Supermolecular Wave Function Theory WFT

Because dispersion is a genuine electron correlation effect, a common approximation in WFT is to compute it as 

WFT treatment such as Moeller-Plesset second-order perturbation theory (MP2) or coupled-cluster with single and double excitations (CCSD(T)) with correlation energy [51]. This approximation works fairly well for large interfragment distances but is obscured for shorter bonds by exchange and intrafragment correlation effects. 

An appealing feature of this partitioning is that the correlation (dispersion) energy computationally can be assigned exactly to contributions from orbital pairs. If localized molecular orbitals (LMOs) are used in the correlation treatment, this allows a local (group- or fragment-wise) description of dispersion effects [52]. The correlation energy ( [,) for an HF reference state can be written as a sum over occupied orbital pairs ij 

In the simplest correlated WFT, which is second-order M0ller-Plesset perturbation theory (MP2) [53, 54], the pair energies e are given by a sum over all virtual orbital pairs at 

Fj and F2 denote sets of orbitals that define molecular fragments or orbital spaces (i.e., core, a, n, lone-pair). The decision on the type of orbital and the atom to which it belongs can (automatically) be made on the basis of a MuUiken population analysis [56] of the LMO in question. Asymptotically, when fragments Fj and F2 are spatially well separated, the interfragment correlation energy is equal to the interaction energy, which can be further interpreted as their dispersion interaction 

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