For nondegenerate atom–atom and atom–ion interactions the long-range interaction energy is expressed as a sum of “nonexpanded” angular components. If charge overlap is neglected each of the nonexpanded energies goes to a well-defined limit; namely to one of the usual R−1-expanded induction or dispersion energies or else to zero (R is the internuclear separation). The R−1 expansions appear to be asymptotic expansions of the nonexpanded results and are valid only for large R. As specific examples the H–H+ and H–H interactions are considered as model systems for studying charge overlap effects in induction and dispersion forces. The calculations are carried out variationally using the complete discrete Laguerre functions of degree (2l + 2) as a radial basis set. The asymptotic nature of the R−1 expansions for these interactions is discussed by comparing the various expanded and nonexpanded results. The importance of the nonexpanded interaction energies is also discussed briefly in general.

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Numerical results on the integral expression for the semiclassical S matrix are compared with exact quantum results for a multidimensional problem. The collision of a rigid rotor with an atom is treated. The integral method proves to be easy to ·apply. Within its range of maximum validity (no sign changes in the pre-exponential factor of the semiclassical wavefunction) the agreement was typically within 20%. When sign changes occurred, the agreement was about a factor of 2 or better. Conditions affecting sign changes are described.

An exact power series expansion is derived which interrelates the coefficients of the Legendre expansions for an atom–diatomic molecule potential function expanded about the centers of mass of two different isotopes of the diatomic. Its application to the anisotropic potential recently obtained for H2– and D2–Ar yields a potential for HD–Ar, which is then used to predict the transition frequencies in the infrared absorption spectrum of the latter. The relatively large discrepancies between these predictions and the recent measurements of McKellar [J. Chem. Phys. 61, 4636 (1974)] are attributed to the unusual sensitivity of such predictions to the shape of the isotropic potential in the region between its minimum at Re(0) and its zero energy turning point, σ(0).

A complete treatment of the electron propagator through third order