******************************************************************************* DESCRIPTION OF THE ARGONNE - OHIO STATE SYMMETRY-ADAPTED, GENERAL-CONTRACTION INTEGRAL PROGRAM (ARGOS) ******************************************************************************* PROCEDURE NAME: ARGOS DESCRIPTION: This program evaluates integrals over symmetry-adapted linear combinations of generally contracted gaussian atomic orbitals. In addition to energy-related integrals, overlap kinetic energy nuclear attraction effective core potential spin-orbit (core) electron repulsion it evaluates the property integrals: dipole moment linear momentum angular momentum second moment INPUT FILE: ARGOSIN PRINT OUTPUT FILE: ARGOSLS LABELED INTEGRAL FILES: AOINTS, AOINTS2 DOCUMENTATION: Russell M. Pitzer Department of Chemistry Internet: The Ohio State University pitzer.3@osu.edu 100 W. 18th Ave. Columbus, OH 43210 USA LAST REVISION: September, 2000 REFERENCES: Symmetry analysis (equal contributions), R. M. Pitzer, J. Chem. Phys. 58, 3111 (1973) AO integral evaluation (HONDO), M. Dupuis, J. Rys, & H. F. King, J. Chem. Phys. 65, 111 (1976) General contraction of gaussian atomic orbitals, R. C. Raffenetti, J. Chem. Phys. 58, 4452 (1973) Core potential AO integrals (MELDPS), L. E. McMurchie & E. R. Davidson, J. Comput. Phys. 44, 289 (1981) Spin-orbit and core potential integrals, R. M. Pitzer & N. W. Winter, Int. J. Quantum Chem. 40, 773 (1991) ******************************************************************************* EXPLANATION OF TERMS ******************************************************************************* ATOMIC ORBITALS (AOs) Cartesian gaussians of the form l m n 2 N X Y Z EXP(-ZETA*R ) where the AO normalization factor, N, is such that the integrals are normalized to (2l-1)!!(2m-1)!!(2n-1)!! and where !! denotes the odd number factorial. This leads to the same normalization factor, N, for all AOs with the same principal quantum number. PRINCIPAL QUANTUM NUMBER l+m+n+1 AO SETS AOs must be included in sets according to the value of the principal quantum number QUANTUM TYPE AO SET NUMBER 1 (1s) 1 AO 2 (2p) 3 AOs (X,Y,Z) 2 2 2 3 (3d) 6 AOs (X ,Y ,Z ,XY,XZ,YZ) 3 3 3 2 2 2 4 (4f) 10 AOs (X ,Y ,Z ,X Y,X Z,Y X, 2 2 2 Y Z,Z X,Z Y,XYZ) 4 4 4 3 3 3 5 (5g) 15 AOs (X ,Y ,Z ,X Y,X Z,Y X, 3 3 3 2 2 2 2 2 2 2 2 2 Y Z,Z X,Z Y,X Y ,X Z ,Y Z ,X YZ,Y XZ,Z XY) If some of the AOs in a set are not desired, they can be eliminated by omitting appropriate symmetry orbitals. SYMMETRY ORBITALS (SOs) Linear combinations of AOs that transform according to an irreducible representation. The current version of the program can only handle D2h and its subgroups. NUCLEAR INTERCHANGE GROUP Group that describes how the nuclei are transformed by symmetry operators. This will always be the same as, or a subgroup of, the point group of the molecule. For example, for H2O the group is of order 2 and can be considered to be either Cs or C2. For C2H4 the group is of order 4, while for F2 the group is of order 2. The group will be the same as the point group when there are no operators, other than the identity, whose effect on the nuclei is the same as that of the identity. AO REDUCTION SETS The irreducible representations that make up the representation formed by a given set of symmetry-related AOs. For CH2 with a (s,p,d/s,p) basis there are five AO reduction sets: C(s) - A1 C(p) - A1+B1+B2 C(d) - A1+A1+A1+A2+B1+B2 H(s) - A1+B2 H(p) - A1+A1+A2+B1+B2+B2 SO TRANSFORMATION MATRICES Transformation matrices that