Potential energy surface perturbation approach

Jeziorski B, Moszynski R and Szalewicz K 1994 Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes Chem. Rev. 94 1887... 

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

B. Jeziorski, R. Moszynski, and K. Szalewicz, Chem. Rev., 94, 1887 (1994). Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes. 

A much more common procedure for reference selection is to accept references whose estimated importance is greater than some given threshold this can involve perturbative estimates of a function s energetic contribution or its coefficient in some preliminary wavefunction. These approaches are more successful at obtaining the best wavefunction at the lowest expense, but they sacrifice the simplicity of the excitation class selection and can become more difficult to implement and to use. One complication is that potential energy surfaces determined using such methods may not be smooth to alleviate this, one may need to determine the important references at each geometry and use the union of these sets at every point. 

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