Ab Initio Approach to Intermolecular Forces

All the information that is needed to describe a particular intermolecular interaction in mathematical and physical terms is included in the Schrodinger equation for a system under consideration 

The calculation of PESs is most easily accomplished by evaluating the interaction energy, E nt, which is defined as the difference between the energy of the dimer, Eab. and the energies of the monomers, and Eg 

The procedure chosen to calculate E nt must ensure that electronic energies of the dimer and monomers are evaluated in a consistent manner [19,21-24], It should be stressed that this requirement is absolutely crucial, as no method at present can in practice yield EAg, Ea and Eg energies with an absolute error smaller than E nt. Therefore, Eq. (2), which defines the interaction energy does not offer so simple a computational approach as might be expected at first glance. Two notorious inconsistencies to be alleviated in practice are basis set inconsistency (same basis set expansion or numerical grid for A, B, and AB must be used, otherwise the basis set superposition error (BSSE) arises [21,23,24]) and the size inconsistency (a theory to describe AB must guarantee a correct dissociation into A and B, at the same level of theory [25]). 

The details of SAPT are beyond the scope of the present work. For our purposes it is enough to say that the fundamental components of the interaction energy are ordinarily expanded in terms of two perturbations the intermonomer interaction operator and the intramonomer electron correlation operator. Such a treatment provides us with fundamental components in the form of a double perturbation series, which should be judiciously limited to some low order, which produces a compromise between efficiency and accuracy. The most important corrections for two- and three-body terms in the interaction energy are described in Table 1. The SAPT corrections are directly related to the interaction energy evaluated by the supermolecular approach, Eq.(2), provided that many body perturbation theory (MBPT) is used [19,28]. Assignment of different perturbation and supermolecular energies is shown in Table 1. The power of this approach is its open-ended character. One can thoroughly analyse the role of individual corrections and evaluate them with carefully controlled effort and desired 

Decomposition of two- and three-body supermolecular (S-MPPT) interaction energies. The contents of S-MPPT terms is described and the leading SAPT terms are indicated in square brackets. 

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