This document is a guide for students who perform GMCPT or GMCQDPT
(MCSCF+PT) calculations on GAMESS. GMCPT is a single-state theory
corresponding to MRMP PT in the CAS reference case and GMCQDPT is a
multi-state theory. Use the names properly according to the
definition.

$CONTRL SCFTYP=MCSCF RUNTYP=ENERGY MPLEVL=2 ... $END $MRMP MRPT=GMCPT RDVECS=.T. $END *T->F for also MCSCF calculation $MCSCF CISTEP=GMCCI $END

### GMCPT for RASSCF reference function (RASSCF+GMCPT)

$GMCPT REFTYP=RAS MSTART(1)=30,34,36 NEXCIT=2 NMOCOR=29 NMOACT=10 KSTATE(1)=1 ISTSYM=1 $END

Typical input [Input example] [Input file] [Output file]### GMCPT for ORMASSCF reference functions (ORMASSCF+GMCPT)

$GMCPT REFTYP=ORMAS NSPACE=3 MSTART(1)=3,8,10 MINE(1)=4,0,0 MAXE(1)=8,4,4 NMOFZC=0 NMODOC=2 NMOACT=9 $END

Typical input [Input example] [Input file] [Output file]### GMCPT for CISD reference functions (CISD+GMCPT)

$GMCPT REFTYP=MRX NPDET=1 NEXCIT=2 NMOCOR=8 NMOACT=16 KSTATE(1)=1 ISTSYM=1 $END $PDET 2222222200000000 $END

Typical input [Input example] [Input file] [Output file]### GMCQDPT for MRSD reference function (MRSD+GMCQDPT)

$GMCPT REFTYP=MRX NPDET=13 NEXCIT=2 NMOCOR=3 NMOACT=25 KSTATE(1)=1,1,1,1,1,1,1 KNOSYM=.T. $END $PDET 2222200000000000000000000 222-2+0000000000000000000 222+2-0000000000000000000 2222-00+00000000000000000 2222+00-00000000000000000 2222-+0000000000000000000 2222+-0000000000000000000 2-222+0000000000000000000 2+222-0000000000000000000 22-22+0000000000000000000 22+22-0000000000000000000 2222-0+000000000000000000 2222+0-000000000000000000 $END

Typical input [Input example] [Input file] [Output file]

