LONG-RANGE, COLLISION-INDUCED HYPERPOLARIZABILITIES OF ATOMS OR CENTROSYMMETRIC LINEAR-MOLECULES - THEORY AND NUMERICAL RESULTS FOR PAIRS CONTAINING H OR HE

For atoms or molecules of D-infinity h or higher symmetry, this work g ives equations for the long-range, collision-induced changes in the fi rst (Delta beta) and second (Delta gamma) hyperpolarizabilities, compl ete to order R(-7) in the intermolecular separation R for Delta beta, and order R(-6) for Delta gamma. The results include nonlinear dipole- induced-dipole (DID) interactions, higher multipole induction, inducti on due to the nonuniformity of the local fields, back induction, and d ispersion. For pairs containing H or He, we have used ab initio values of the static (hyper)polarizabilities to obtain numerical results for the induction terms in Delta beta and Delta gamma. For dispersion eff ects, we have derived analytic results in the form of integrals of the dynamic (hyper)polarizabilities over imaginary frequencies, and we ha ve evaluated these numerically for the pairs H ... H, H ... He, and He ... He using the values of the fourth dipole hyperpolarizability epsi lon(-i omega; i omega, 0, 0, 0, 0) obtained in this work, along with o ther hyperpolarizabilities calculated previously by Bishop and Pipin. For later numerical applications to molecular pairs, we have developed constant ratio approximations (CRA1 and CRA2) to estimate the dispers ion effects in terms of static (hyper)polarizabilities and van der Waa ls energy or polarizability coefficients. Tests of the approximations against accurate results for the pairs H ... H, H ... He, and He ... H e show that the root mean square (rms) error in CRA1 is similar to 20% -25% for Delta beta and Delta gamma for CRA2 the error in Delta beta i s similar, but the rms error in Delta gamma is less than 4%. At separa tions similar to 1.0 a.u. outside the van der Waals minima of the pair potentials for H ... H, H ... He, and He ... He, the nonlinear DID in teractions make the dominant contributions to Delta gamma(zzzz) (where z is the interatomic axis) and to Delta gamma(xxxx), accounting for s imilar to 80%-123% of the total value. Contributions due to higher-mul tipole induction and the nonuniformity of the local field (Q alpha ter ms) may exceed 15%, while dispersion effects contribute similar to 4%- 9% of the total Delta gamma(zzzz) and Delta gamma(xxxx). For Delta gam ma(zzzz) the Q alpha termis roughly equal to the nonlinear DID term in absolute value, but opposite in sign. Other terms in Delta gamma(xxzz ) are smaller, but they are important in determining its net value bec ause of the near cancellation of the two dominant terms. When by is av eraged isotropically over the orientations of the interatomic vector t o give a <Delta(gamma)over bar> dispersion effects dominate, contribut ing 76% of the total <Delta(gamma)over bar> (through order R(-6)) for H ... H, 81% for H ... He, and 73% for He ... He. (C) 1996 American In stitute of Physics.