in the directory MOAN acronym for MO ANalysis The input files and the results of ehmo calculations must be in subdirectories of MOAN Another directory PRINTGL containing the printing routines must be at the same level as MOAN The subdirectory FILES MOAN FILES is provided with some test input files extension IN 2 The programs can be run by either a DOS shell or by clicking in the WINCACAO icon under Windows In the latter case the basic operations are menu driven as an option your favorite ascii editor can be selected default notepad From the DOSshell the command file EH BAT controls both the EHC and CACAO programs by concatenating the operations From the box opened on clicking on WINCACAO browse the directory moan files and select the file N2 IN Than click on the CALCULATE button to run EHC with MOL set At the end click on the button CACAO to construct an Interaction Diagram for the nitrogen molecule Alternatively the File CO2 IN can be selected and used to construct a Walsh Diagram relative to the bending of carbon dioxide In this way the user can familiarize with most of the options offered by the package 3 Each drawing appearing on the screen can be printed on a Laserjet or on a Postscript Printer a postscript file can be cr
38. he subsequent atoms belonging to the same species being referenced to by the same symbol SYMB which appears in the STO line The following magnitueds must be given in the order SYMB NE NS EXPS Hss NP EXPP Hpp ND Hdd EXPD1 C1 EXPD2 C2 where SYMB atomic symbol NE number of valence electrons in the neutral atom NS NP ND quantum numbers for s p d orbitals EXPS EXPP exponents for s and p orbitals EXPD1 EXPD2 C1 and C2 coefficients for the double expansion of d orbitals Hss Hpp Hdd Values of the valence orbital ionization energy for s p d orbitals kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk following directives are used only for Fragment Orbital Analysis kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk FMO step required The presence of the keyvvord FMO forces the program to perform Fragment Orbital Analysis STEP optional The step number at which the Fragment Orbital Analysis is performed if a multiple set of geometries has been defined by FREE Variables input file set to create a VValsh Diagram Warning STEP 0 supersedes the construction of the Walsh diagram even if IPOINT gt 1 in the PAR card Rather a FMO analysis is made only for the molecular model with the geometry fixed by the free variable s at 32 step STEP Interaction Diagram By contrast even if a FMO card is present tog
39. lap population matrix RO reduced overlap matrix CM charge matrix RC reduced charge matix EL energy levels NC net charges HM Htckel matrix DE density matrix BO bond order Tips If no line KEYW is present the output is limited to Energy levels Total Energy Reduced Overlap Net charges DI is disregarded if the keyword DIST is already specified in the PAR card OVDEL at orb 1 at orb 2 optional The user may set up to nine overlap matrix elements to zero thereby negating the interaction between these elements Pairs of negative numbers refer to atomic orbitals while pairs of positive numbers refer to atoms so all the overlap integrals between the two selected atoms will be zeroed E g OVDEL 23 34 2 3 26 The overlap between AO 23 and 34 and the overlaps between all the AO s Of atoms 2 and 3 will be zeroed To check the selection it is suggested that the overlap matrix keyword OV in KEYW card is also printed MOOP MO 1 MO 2 optional Used to control the range of Molecular Orbital Reduced Overlap Population matrices to be printed Only those M O O P matrices between the pairs given will be printed E g The command MOOP 23 34 41 55 causes the M O O P for levels from 23 to 34 and from 41 to 55 to be printed SYMM symbol of the molecule s pointgroup optional This directive allows to generate the entire molecule given the coordinates of the asymmetric part define
40. le is generated with extension ene Also the file name terminates with the characters s h or I for total energy homo or lumo respectively Otherwise with the number of the selected At this point you can run MATLAB From the menu open the file Matlab M in the directory moan and change opportunely the name of the file xxxx ene and save it Then select from the menu the option for running the matlab m command file The surface will appear You can modify the view point with the command view az el where az azimuth and el elevation In addition CACAO allows a real time visualization of the numerical quantities associated the Mulliken population analysys composition of the MOs in terms of Atomic or fragment Orbitals energies of the levels overlap populations charges etc The program allows visualization of the graphics of type a b c and d and the numerical information associated with them Easily the user can switch back and forth among different datasets During a single CACAO session diagrams and MO dravvings can be generated for all of the structures vvith avallable files of the type COR and BIN The results of many different calculations and their graphic representations can be then compared in real time Also hard copies of the graphs displayed on the screen can be produced at any moment laser or inkjet color printers by using the shareware package PRINTGL EHC detailed technical information
