Natural states of interacting systems and their use for the calculation of intermolecular forces.: III. One-term approximations of oscillator strength sums and dynamic polarizabilities

Abstract

A reinterpretation of the method outlined in the two first parts of this series for the calculation of van der Waals constants in terms of asymptotic natural states is is related to the one-term approximation of oscillator strength sums S l( itn) and dynamic polarizabilities α l (ω). The properties of these one-term approximations are discussed in detail. It is shown that the best one-term approximations to S l (−1) and S l (−2) are exact while the best one-term approximation to S l ( −3 2 ), is a lower bound and typically 98–99% of S l ( −3 2 ). Exact results for S l (O) and S l (−3) and good approximations for S l ( −1 2 ) and S l ( −5 2 ) are also obtained. Effective oscillator strengths and oscillation frequencies are defined and in terms of these best one-term approximations to α l (ω) are obtained. Two alternative approximations are proposed, one, α l (−2, ω), that is exact in the limit ω → 0 and another one, α l ( 3 2 , ω), that yields the best overall approximation alone the imaginary ω axis and the best approximation to the van der Waals constants. Upper and lower bonds for C 6 are discussed and a new justification of a well-known rule for C 6 constants between different atoms from those of like atoms is given.