Anisotropy supermolecule

Molecules generally interact with anisotropic forces. The accounting for the anisotropy of intermolecular interactions introduces substantial complexity, especially for the quantum mechanical treatment. We will, therefore, use as much as possible the isotropic interactions isotropic interaction approximation (IIA), where the Hamiltonian is given by a sum of two independent terms representing rotovibrational and translational motion. The total energy of the complex is then given by the sum of rotovibrational and translational energies. The state of the supermolecule is described by the product of rotovibrational and translational wavefunc-tions, with an associated set of quantum numbers r and t, respectively. 

For example, in the case of two interacting atoms, an induced optical anisotropy of the supermolecule arises, given by... 

Basis set superposition error (BSSE) is a particular problem for supermolecule treatments of intermolecular forces. As two moieties with incomplete basis sets are brought together, there is an unavoidable improvement in the overall quality of the supermolecule basis set, and thus an artificial energy lowering. Various approximate corrections to BSSE are available, with the most widely used being those based on the counterpoise method (CP) proposed by Boys and Bemardi [3]. There are indications that potential energy surfaces corrected via the CP method may not describe correctly the anisotropy of the molecular interactions, and there have been some suggestions of a bias in the description of the electrostatic properties of the monomers (secondary basis set superposition errors). 

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