express the SOs in terms of a set of AOs. Each SO transformation matrix is indexed in data set 9 to an AO reduction set which defines the symmetries of the components. STANDARD SYMMETRY TABLE ARGOS requires that the first symmetry block be that of the totally symmetric irreducible representation, but the other symmetry blocks can be in any order (the symmetry multiplication table is specified by the user in data sets 4 and 5). The transformation, MCSCF, and CI programs require that the symmetry blocks be ordered in a manner consistent with a standard multiplication table: irrep * | 1 2 3 4 5 6 7 8 --|----------------------- 1 | 1 2 3 4 5 6 7 8 i 2 | 2 1 4 3 6 5 8 7 r 3 | 3 4 1 2 7 8 5 6 r 4 | 4 3 2 1 8 7 6 5 e 5 | 5 6 7 8 1 2 3 4 p 6 | 6 5 8 7 2 1 4 3 7 | 7 8 5 6 3 4 1 2 8 | 8 7 6 5 4 3 2 1 Consistent orderings include C2v: A1 A2 B1 B2 z x y Rz Ry Rx D2: A B1 B2 B3 z y x Rz Ry Rx D2h: Ag B1g B2g B3g Au B1u B2u B3u z y x Rz Ry Rx where the suggested transformation properties of the cartesian coordinates and of the components of angular momentum are indicated as well. These imply the orientation of the coordinate axes with respect to the symmetry elements. CIDBG, one of the spin-orbit CI programs, requires the above angular momentum transformation properties. ******************************************************************************* INPUT DATA ******************************************************************************* The input is list directed except where a FORMAT statement is given. It is recommended that a / be put at the end of each input record, as is done on line 2 and many other lines in the sample input data sets, in order to allow for future extensions. 1) TITLE(1) FORMAT(A80) 2) NGEN, NS, NAORDS, NCONS, NGCS, ITOL, ICUT, AOINTS, ONLY1E, INRM, NCRS, L1REC, L2REC, AOINT2, FSPLIT 3) NST, (ND(I), ITYP(I), I = 1, NST) FORMAT(I3,12(I3,A3)) 4) NDPT 5) DO I = 1, NDPT P1(I), P2(I), P3(I) ENDDO 6) DO I = 1, NAORDS NREP(I), (IREP(J), J = 1, NREP(I)) ENDDO 7) DO I = 1, NGCS ICSU(I), ICTU(I), IAORDS(I) DO J = 1, ICSU(I) (ISOCOEF(K,J), K = 1, ICTU(I)) ENDDO ENDDO 8) DO I = 1, NCONS ICONU(I), LMNP1(I), NRCR(I) DO J = 1, ICONU(I) ZET(J,I), (ETA(K,J,I), K = 1, NRCR(I)) ENDDO ENDDO 9) IF(NCRS .NE. 0) THEN DO ICRS = 1, NCRS LCRU, LLSU IF(LCRU .GE. 0) THEN DO L = 0, LCRU NBFCR DO K = 1, NBFCR NCR(K), ZCR(K), CCR(K) ENDDO ENDDO ENDIF IF(LLSU .GE. 1) THEN DO L = 1, LLSU NBFCR DO K = 1, NBFCR NCR(K), ZCR(K), CCR(K) ENDDO ENDDO ENDIF ENDDO ENDIF 10) DO IS = 1, NS MTYPE(IS), NF(IS), NC(IS), CHG(IS) FORMAT(A3,2I3,F3.0) DO J = 1, NC X(J), Y(J), Z(J) ENDDO IF(NC(IS) .NE. 1) THEN DO J = 1, NGEN (IGEN(K,J), K = 1, NC) ENDDO ENDIF DO J = 1, NF MCONS(J), IGCS(J) ENDDO IF(NCRS .NE. 0) THEN MCRS(IS) ENDIF ENDDO 11) DO I = 2, 4 TITLE(I) IF(TITLE(I) .EQ. ' ') EXIT ENDDO ******************************************************************************* EXPLANATION OF DATA ******************************************************************************* 1) TITLE This should include the name of the molecule and basis set and geometry information; it is used to label data sets used in all subsequent programs. 