$GMCPT group (relevant if CISTEP=GMCCI in $MCSCF) (relevant if MRPT=GMCPT in $MRMP) This group specifies the determinants to be used in a general MCSCF wavefunction. It also gives the necessary information to compute a 2nd order perturbation energy correction to the MCSCF energy of such a MCSCF reference, by choosing MPLEVL=2 in $CONTRL and MRPT=GMCPT. The PT is of quasidegenerate type, in which several MCSCF states can be perturbed simultaneously. If more than one state is considered, the unperturbed model Hamiltonian is diagonal in the MCSCF state basis. After 2nd order correction to both its diagonal and off-diagonal matrix elements, this model Hamiltonian is diagonalized to give the GMCQDPT energies. The diagonalization also yields some information about the remixing of the reference states at 2nd order. GMCQDPT is therefore analogous to the two equivalent MCQDPT programs (MRPT=MCQDPT or DETMRPT) for CAS-references, but allows more general types of MCSCF reference. The letters GMCPT should be understood as standing for GMCQDPT, and have been shortened only because of the constraints on input group names to 6 or fewer letters. Of course, the program can also be used to obtain the 2nd order correction to the energy of just one state. At the present time, this program does not support EXETYP=CHECK. It is enabled for parallel execution. 1. data to specify active space and electronic state: NMOFZC: number of frozen core orbitals, during the PT the shape of these orbitals will be optimized in the MCSCF stage, so they are "frozen" in the sense of not being correlated in the PT. The default is the number of chemical core orbitals. NMODOC: number of orbitals restricted to double occupancy during MCSCF, but which are correlated in the PT calculation. In other words, the filled valence orbitals. (no default). (It is possible to enter a different keyword NMOCOR which is the total number of doubly occupied orbitals, and NMOFZC. In this case the program will obtain NMODOC by subtraction, namely NMODOC = NMOCOR - NMOFZC). NMOACT: number of active orbitals in the MCSCF (no default) NMOFZV: number of virtual orbitals to be omitted from the PT step. The default is 0, retaining all virtuals. NELACT: number of active electrons. Since the default is computed from the total number of electrons given in $DATA and $CONTRL's ICHARG, minus 2*NMOFZC minus 2*NMODOC, there is little reason to input this. MULT: multiplicity of the state, with the default being taken from MULT in $CONTRL. ISTSYM: a set of integers specifying the spatial symmetry of the electronic state. Choose from the table ISTSYM= 1 2 3 4 5 6 7 8 C1 A Ci Ag Au Cs A' A'' C2 A B C2v A1 A2 B1 B2 C2h Ag Au Bu Bg D2 A B1 B3 B2 D2h Ag Au B3u B3g B1g B1u B2u B2g Caution, this table differs from ISTSYM tables in other input groups. Default is ISTSYM(1)=1,0,0 If you are treating a system with degenerate states in an appropriate Abelian subgroup of the true group, up to three ISTSYM values can be given, to specify all components of that originally degenerate state. 2. data to specify the MCSCF CI (and PT's reference CI): The type of general MCSCF reference is specified by REFTYP, which can be MRX, ORMAS, or RAS: REFTYP= MRX means multi-reference determinant list, plus excitations (default). The determinants will be given in a $PDET group, and the keywords NPDET and NEXCIT defined below are required. REFTYP= RAS means the active space is divided into three subspaces, known as RAS1, RAS2, and RAS3. Keywords MSTART and NEXCIT defined below are required. For example, MSTART(1)=4,6,9 defines a RAS with three orbitals in the NMOFZC/NMODOC spaces, while the RAS1, RAS2, and RAS3 subspaces contain 2, 3, and NMOACT-5 orbitals. It remains only to specify the excitation level NEXCIT between these spaces. REFTYP= ORMAS defines even more general subspaces than RAS, and requires inputs NSPACE, MSTART, MINE, and MAXE. These have the same meaning as the $ORMAS keywords. NPDET is the number of parent determinants, to be given as NPDET lines in the $PDET group. A value is required for REFTYP=MRX. NEXCIT is an excitation level. A value is required for REFTYP=MRX or REFTYP=RAS. NSPACE is the number of subspaces into which the active space is divided. Required for REFTYP=ORMAS. MSTART is an array telling the starting MO of each orbital space. It is required for REFTYP=RAS and ORMAS. MINE is an array giving the minimum number of electrons occupying each subspace. Required for REFTYP=ORMAS. MAXE is an array giving the maximum number of electrons occupying each subspace. Required for REFTYP=ORMAS. NSPACE, MSTART, MINE, and MAXE have the same meaning as in the $ORMAS group. See there, and also in the MCSCF/CI section of REFS.DOC, for help in understanding the power of the ORMAS type of reference determinant list. 3. data to define the reference CI states: KSTATE is an array of states to be used. As an example, KSTATE(1)=0,1,0,1 means use states 2 and 4. The default is the ground state, KSTATE(1)=1,0,0... WSTATE is a set of weights for each state. The default is equal weight assigned to every state selected by KSTATE (WSTATE(1)=1.0, 1.0, 1.0, ...) ISPINA spin adaptation (default=0) 0 means off, 1 means on (strictly), -1 means on (loosely). Proper spin states are picked up automatically so this input is usually skipped. See NSOLUT in this context. KNOSYM a flag to turn off space symmetry use, i.e. ISTSYM. .FALSE. will ignore symmetry (default=.TRUE.) KNOSPN a flag to ignore spin symmetry, i.e. MULT. Give as .FALSE. to ignore the spin (default=.TRUE.) The next few influence the Davidson CI diagonalization, and are quite similar to $MCQDPT keywords, so the description here is terse. NSOLUT is the number of roots to be obtained. If there are not enough states of the correct spin found in the first NSOLUT states to satisfy KSTATE/WSTATE, increase this parameter to find enough. MXITER is the maximum number of Davidson iterations to find the states (default=200) THRCON is the convergence criterion on the CI coefficient convergence (default= 1.0d-6) THRENE is a convergence criterion on the total energy of the states. This is ignored if given as a negative number. (default = -1.0d-12 Hartree) MAXBAS maximum expansion space size in the Davidson diagonalization subspace (default=100) MDI dimension of the initial guess subspace used to initiate the Davidson iterative CI solver. See NHGSS in $DET for more information (default=300). 4. data to define the perturbation computation: IWGT selects wavefunction analysis (default=1) 0 means off, 1 means on (external), -1 means on (internal orbitals). This will compute the approximate weight of the MCSCF reference CI in the first order wavefunction. It is therefore a very useful diagnostic for the quality of the calculation, as the MCSCF state should be a high percentage. The formula for the decomposition is changed from the original CAS-type MCQDPT (REFWGT in $MCQDPT). The reference for this option is given below. Select IWGT=0 if the fastest speed is desired. KFORB flag to request canonicalization (default=.TRUE.) Canonicalization within the core, virtual, and any rotationally invariant active subspaces yields a well defined theoretical model. You would not normally turn this option off. KSZDOE flag to use spin (Sz) dependent orbital energies. If .TRUE., alpha and beta orbital canonicalization will involve unequal energies. Default=.TRUE. THRWGT threshold weight on the square of CI coefficients, for determinant selection. The default is 1.0d-8. Give as a negative number to retain all of the determinants, even those of very little importance, in the reference of the perturbation treatment. THRGEN threshold on generator constants. Default=1.0d-9 Raising lowers accuracy but produces speedups. Lowering to 1.0d-12 should give full accuracy for benchmarking purposes. The next two deal with the so-called "intruder states". There are theoretical difficulties with either one. THRDE just drops terms, so the potential surface may have small discontinuities. EDSHFT always shifts results a little bit, even if no small denominators (aka intruder states) are actually present. Clearly both are "band-aids"! THRDE is a threshold to simply drop out any term whose energy denominator is too small. The default for this is 0.005 Hartree. Change to zero to turn this option off. EDSHFT is similar to the same keyword in $MCQDPT. The denominators D are changed to D + EDSHFT/D. Turn off THRDE if you select this option. A reasonable value to try is 0.02, the default is 0.0. 5. miscellaneous data CEXCEN = string defining the units for the excitation energy. Choose from these 4 strings (any case): eV (default), cm-1, Kcal/mol, KJ/mol DDTFPT = a flag requesting the distributed data integral transformation be used, if the run is parallel. This option requires MEMDDI in $SYSTEM. If there is not enough memory to allow this, turn this option off to use an alternate parallel transformation (DEFAULT=.TRUE.). There are additional technical parameters documented in the source code file gmcpt.src.

