Intramonomer correlation

In principle, the theory reviewed in Sections 4-6 can be applied to interactions of arbitrary systems if the full configuration interaction (FCI) wave functions of the monomers are available, and if the matrix elements of H0 and V can be constructed in the space spanned by the products of the configuration state functions of the monomers. For the interactions of many-electron monomers the resulting perturbation equations are difficult to solve, however. A many-electron version of SAPT, which systematically treat the intramonomer correlation effects, offers a solution to this problem. 

A general approach to the intramonomer correlation problem is known as the many-electron (or many-body) SAPT method88,141 213-215. In this method the zeroth-order Hamiltonian H0 is decomposed as H0 = F + W, where F = FA + FB is the sum of the Fock operators, FA and FB, of monomer A and B, respectively, and W is the intramonomer correlation operator. The correlation operator can be written as W = WA + WB, where Wx = Hx — Fx, X = A or B. The total Hamiltonian can be now be represented as H = F + V + W. This partitioning of H defines a double perturbation expansion of the wave function and interaction energy. In the SRS theory the wave function is obtained by expanding the parametrized Schrodinger equation as a power series in and A,... 

The multipole part can efficiently be estimated from the distributed multipole analysis191. In this way the electrostatic penetration contribution is obtained. One may note that the accuracy of the electrostatic term can be increased by keeping the penetration part from Eq. (1-184), and replacing the Hartree-Fock distributed multipole moments by some correlated, e.g. MP2 moments. Finally, the intramonomer correlation term and the dispersion energy can be evaluated from the expression,... 

Wormer PES, Moszynski R, Van der Avoird A (2000) Intramonomer correlation contributions to first-order exchange nonadditivity in trimer. J Chem Phys 112 3159-3169... 

In practical applications of the sapt approach to interactions of many-elect ron systems, one has to use the many-body version of sapt, which includes order-by-order the intramonomer correlation effects. The many-body SAPT is based on the partitioning of the total Hamiltonian as H = F+V+W, where the zeroth-order operator F = Fa + Fb is the sum of the Fock operators for the monomers A and B. The intermolecular interaction operator V = H — Ha — Hb is the difference between the Hamiltonians of interacting and noninteracting systems, and the intramonomer correlation operator W = Wa + Wb is the sum of the Moller-Plesset fluctuation potentials of the monomers Wx — Hx — Fx, X — A or B. The interaction operator V is taken in the non-expanded form, i.e., it is not approximated by the multipole expansion. The interaction energy components of Eq. (1) are now given in the form of a double perturbation series,... 

If we introduce the intramonomer correlation cf. Eq. (Al), multiphed by the perturbation parameter /r, the Schrodinger equation for monomer A becomes... 

Hohenstein EG, Sherrill CD (2010) Density fitting of intramonomer correlation effects in symmetry-adapted perturbation theory. J Chem Phys 133 014101... 

All energies in kelvin (1 phartree = 0.315778 kelvin). Geometries and basis sets are specified in Ref. 120. RPA denotes random phase approximation, S, D, and T denote single, double, and triple excitations, respectively, (2) denotes the sum of intramonomer correlation contributions through second order in W and ST(CCSD) indicates that the single and triple excitation amplitude.s were computed using the converged CCD double excitation amplitudes. 

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