41. nates card required one per atom Second group internal coordinates ORIG Atom in the origin required as first INT Internal coordinates definition required may alternate with simplified Z Matrix with INTZM INTZM Internal coordinates definition required may alternate with complete Z Matrix with INT Third group optional GR Rigid group rotation or translation line optional STO Atomic parameters redefinition line optional referred to in ATOM ORIG INT or INTZM lines Fourth group optional follow the order FMO Request for a FMO calculation required as first FKEYW Fragment MO keyword card optional FRAG Fragment definition card required FCOMP Fragment composition card optional FDEF Fragment information card optional END End of calculation optional
42. nd is independent of the order with which the atoms are entered in the input file The number can be optionally negative allowed range from 99 to 999 It may be useful to refer to Dummy Atoms Symb DU with a negative number although it is not necessary The usege of the Dummies simplify the construction of the Molecule DIST Length in A of the vector AT N 1 AT N ALPHA Bond angle defined by the vectors AT N 2 AT N 1 and AT N 1 AT N If AT N 2 was never defined the vector AT N 2 AT N 1 is taken as the cartesian axis Z TAU Torsion angle defined by the vectors AT N 3 AT N 2 AT N 2 AT N 1 and AT N 1 AT N If AT N 3 and AT N 2 were never defined they are taken as the cartesian axes X and Z respectively 29 optional Number of the Group to which the atom N currently being defined belongs to A rigid group is formed by all the atoms for which NGROUP has the same value The group NGROUP h see GR card can be rotated and or translated thus making simpler the construction of VValsh Diagrams for given structural rearrangements By default all of the atoms belong to rigid group 0 i e the molecule is a rigid group itself TOR2 optional Rotation angle of a predefined Fragment about the axis leading to its pivotal atom e g the carbon atom of a methyl group or the center of a CP ring eta5 bonded dummy If TOR2 is defined also NGROUP must be given usually 0 Tips Any DIST ALPHA
43. ne a subgroup of a larger group For example it is possible to translate a whole group and then to rotate only one of its 31 substituent This is done by defining the NGROUP variable in directives 10 11 as n x 10 m where n is the number of the main group and m is that of the subgroup Tvvo GR for n and m must then follovv in the order If AT1 AT2 1 2 or 3 the rigid group is rotated translated about the X Y or Z principal axes respectively The same thing can be done by writing X Y or Z in place of the pairs AT1 AT2 namely 1 1 or 2 2 or 3 3 What already specified in INT card for the synchronous or asynchronous variation of free variables holds in this case as well STO symb ne ns exps hss np expp hpp nd hdd expd1 c1 expd2 211 optional one STO line is required for any atomic symbol SYMB given as in any of the previous ORIG INT or INTZM lines The purpose is to redefine the Slater Type Orbitals STO and the valence orbital ionization energies Hj used in the calculations Standard parameters are either defined in the program or read from the file PARAM DAT and in general there is no need for a STO directive For a given atomic species to be redefined only one STO line is expected This must be referenced to by an appearing in a line of the type INT INTZM ATOM etc Concerning the sequence of the latter the must be supplied only for the first atom of the given type all of t
44. ns the basic structure vvith the programs EHC for extended H ckel calculations and CACAO for graphic analysis The programs written for DOS are now operated under the VVindovvs95 98 systems through the usage of an handy graphic interface The basic idea behind CACAO is to run MO calculations and to examine the results visually and intuitively via the uasge of different graphs including 3D drawings of the Molecular Orbitals Thus the examination of long numerical outputs is not strictly necessary although these are easily produced In any event the important numbers can be retrieved interactively during the visual analysis of the graphs Generation of input files is greatly simplified with free format directives characterized by keywords and the data to be provided by the user are minimal The ehmo method is still one of the simplest ways to determine the symmetry properties of the Molecular Orbitals full of chemical information Accordingly much care is taken to permit the construction of models with the highest possible symmetry As a very helpful tool any generated molecule trial input file appears in a graphic window run EHC with the option MOL The molecular animation and the easy analysis of the geometrical parameters allow the user to establish the correctness of the model On line help allows to understand easily the meaning of each single operation One strategy is to return immediately to the ascii editor and make the opp