- H. Nakano, R. Uchiyama, and K. Hirao,
J. Comput. Chem.
**23**, 1166-1175 (2002) - R. Ebisuzaki, Y. Watanabe, and H. Nakano,
Chem. Phys. Lett.
**442**, 164-169 (2007)

- M. Miyajima, Y. Watanabe, and H. Nakano,
J. Chem. Phys.
**124**, 044101/1-9 (2006)

Note:

The present program is based on a scheme that uses matrix elements
between the reference and ionized determinants [See Ref.2]. It is
different from our original MC-QDPT scheme used in mcqdpt.src, which
is based on the Goldstone diagrams, and also different from the
original MRMP scheme by Hirao, which uses the matrix elements between
CSFs, i.e. the Boys-Reeves formalism with the use of bonded functions.
(It has been sometimes confused recent days, but historically the
original MRMP and MC-QDPT computational schemes and codes were
developed in different groups at Nagoya and Kyoto at that time, and
hence quite independent.) The current scheme is also related to the
Kozlowski-Davidson (adopted by Dr. Ivanic in demrpt.src) and
Celani-Werner schemes.

(GMC-PT, GMC-QDPT, RAS-SCF, RAS-PT, ORMAS-SCF, ORMAS-PT, MC-QDPT, MRMP) Haruyuki Nakano

Department of Chemistry, Graduate School of Science

Kyushu University

744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan