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Intermolecular Perturbation Theory

This package performs intermolecular perturbation theory (IMPT) calculations of the interaction energy between two closed shell molecules. The perturbation theory used involves full overlap treatment and non-orthogonal orbitals (Hayes & Stone, Molec. Phys. (1984) 53, 83-105).

Data input and integral/SCF options are as for the standard program, except for these changes:

`SYMMETRY`	should not be used (nonsense will result).
`ATOMS`	`NEXT` appearing where an atom name is expected divides the fragments. It is followed directly by the next atom specification.
`CHARGE`	If required, should give values for both fragments.
`ACCURACY`	Separate values may also be set for intermolecular integrals using the form: `ACCURACY itol icut <itoli icuti>` where `itoli` and `icuti` denote the intermolecular values (which default to the intramolecular values).
`SUPERMATRIX`	should be `OFF`.

The directive required to invoke this part of the program takes the form:

INTERMOL
(options)
START

This initiates calculation of the SCF orbitals of the non-interacting fragments; all inter-fragment integrals being set to zero. The inter-fragment integrals are then evaluated and the perturbation calculation performed as specified by the options. The options specific to this step in the calculation are:

ORDER norder

norder is the order to which the calculation is to be be carried. Valid values are -1, 0, 1, 2 (default) and 3:

-1	zeroth order SCF of isolated molecules only; unperturbed density matrix, orbitals and eigenvalues are saved on the dumpfile (default sections 47-49 respectively). Useful to break up large calculations with sequential mainfile so that only intramolecular integrals are dumped to tape.
0	zeroth order SCF (as for -1) and intermolecular integrals.
1	calculation to first order only.
2	calculation to second order, single excitations only; matrices required for double excitation calculations are saved on the dumpfile (default sections 94-99).
3	calculation to third order, single excitations only; supersystem energy calculated from approximate first-order wavefunction.

MOROKUMA

Carry out a Morokuma analysis. At present this is only partly implemented; an SCF calculation is done in which each molecule experiences only the classical electrostatic interactions with the other (no exchange terms). The difference in energy between the resulting energy and the zeroth-order energy is the sum of the electrostatic and induction energies.

IGNORE

Carry out calculation with intermolecular overlap ignored.

EPSNES

Calculate and use Epstein-Nesbet denominators (as well as Moller-Plesset). This is very time-consuming for larger systems, as it involves, in effect, a four-index transformation.

IRESTI iresti

This resets the INTERMOL restart option and shouldn't normally be needed. The values of iresti correspond to:

0	beginning of calculation.
1	unperturbed orbitals stored on dumpfile. This is set in the calculation so that only intermolecular integrals are recalculated in subsequent runs with the same dumpfile (so that different intermolecular separations may be used).
2	matrices for double excitations stored on dumpfile.
3	Dispersion calculation (see below) stopped while in four-index transformation or in calculation of double excitation terms. (Reset to previous value if calculation restarted and finished.)

PRINT [NORMAL] [DETAILS] [MINUTIAE] [EXTRA] [MAXIMUM]

This controls the printing in the perturbation calculation. Multiple occurences of PRINT may be used to change values as the calculation proceeds. The options are:

`NORMAL`	Default printing: summary of results only.
`DETAILS`	Print details of the main orbital contributions to the polarization and charge-transfer energies.
`MINUTIAE`	Print all non-zero orbital contributions.
`EXTRA`	Print some of the matrices calculated in the intermediate steps of the calculation. This produces a good deal of output.
`MAXIMUM`	Print all intermediate information. This produces even more output and should normally be avoided.

If the INTERMOL calculation has successfully executed to second order (i.e. if iresti is greater than 1) then the dispersion and other double-excitation terms in the second-order interaction energy may be calculated. (If iresti is less than 2 the program assumes that the orbitals are orthogonal.) The calculation calls the four index transformation routine with (if iresti greater than 1) modified orbitals (which are overwritten onto the sections with default numbers 7-9). The directive takes the form:

IMPTDISP
(options)
START

The options include those for the four-index transformation (outlined in section 10) except that the defaults are:
RESTRICT 1
ACCURACY icuti (if icuti is greater than 10).
Additional options for the DISPERSION directive are:

PRINT [NORMAL] [DETAILS] [EXTRA]

`NORMAL`	Default printing: summary of results only.
`DETAILS`	Print an analysis of the contribution to the dispersion energy from each pair of occupied orbitals.
`EXTRA`	Print the modified orbitals used in the 4-index transformation.