45. nternal coordinate alpha angle Obviously it is necessary to refer to the atom number 2 A2 from which A was generated Finally the third internal coordinate torsion angle tau is given by the torsion angle defined by four atoms A j Az A3 A4 Aq generator of This is also the dihedral angle defined by two planes namely i the plane A2 A3 A4 formed by the vector being defined and the immediately preceeding one A2 Aa ii the plane formed by the vectors Az A3 and A4 A2 whose atoms have been previously defined 10 n the simplified Z Matrix INT directive shovvn belovv it is assumed that the order of the four atoms is sequential In other words the pathway that allows to define A is fixed and it goes through the previous atoms A4 Az and INT SYMB AT N 1 AT N DIST ALPHA TAU A 3 4 d1 a T By choosing a full Z Matrix the sequentiality of the four atoms is not required Thus one needs to specify each time in a INTZM directive shovvn belovv the numbers of any four atoms Aq A and with the first three however defined INTZM AT N SYMB AT N 1 DIST AT N 2 ALPHA AT N 3 TAU 4 A 3 d1 2 a 1 1 Notice that the orders of the parameters in the INTZM card is consistent with that of other quantomechanical programs In preparing the INPUT for EHC the INT or INTZM directives may be mixed at will The sign of torsion angle tau depends on the movement needed to bring the vector
46. on belongs to a different dataset the corresponding files are reopened so it is possible to do more work with it When building an Interaction or Walsh Diagram the user can select the width of the energy window This can be varied at will in order to focous on a selected group of MOs usually the Frontier ones that carry relevant chemical information Essentially the user supplies the length of the Y axis in eV Optionally he can also select the levels to be plotted based on their symmetry class or more simply on their progressive numbering In the Interaction diagrams a threshold for the minimum FMO contribution to a given MO is provided In this manner the connection lines between MOs and FMOs can be limited in number Also the connecting lines appear with different colours each colour corresponding to a different percent group as an indication the legend at the top of the diagram prompts that a green line corresponds to a maximum of 50 contribution of the FMO to the connected MO In this manner one gains a quick idea of the composition of a certain MO withouth looking at the actual numbers The latter can be anyway retrieved through the Mulliken population analysis option 3 of the menu The legend at the right side of the interaction diagram reports the number and the proper symmetry labels of the each MO and FMO A little segment shows their actual energy position Notice that in the main diagram itself the levels which are d
47. only the limited necessary INT or INTZM directives If some information is redundant symmetry related atoms are defined with different INT or INTZM lines the program realizes this and discard the equal atoms The pointgroup Cs indicates mirror symmetry about the plane xy Specify Csx or Csy for mirror planes coinciding with either xz or yz For pointgroups with only o planes e g D3h or D5h impose one of them coinciding vvith the plane yz For pointgroups vvith oq planes e g D3d impose one of them coinciding with the plane xz Don t forget these constraints when constructing the molecule If the great part of the molecule are symmetry related by a given symmetry but a few atoms do not comply with the pointgroup it is still possible to generating the symmetric part of the molecule by using the SYMM directive The atoms for which not all of the given symmetry operations apply must defined singularly with the opportune INT or INTZM directives In the latter it is necessary to append the character to the symbol of the atom KERR kk k ER ER ER EKER EKER ER ER ER ER ER ER RR ER ERE ER ER ERER EERE kk kk kk ai skip the following CELL and ATOM cards if INTERNAL COORDINATES are used kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Crystallographic or Cartesian Coordinates CELL a b c alpha beta gamma required Lattice parameters to be used only with crystallographic or cartesi
48. ortune modifications to the input file trial and error proceeding The alternative strategy is to access the graphic Molecular Editor which allows to delete or add atoms replace substituents etc While editing the molecule an algorithm allows to adapt the nearest symmetry pointgroup Simmol routines in order to exploit the ehmo method at the best In the input file the whole molecule can be constructed by defining only its asymmetric portion and by specifying the point group symmetry see the directive SYMM The atoms generated with a minimum number of internal coordinates are then expanded by the symmetry elements of the pointgroup please remember that the main symmetry axis of the molecule must coincide with the cartesian Z axis To have a better picture of the structure and an hardcopy always handy the program PLUTO Cambridge 1988 can be launched from EHC or CACAO while the molecule appears in the screen same orientation Also crystallographic coordinates can be used as input and in particular the program can process a Cambridge Structural Database coordinate file In this case the Molecular Editor is automatically accessed and the experimental molecule can be manipulated to obtain the best model based on it Thus the orientation consistent with the highest possible symmetry is selected Simmol routines bulky substituents can be discarded and replaced with new atoms defined through internal coordinates Mixed usage of cartesian