2) NGEN Number of symmetry operators (on nuclei) to be read in. Only the generators are required NS Number of symmetry-distinct types of atoms NAORDS Number of AO reduction sets. Usually there will be one AO reduction set for each class of function (s,p,d,...) on each symmetry-distinct atom. Other atoms can use the same AO reduction set. NCONS Number of sets of exponents and contraction coefficients to be read in. All of the contraction coefficients for a given set of primitives are contained in one set. For p,d,... functions, all components (x,y,z etc.) are in one set. NGCS Number of transformation matrices relating AOs to SOs to be read in. Usually this will be the same as the number of AO reduction sets. ITOL AO integrals with overlap exponential factors less than 10**(-ITOL) will be omitted. The default is 20. ICUT Both AO and SO integrals with values less than 10**(-ICUT) will be omitted. The default is 9. AOINTS Unit number for output integral file. The default is 4 and the default name is 'aoints'. ONLY1E 0 to compute both 1-e and 2-e integrals. 1 to compute only 1-e integrals (note that FSPLIT=2 is also required in this case; see below.) This is used for cases in which a set of 2-e integrals is associated with several sets of 1-e integrals. Examples include external fields, the use of point charges to simulate a changing environment, and the computation of basis set superposition errors. The default is 0. INRM Set to 1 for symmetry orbitals normalized with respect to one-center integrals. NCRS Number of distinct sets of expansions for core and spin-orbit potentials L1REC Maximum record length for 1-e integral records. The default value is 0, which invokes the ARGOS value of 4096. A value of -1 invokes the SIFS value. L2REC Maximum record length for 2-e integral records. The default value is 0, which invokes the ARGOS value of 4096. A value of -1 invokes the SIFS value. AOINT2 Unit number for the 2-e integral file. Accessed only if ONLY1E=0 and FSPLIT=2. The default unit is 8 and the default filename is 'aoints2'. FSPLIT File-split parameter. FSPLIT=1 forces both 1-e and 2-e integrals to be written to the same file, AOINTS. FSPLIT=2 causes the 2-e integrals to be written to the separate AOINT2 file. The default value is 2. 3) NST Number of irreducible representations ND(I) Degeneracy of the Ith irreducible representation (must be 1 in this version of the program) ITYP(I) Label for the Ith irreducible representation 4) NDPT Number of distinct products of irreducible representations to be read in. Do not include any products involving the totally symmetric irreducible representation. It is 0 for C1, C2, Cs, Ci; 1 for C2v, D2, C2h; 7 for D2h. If NDPT<0, then P1,P2,P3 values consistent with the standard 8x8 multiplication table are generated internally. 5) P1(I),P2(I),P3(I) Numbers corresponding to irreducible representations as defined in data set 3 such that P1 X P2 = P3. For C2v, D2, and C2h, these must be 2 3 4 (in any order). See example 1 for D2h. These records are read only if NDPT>0. 6) NREP(I) Number of irreducible representations in the Ith AO reduction set IREP(J) List of the irreducible representations in the Ith AO reduction set 7) ICSU(I) Number of SOs in the Ith set of SO coefficients ICTU(I) Number of AOs in the Ith set of SO coefficients IAORDS(I) Index of the AO reduction set corresponding to the Ith set of SO coefficients ISOCOEF(K,J) The coefficient of the Kth AO in the Jth SO of this set. The input values have the sign of the desired SO coefficient but the magnitude is equal to the square of the coefficient. This allows the coefficients for almost all point groups to be expressed in integer form. 8) ICONU(I) Number of primitives in the Ith contraction set LMNP1(I) Principal quantum number for the Ith contraction set (1 for 1s, 2 for 2p, 3 for 3d, etc.) NRCR(I) Number of contractions in the Ith contraction set ZET(J,I) Exponent of the Jth primitive in the Ith contraction set ETA(K,J,I) Contraction coefficient of the Jth primitive in the Kth contraction in the Ith contraction set 9) LCRU l value for the first type of shell not included in core LLSU Highest l value for shells with spin-orbit potentials NBFCR Number of functions in potential expansion 2 NCR(K) n value for expansion function, R (V-ZCORE/R) form ZCR(K) Exponent for expansion function CCR(K) Coefficient for expansion function Expansions in order: V(l=LCRU), V(s)-V(l=LCRU), V(p)-V(l=LCRU), ... for core; V(p), V(d), ..., V(l=LLSU) for spin-orbit 10) MTYPE(IS) Label for the Ith type of symmetry-distinct atom NF(IS) Number of AO sets for each of these atoms NC(IS) Number of symmetry-related atoms of the Ith type CHG(IS) Charge on the Ith type of atom (do not include core charge if core potentials are used) X(J),Y(J),Z(J) Coordinates (a.u.) for the Jth atom of this type IGEN(K,J) The effect the Jth generator of the nuclear interchange group has on the Kth atom of this type. A 2-fold rotation would be represented by 2 1 It is always assumed the starting order is 1 2 ... MCONS(J) Index of the Jth contraction set to be placed on all atoms of this type IGCS(J) Index of the Jth set of SO coefficients to be applied to the Jth contraction set. MCRS(IS) Index for the core and spin-orbit expansion set ******************************************************************************* PROGRAM OPERATION ******************************************************************************* REDIMENSIONING: All dimensions are set in ARGOS and SEG1MN, as explained by comment cards there. The following are the quantities involved: MSUP Maximum number of symmetry-inequivalent types of atoms MSTUP Maximum number of irreducible representations MRCRUP Maximum number of contractions in a contraction set MCONUP Maximum number of primitives in a contraction set MCUP Maximum number of symmetry-equivalent atoms KAORDP Maximum number of AO reduction sets MCONSP Maximum number of contraction sets MGCSUP Maximum number of SO transformation sets MRUP Maximum number of irreducible representations in an AO reduction set MCSUP Maximum number of SOs in a transformation matrix MCTUP Maximum number of AOs in a transformation matrix MCRUP Maximum number of expansion functions for potentials MSFUP Maximum number of function sets MGUP Maximum number of operators in the nuclear interchange group MSFRUP Maximum number of SOs MNRUP Maximum number of charge distributions from a pair of function sets MCCUP Maximum number of symmetry-unique center combinations for 4 types of atoms MBLUP Maximum amount of work space for SO matrices, products of SO coefficients, and integral arrays Messages are printed if dimensions are exceeded; most are set to fairly high values and only rarely need to be changed. If a message is printed, look for PARAMETER statement(s) in ARGOS and SEG1MN containing the variable name printed. SEGMENTING (overlaying): The program can be run in a simple segmented form (one-electron code, then two-electron code): Segments: root (main,argos,rt123,root4,root5) one-electron (seg1mn) two-electron (twoint) VMS: On VAX VMS computers, all filenames are translated using the standard logical name tables. If ARGOS is defined as a foreign command with the VMS DCL statement "DEFINE ARGOS:==$DEVICE:[DIRECTORY]ARGOS.EXE" (the $ is important), then the workspace memory may be set from the command line. For example, $ ASSIGN MY_DEVICE:[MY.DIRECTORY]MY_AOINTS.DAT AOINTS $ ARGOS /M=50000 would cause argos to use the indicated device and filename instead of the default []AOINTS.DAT file in the default directory. Argos would only use 50000 REAL*8 words of workspace, allocated from a blank common pool, instead of the usual default value. The maximum allowable value is determined by the dimensioned size of the blank common pool. Unix: On unix computers, all filenames are translated using the process environment variables. Upper-case variables only are valid matches. Workspace size may be set from the command line using "-M nnnnnn". Both upper- and lower-case "M" are valid. For example, from the Bourne shell: $ AOINTS=my/directory/my_aoints $COLUMBUS/argos.x -m 50000 or $ AOINTS=my/directory/my_aoints $ export AOINTS $ $COLUMBUS/argos.x -m 50000 or from the C shell: % setenv AOINTS my/directory/my_aoints % $COLUMBUS/argos.x -m 50000 causes the integral file to be redirected and the workspace size to be set as indicated. On unix machines, there is no upper limit on the workspace allocation imposed by argos; invalid requests result in a nonzero return status. PARALLEL EXECUTION: On unix machines, ARGOS may be prepared to run in a parallel message-passing environment. In this mode of execution, the output filenames, argosls, aoints, and aoints2 are all appended with a 3-digit parallel process number (e.g. argosls_000, argosls_001, etc.). FSPLIT=2 is required in this mode. A simple deterministic distribution of the workload is used to distribute the effort across several CPUs or across a heterogeneous network of machines. The TCGMSG library and documentation should be consulted for details. The TCGMSG library may be obtained using anonymous FTP from ftp.tcg.anl.gov. See the directory $COLUMBUS/source/p_argos for more information and for sample test cases. ******************************************************************************* NOTES ******************************************************************************* ARGOS was written at Argonne National Laboratory and Ohio State University in 1982 and 1983 with help from R. L. Shepard. It was based on I94720, a corresponding program for segmented contractions, which was written in 1979 at the National Resource for Computation in Chemistry with support from the H. F. Schaefer group at the University of California, Berkeley. I94720, in turn, was based on SAINT (I43210). Core-potential and spin-orbit integrals were added to ARGOS in 1983 and 1984 at Lawrence Livermore National Laboratory with help from N. W. Winter. Parallel operation was added at Argonne National Laboratory in 1991 by R. J. Harrison. Support has been provided by the above institutions, the Department of Energy, the National Science Foundation, and Cray Research, Inc. Some subroutines for primitive AO integral evaluation were provided from the HONDO and MELDPS systems (see REFERENCES) and have been modified to varying degrees. Distribution of this program is handled primarily through the University of Vienna as part of the COLUMBUS system of programs. Contact hans.lischka@univie.ac.at ******************************************************************** This computer program contains work performed partially by the Argonne National Laboratory Theoretical Chemistry Group under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy, under contract W-31-109-ENG-38. Since these programs are under development, correct results are not