To restart the DISPERSION calculation the directives are:

RESTORE
IMPTDISP
RESTART

For further details of the method see
I. C. Hayes and A. J. Stone, `An intermolecular perturbation theory for the region of moderate overlap', Molec. Phys. (1984) 53, 83-105.
A. J. Stone, `Computation of charge-transfer energies by perturbation theory', Chem. Phys. Letters (1993) 211, 101-109.
Note that the dispersion calculation prints values for several quantities, discussed in the first of the above papers. Contrary to what is stated in that paper, only the value for `Dispersion' has physical significance.

Example Dataset 1.

TITLE
HCCH...N2 [6311G*] linear, Rcm = 8.0 B

CONVERGENCE 9

CONSTANTS
zH    3.139781 B
zC    1.136671 B
zN    1.03368 B
R 8.0 B
END

ATOMS
C1    6 0.0 0.0 zC
LIBRARY C6311G*
END
H1    1 0.0 0.0 zH
LIBRARY H6311G*
END
C2    6 0.0 0.0 - zC
LIBRARY C6311G*
END
H2    1 0.0 0.0 - zH
LIBRARY H6311G*
END
NEXT
ORIGIN 0.0 0.0 R
N1   7   0.0 0.0 zN
LIBRARY N6311G*
END
N2   7   0.0 0.0 - zN
LIBRARY N6311G*
END
END

NOPRINT OCCVECTORS
INTERMOL
ORDER 2
START
FINISH

Example Dataset 2)

TITLE
HF...HOH Linear H-bond RF..O = 3.11 A, theta = 110.2 6-31G*
NOTE Geometry from Dill et al., JACS (1975) 97, 7220
NOTE Expt. monomer geometry, 6-31G* dimer geometry.

NOTE     Geometry:
NOTE
NOTE             Y
NOTE
NOTE          H
NOTE           \                        2
NOTE            \ theta
NOTE             F                H----O       ------> Z
NOTE           1                        \
NOTE             ^                     ^ \
NOTE             |...      R        ...| H
NOTE
NOPRINT OCCVECTORS
CONVERGE 8
SUPERMATRIX OFF
CONSTANTS
RFO   3.11 A
theta 110.2 D
FH    0.917 A
OH    0.957 A
HOz   127.75 D
HOH/2 52.25 D
END

ATOMS
O        -9   0. 0. 0.
X        -9   1. 0. 0.
Y        -9   0. 1. 0.
Y'       -9   0. -1. 0.
Z        -9   0. 0. 1.
Fluorine 9   0.0 0.0 0.0
LIBRARY F631G*
END
Hydrogen 1   PTC Fluorine Z Y FH theta
LIBRARY H631G
END
NEXT
ORIGIN   0.0 0.0 RFO
Oxygen   8   0.0 0.0 0.0
LIBRARY O631G*
END
Hydrogen 1   LC Oxygen Z - OH
LIBRARY H631G
END
z        -9   PTC Oxygen Hydrogen Y 1.0 - HOH/2
Hydrogen 1   PTC Oxygen z Y OH - HOH/2
LIBRARY H631G
END
END

INTERMOL
EPSNES
ORDER 2
START
IMPTDISP
START

FINISH

The first of these datasets produces the following output (after the initial SCF )

SUMMARY OF RESULTS
HCCH...N2 [6311G*] linear, Rcm = 8.0 B

Zeroth order energies

Fragment 1
             Electronic energy      -101.632315234
             Nuclear repulsion        24.791712483
             Total energy                                -76.840602751
Fragment 2
             Electronic energy      -132.671903806
             Nuclear repulsion        23.701725873
             Total energy                               -108.970177933
First-order energy for supersystem
             Electronic energy      -260.418654309
             Nuclear repulsion        74.614050643
             Total energy                               -185.804603665

Contributions to the interaction energy in milliHartree

FIRST ORDER

One-electron electrostatic energy   -52087.604762
Two-electron electrostatic energy    25961.879098
Nuclear electrostatic energy         26120.612288
Total electrostatic energy                           -5.113376

Exchange energy                        -13.213880
Repulsion energy                        24.504275
Exchange-repulsion energy                            11.290395

Total interaction energy to first order 6.177019

SECOND ORDER (single-excitation terms)

Induction         Moller-Plesset
        1 -> 1       -0.173196
        2 -> 2       -0.369098
         Total       -0.542294

Charge transfer   Moller-Plesset
        1 -> 2       -0.177894
        2 -> 1       -0.823464
         Total       -1.001358

TOTAL INTERACTION
At first order 6.177019
At second order -- Moller-Plesset 4.633367

Contents: Table of Contents Next: About this document ... Up: Chapter 6 Previous: Distributed Polarizabilities