49. ot of the Reduce Charge Matrix RCM and that of the Molecular Orbital Overlap Popolation MOOP The RCM diagram permits an overview of the percentage contribution of a group of atoms one or more to a number of MOs within a given energy range additionally the contribution of the remaining atoms is also plotted The MOOP diagram allows to evaluate visually how much each MO contributes to the overall overlap population between two selected atoms Again more MOs can be selected vvithin a given energy range Incidentally after a FMO calculation a special MOOP diagram can be constructed which allows to evaluate how much each MO contributes to build up the total overlap population between the two fragments A new feature allows to construct 3D surfaces of the Total energy as well as of any chosen MO Two independent groups of variables which map the nxn grid can be defined with the simple logic of the Free Variables When CACAO processes a file containing the data relative to the bidimensional grid it produces on request suitable ascii datafiles to be exported to other packages such as Matlab As in the previous CACAO versions the results of many different calculations can be graphically analyzed in a single interactive session Each single drawing appearing on the PC screen can be printed with a keystroke laserjet or postscript printers without exiting the program GETTING STARTED WARNING The programs require at least 486 Hardware T
50. r 270 ORIG 0 0 0 Pt ORIGIN M 1 INT 1 1 DU 2 0 180 0 dummy atom INT 1 2 C 0 66 90 0 C 2 INT 1 3 C 0 66 90 180 C 3 INT 24 270 H 4 INT 2 5 INT 3 6 l INT 3 7 5270 INT 1 8 7 90 180 L 8 L 9 L 10 More examples at the end of this document will help to clarify the strategy followed case by case 12 By specifying the internal coordinates the user determines the orientation of the molecule with respect to the cartesian basis set X Y Z The main symmetry axis twofold threefold etc must coincide with the cartesian Z axis Specific routines in EHC allow the determination of the symmetry pointgroup from the analysis of the atomic coordinates After the calculation of the MOs and their energies each MO is assigned the appropriate symmetry label Failures are still possible for a restricted number of pointgroups For example the program does not recognize the highest symmetries such as k or Th while in Tg and pointgroups not all of the classes are properly assigned to the levels Moreover the symmetry is properly recognized only if the molecule is centered on the origin of the cartesian system with a canonical orientation of the axes the same as that in the Character Tables for Symmetry Groups in Chemical Applications of Group Theory by F A Cotton Warning in the FMO calculations the fragments are not searched for the highest symmetry no molecular riorentation is made Consequently
51. r of the graph reporting either an Interaction or a Walsh Diagrams REM optional Any 72 alphanumeric characters This keyword allows to insert a line of remarks in any place of the INPUT file It is completely ignored by the program IMP optional filetype path Import coordinates from a given file filetype can be CSD cambridge PAR optional cha key ipoint fH ckel Constant 23 Default values if PAR is omitted Charge 0 key set for no output of distances ipoint 1 H ckel constant 1 75 CHA Molecular Charge KEY for distances The alphanumeric keyword d or dist determines the initial output of the generated cartesian coordinates from the internal ones and all of the interatomic separations Matrix of Distances If omitted no distance matrix is generated IPOINT Number of steps to be sequentially calculated in order to produce in CACAO a Walsh Diagram Sets of Free Variables must be supplied in FVn lines see below Each FVn line contains a set of IPOINT values which vary dependently or independently from the others at each different step If IPOINT is 0 or not specified IPOINT is set 1 CON H ckel Constant with default value 1 75 optional POP popul pop 1 pop 2 pop norb optional The directive POP allows to fix the electron occupation of the MO levels If the directive is not present the MO occupation is automatically determined i e all of the valence electrons
52. rent values of the reaction coordinate in a Walsh Diagram d One MO with its FMO components if the option for Fragment Orbital Analysis FMO is activated If two sets of independent variables FVn and Fv m have been selected in the previous EHC calculation CACAO prepares an ascii file NAME ENE which contains data for plotting a surface of the total energies This file can be processed by typical commercial programs such as MATLAB a command file MATLAB M can be found in the directory Moan Also in this case the user may select one row or one column or one diagonal of the square surface of dimension IPOINTxIPOINT in order to analyze the data in the usual manner Walsh Diagrams 3D MO drawings etc Hints on the preparation of the data for MATLAB and its usage Generate the grid of points by properly selecting the free variable Fvn and Fv m and by running EHC At the end run Cacao The graphic capabilities of the latter are not immediately available as usual Thus you are asked whether you want to generate a surface of total energy or of the energies of a given MO or to select any row column or diagonal of the bidimensional grid in order to visualize a monodimensional dataset as usual In this latter case you will be presented the list of available datasets which contains one or more new files corresponding to the selected colums rows or diagonal Select any of them by number and proceed as usual If a grid has been chosen a new fi