guaranteed. ******************************************************************** ******************************************************************************* SAMPLE DATA SETS ******************************************************************************* EXAMPLE 1. This data set is for F2 using D2h symmetry. Note that there is only one nuclear interchange operator. For D2h, 7 irrep products need to be specified; the ones given here are consistent with the standard 8x8 multiplication table. The basis set is generally contracted and omits the 3s combination of cartesian d orbitals, the 4p combination of cartesian f orbitals, and the 5s and 5d combinations of cartesian g orbitals. F2 R=2.7 BASIS SET: cc-pVQZ (5s, 4p, 3d, 2f, 1g) 1 1 5 5 5 20 15 0 0 1 / !NGEN,NS,NAORDS,NCONS,NGCS,ITOL,ICUT,,,INRM 8 1ag 1b1g 1b2g 1b3g 1au 1b1u 1b2u 1b3u 7 / !No. of irrep products 2 3 4 / !S1 = S2xS3 2 5 6 2 7 8 3 5 7 3 6 8 4 5 8 4 6 7 / !7 irrep products required for D2h 2 1 6 / !Length, list of irreps (s set) 6 8 7 6 3 4 1 / !(p set) 10 1 1 2 3 4 6 6 5 8 7/ !(d set) 14 1 1 2 3 3 4 4 5 6 6 7 7 8 8/ !(f set) 18 1 1 1 2 3 4 2 3 4 6 6 6 5 8 7 5 8 7 / !(g set) 2 2 1 / !No. of SOs, No. of AOs, AO set index (s set) 1 1 / !AO to SO transformation (s set) 1 -1 / 6 6 2 / !No. of SOs, No. of AOs, AO set index (p set) 1 0 0 1 0 0 / !AO to SO transformation (p set) 0 1 0 0 1 0 / 0 0 1 0 0 1 / 1 0 0 -1 0 0 / 0 1 0 0 -1 0 / 0 0 1 0 0 -1 / 10 12 3 / !No. of SOs, No. of AOs, AO set index (d set) 1 1 -4 0 0 0 1 1 -4 0 0 0 / !AO to SO transformation (d set) 1 -1 0 0 0 0 1 -1 0 0 0 0 / 0 0 0 1 0 0 0 0 0 1 0 0 / 0 0 0 0 1 0 0 0 0 0 1 0 / 0 0 0 0 0 1 0 0 0 0 0 1 / 1 1 -4 0 0 0 -1 -1 4 0 0 0 / 1 -1 0 0 0 0 -1 1 0 0 0 0 / 0 0 0 1 0 0 0 0 0 -1 0 0 / 0 0 0 0 1 0 0 0 0 0 -1 0 / 0 0 0 0 0 1 0 0 0 0 0 -1 / 14 20 4 / !No. of SOs, No. of AOs, AO set index (f set) 0 0 4 0 -9 0 -9 0 0 0 0 0 -4 0 9 0 9 0 0 0 / !(f set) 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 -1 0 1 0 0 0 / 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 / 4 0 0 0 0 -9 0 -9 0 0 -4 0 0 0 0 9 0 9 0 0 / 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 -1 0 1 0 0 / 0 4 0 -9 0 0 0 0 -9 0 0 -4 0 9 0 0 0 0 9 0 / 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 / 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 / 0 0 4 0 -9 0 -9 0 0 0 0 0 4 0 -9 0 -9 0 0 0 / 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 -1 0 0 0 / 0 4 0 -9 0 0 0 0 -9 0 0 4 0 -9 0 0 0 0 -9 0 / 0 0 0 1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 -1 0 / 4 0 0 0 0 -9 0 -9 0 0 4 0 0 0 0 -9 0 -9 0 0 / 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 -1 0 0 / 18 30 5 / !No. of SOs, No. of AOs, AO set index (g set) 1 1 1 0 0 0 0 0 0 -9 -9 -9 0 0 0 1 1 1 0 0 0 0 0 0 -9 -9 -9 0 0 0 / -1 -1 4 0 0 0 0 0 0 144 -36 -36 0 0 0 -1 -1 4 0 0 0 0 0 0 144 -36 -36 0 0 0 / 1 -1 0 0 0 0 0 0 0 0 -36 36 0 0 0 1 -1 0 0 0 0 0 0 0 0 -36 36 0 0 0 / 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 36 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 36 / 0 0 0 0 -1 0 0 -1 0 0 0 0 0 36 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 36 0 / 0 0 0 0 0 0 -1 0 -1 0 0 0 36 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 36 0 0 / 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 / 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 / 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 / 1 1 1 0 0 0 0 0 0 -9 -9 -9 0 0 0 -1 -1 -1 0 0 0 0 0 0 9 9 9 0 0 0 / -1 -1 4 0 0 0 0 0 0 144 -36 -36 0 0 0 1 1 -4 0 0 0 0 0 0 -144 36 36 0 0 0 / 1 -1 0 0 0 0 0 0 0 0 -36 36 0 0 0 -1 1 0 0 0 0 0 0 0 0 36 -36 0 0 0 / 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 36 0 0 0 1 0 1 0 0 0 0 0 0 0 0 -36 / 0 0 0 0 -1 0 0 -1 0 0 0 0 0 36 0 0 0 0 0 1 0 0 1 0 0 0 0 0 -36 0 / 0 0 0 0 0 0 -1 0 -1 0 0 0 36 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -36 0 0 / 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 / 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 / 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 / 12 1 5 / !No. primitives, PQN, No. contracted fct. (s set) 74530. 