Convergence Radii of the Polarization Expansion of Intermolecular Potentials

摘要

A new method is presented to evaluate convergence radii of the polarization expansion of interaction energies for pairs of atoms or molecules. The method is based on an analysis of the variation of the perturbed state vector as a function of the coupling constant A and does not require a calculation of perturbation corrections to high order. The convergence radii at infinite interatomic/intermolecular distances R, as well as a remarkably accurate representation of the R dependence of the convergence radii are obtained from simple calculations involving only monomer wave functions. For the interaction of the lithium and hydrogen atoms, the obtained convergence radii agree well with those obtained previously from the large-order calculations of Patkowski et al. (Patkowski et al., J Chem Phys, 2002, 117, 5124), but are expected to be considerably more accurate. Rigorous upper bounds and reasonable approximations to the convergence radii at R = infinity are obtained for the pairs of lithium, beryllium, boron, neon, and sodium atoms, as well as for the dimer consisting of two LiH molecules. For all the systems studied, the convergence radii are significantly smaller than the unity and rapidly decrease with the increase of the nuclear charge. It is hoped that the results of this investigation will help to analyze and eventually to compute the convergence radii of the symmetry-adapted perturbation theories which utilize the same partitioning of the Hamiltonian as the polarization expansion.