53. rogen with FMO analysis Notice the definition of a Dummy Atom 1 in the origin cartesian coordinates 0 0 0 The parameters are separated either by spaces or commas TITL nitrogen molecule Interaction Diagram PAR 0 DIST KEYW EL WF CM OV OP RO NC ORIG DU INT N 1 1 0 564 180 INT N 12 0 5640 FMO FRAG 2 1 END 2 O2 IN Molecular oxygen with FMO analysis for a high spin molecule The unpairing of two electrons will be automatically determined by the program in view of the degeneracy of the highest occupied MOs Notice that all the keywords controlling the output directives KEYW and FKEYW have been omitted Only standard output will be obtained TITL molecular oxygen Automatic unpairing of two electrons INT 1 1 0 600 180 0 INTO 1 2 0 600 000 0 FMO 35 3 ETHYLEN IN The molecule of ethylene is built up and its MOs are analyzed in terms of the interactions betvveen the MOs of tvvo methylene fragments The FCOMP card is used to redefine the order of the atoms in the tvvo fragments as the atoms of the first fragment are C1 H3 H4 and those of the second one C2 H5 H6 In the FCOMP directive only the atoms of the first fragment could be reported automatically the program would reassign the other atoms to the second fragment TITL ETHYLEN Analysis of the interactions between two CH2 groups PAR 0 DIST SYMM D2h ORIG DU INT 1 1 C 0 70 0 0 INT 1 2 H 1 120 180 FMO FRAG 23 END
54. s the need for printing the output unless some specific magnitudes need to be analyzed e g Overlap integrals H ckel matrix etc 14 CACAO technical information More than one set of calculations can be analyzed during an interactive session of CACAO At the start all of the available datasets in the working directory can be listed and selected by their corresponding number Later the list can be reexamined by quitting the present selection key Q in the menu line and subsequently by asking for a new Dataset key D Once the graphics have been constructed it is possible to jump back and forth between them although relative to different models and calculations In this manner the features are compared visually In general the user is driven by the questions appearing in the menus which are in the simplest form e g Yes or No Y N a numeric code 1 2 etc or a key Z G etc Most of the times it is sufficient to type return CR to select the default option DEF Basically one can construct four types of different diagrams Interaction Walsh Reduce Charge MOOP or 3D drawings of the MOs and switch them at will For example the user selects one MO by looking at an Interaction diagram then he can examine the level and also its FMO components Given a Walsh Diagram the user may follow the evolution of the MO along the pathway and try to understand from the variation of the shape bonding antibonding character why
55. significant for the chemical analysis as it may be the case for the inner parts of a bulky ligand in a transition metal complex Notice that the atoms whose orbital contribution is neglected can be optionally represented in the structural skeleton Code 2 Show only the atom Finally the Selection Code 1 cancels from the drawing any presence of the atom in question To speed up the procedure for the assignment of the codes hence the input operations an unique code can be applied to a certain group of atoms The atom range runs from the current atom to the one higher atom specified by the user The range 17 is homogeneus thus it includes only the the atoms in the lists which are of same type as the current atom When defining the range the letter A all specified in place of the upper atom number means that the given Selection Code 0 1 2 applies to all of the atoms of that type If some of the atoms are selected code 0 while some of those related by a symmetry element s planes or center are discarded codes 1 or 2 you may have a wrong MO picture Redraw the picture after a Symmetry Usage Redefinition the option becomes available in the very last question before the computations for drawing are started Discard the use of any symmetry available to the program by entering the string XXXX after you have asked for Symmetry Redefinition with the letter S normally at this point the letter P or CR is striken for continuing the job In