0.000095 -0.000022 0.0 0.0 0.0 11170. 0.000738 -0.000172 0.0 0.0 0.0 2543. 0.003858 -0.000891 0.0 0.0 0.0 721.0 0.015926 -0.003748 0.0 0.0 0.0 235.9 0.054289 -0.012862 0.0 0.0 0.0 85.60 0.149513 -0.038061 0.0 0.0 0.0 33.55 0.308252 -0.086239 0.0 0.0 0.0 13.93 0.394853 -0.155865 0.0 0.0 0.0 5.915 0.211031 -0.110914 0.0 0.0 0.0 1.843 0.017151 0.298761 1.000000 0.0 0.0 0.7124 -0.002015 0.585013 0.0 1.000000 0.0 0.2637 0.000869 0.271159 0.0 0.0 1.000000 6 2 4 / !No. primitives, PQN, No. contracted fct. (p set) 80.39 0.006347 0.0 0.0 0.0 18.63 0.044204 0.0 0.0 0.0 5.694 0.168514 0.0 0.0 0.0 1.953 0.361563 1.000000 0.0 0.0 0.6702 0.442178 0.0 1.000000 0.0 0.2166 0.243435 0.0 0.0 1.000000 3 3 3 / !No. primitives, PQN, No. contracted fct. (d set) 5.014 1.000000 0.0 0.0 1.725 0.0 1.000000 0.0 0.586 0.0 0.0 1.000000 2 4 2 / !No. primitives, PQN, no. contracted fct. (f set) 3.562 1.000000 0.0 1.148 0.0 1.000000 1 5 1 / !No. primitives, PQN, No. contracted fct. (g set) 2.376 1.000000 F 5 2 9. / !Symbol, No. AO sets, No. related atoms, Nuc. charge 0.000000 0.000000 0.000000 0.000000 0.000000 2.70 / !Coordinates for the related atoms 2 1 / !Result of the generator on the nuclei 1 1 / !Index of contraction set, Index of SO set for this atom set 2 2 3 3 4 4 5 5 EXAMPLE 2. This example is for methylene with C2v symmetry. One irrep product is required. Because methylene is planar, there is only one nuclear interchange generator. The 3s combination of cartesian d orbitals is included. An effective core potential and a spin-orbit operator for the carbon atom are used. CH2 (4s5p1d/5s1p)-->(2s2p1d/3s1p) (1.09A, 80) 1 2 5 7 5 0 0 0 0 1 1 / 4 1a1 1a2 1b1 1b2 / Irrep labels 1 4 3 2 / Irrep product 1 1 3 1 3 4 6 1 1 1 2 3 4 2 1 4 6 1 1 2 3 4 4 1 1 1 / C s orbitals 1 3 3 2 / C p orbitals 0 0 1 1 0 0 0 1 0 6 6 3 / C d orbitals 1 1 1 0 0 0 / 3s combination of cartesian d orbitals 1 1 -4 0 0 0 1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 2 4 / H s orbitals 1 1 1 -1 6 6 5 / H p orbitals 0 0 -1 0 0 -1 0 -1 0 0 1 0 1 0 0 -1 0 0 1 0 0 1 0 0 0 0 -1 0 0 1 0 -1 0 0 -1 0 4 1 2 / 25.030520 -0.0107583 0.0 / 3.357825 -0.1374182 0.0 / 0.483314 0.5771984 0.0 / 0.151774 0.5349547 1.0 / 5 2 2 / 18.477038 0.0143242 0.0 / 4.076157 0.0883853 0.0 / 1.185513 0.2920257 0.0 / 0.379641 0.4999565 0.0 / 0.120413 0.3408323 1.0 / 1 3 1 / 0.75 1.0 / 3 1 1 / 33.64 0.02537400 / 5.058 0.18968400 / 1.147 0.85293300 / 1 1 1 / 0.3211 1.0 / 1 1 1 / 0.1013 1.0 / 1 2 1 / 1.0 1.0 / 1 1 3 / C p core potential 1 51.6159 -1.434846 / 2 18.0668 -4.074550 / 2 5.3528 -0.559313 / 4 / C s-p core potential 0 12.2112 3.037970 / 1 6.2707 -4.675364 / 2 4.1732 71.589258 / 2 3.8191 -47.098215 / 3 / C p spin-orbit operator 1 51.6159 0.028402 / 2 18.0668 -0.005600 / 2 5.3528 0.004248 / C 3 1 4 / Nuc. charge reduced because of core potential 0.0 0.0 0.0 / 1 1 2 2 3 3 1 / Core, spin-orbit potential index H 4 2 1 0.0 1.32401540 1.57790010 / 0.0 -1.32401540 1.57790010 / 2 1 / Nuclear interchange generator 4 4 5 4 6 4 7 5 0 / No core, spin-orbit potential