56. the level descends or rises in energy along the pathway The Reduced Charge Matrix RCM diagram permits to overview the percentage contribution of two different groups of atoms to all of the MOs within a given energy range additionally the contribution of the remaining atoms is plotted The MOOP diagram allows to evaluate visually how much each MO contributes to the overall overlap population between two selected atoms To have more quantitative information handy the user can ask interactively for the actual numbers generated by the Mulliken population analysis option 3 of the Menu At this point the composition of a given level is obtainable by typing the positive number of the MO in question The latter magnitude is accompanied by a sign which specifies the phase with which a certain atomic orbital contributes to the given MO Another possibility is to check all the MOs containing a particular atomic orbital e g enter 7 px in order to see how the px orbital of the atom number 7 is distributed among MOs If you are dealing with a dataset containg FMOs Interaction Diagram a negative number given at the MO request identifies the FMO characterized by the corresponding absolute number The FMO composition is hence presented If one enters two FMO numbers both with negative signs and separated by a comma the program identifies the MOs which receive contributions from both of them This is a quick way to individuate bonding an
57. ust follow the whole series of the Internal Coordinates Otherwise the predefined STOs in the file PARAM DAT are used The usage of SYMB supersedes the STOs stored in PARAM DAT The symbol applies only to the first atom of the species which is necessary to redefine and for which a STO line is expected All of the subsequent atoms of the same species must have the same symbol given in the STO line X Y Z optional Cartesian Coordinates of the atom in the origin if not present the origin is assumed to be at coordinates 0 0 0 NGROUP optional Number of the rigid Group to which the atom belongs see INT card for details Tip SYMB may also follow the x y z coordinates kkkkkkkkkkkkkkkkkkkkkkkkk WARNING The following INT INTZM and GR directives can be given in any order provided that the needed reference atoms have been defined in previous lines INT INTZM can be alternatively used to define an atom INT symb at n1 at n2 dist alpha tau ngroup tor2 28 Definition of internal coordinates according to a simplified Z Matrix which implies that three vectors are defined sequentially SYMB symbol of the atom Real or Dummy being currently defined What stated for the ORIG directive applies in this case too Special Symbols are used for Predefined Molecular Fragments At this moment the fragments predefined are CP cyclopentadienyl eta 5 ME methyl FO phosphine AMzamine CM carbon monoxide BZ b
58. ut file FRAG nfr nf 1 nf nfr 1 nc 1 nc nfr 1 needed for the FMO calculations NFR Number of Fragments Note NFR is usually 2 but it can be 3 or more If there are more than two fragments the calculations are run properly but the graphic capabilities of CACAO are not available only the printed output can be examined Please notice that only the number of atoms and the charge must be supplied only for the first NFR 1 fragments NF n Number of atoms in the n Fragment NC n Charge of the n fragment the values are superseded by those in the FDEF cards if any FCOMP 1 nat 1 nat 2 nat 3 optional Sequentially report in FCOMP the original numbers nat n of the atoms belonging to the first and second and third if any fragment respectively 33 If nat n is negative all of the atoms up to that number will be assigned to the current fragment If an atomic symbol is inserted in the directive all of the atoms of the given type will be assigned to the current fragment To simplify the input sequence only the atoms belonging to the first fragment need to be specified and all of the remaining atoms are automatically will be assigned to the second fragment Tips Use the directive only to change the original numbering scheme of the molecule and to select a particular composition of the fragments If FCOMP is not present the first NF1 atoms see FRAG from the main original list are assigned
59. when two frontier levels become almost degenerate so a change of ground state is also assumed However an option is provided for keeping the latter constant see below directive 2 In very complicate cases when the population of the frontier levels changes more than two times along the pathway an option is offered to plot all the levels as they were apparently empty yellow lines Up to 12 three dimensional drawings of the MOs can be shown at one time on the screen for better resolution it is better not to exceed the number of six drawings If dealing with a Walsh diagrams one can visualize more MOs at a given step or the same MO through different steps If dealing with an Interaction diagram one can visualize more MOs or one MO with its FMOs components Also one can ask to draw only a certain number of FMOs The MO drawings are automatically scaled on the screen whereas the scale for the hard copy HPGL file is defined by the user immediatly before the calculation starts The options are 1 1cm Amg 2 automatic rescaling to fit one printed page default 3 allows the introduction of a used defined scale The usage of the options 1 or 3 may cause the problem that the printing of all of the drawings on the screen may require more than one page On the other hand automatic rescaling over one page produces very large drawings even if the molecule is small e g N2 To mantain as much as possible the identity of the Atomic Orbitals in a giv

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