We have determined the dynamic dipole ( a ] ) , quadrupole (a2), octupole (a3), and dipole-dipolequadrupole (B) polarizabilities and the second hyperpolarizability tensor (y) for the helium atom in its lowest triplet state (z3S). We have done so for both real and imaginary frequencies: in the former case, for a range of frequencies (0) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss-Legendre grid running from zero to hw = 20 Eh. We have also determined the dispersion-energy coefficients Cg, Ce, and Clo for the systems H(12S)-He(23S), He(l's)-He(23s). and He(23S)-He(23S) and the Cg, C;, Ci, Ci, and C i coefficients for the interaction He(23s)-H2(X'Zi).Our values of the higher-order multipolar polarizabilities and of y for the z3S state of helium are, we believe, the first to be published.

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Dynamic dipole ( alpha ), quadrupole (C), dipole-quadrupole (B) polarizabilities and hyperpolarizabilities ( gamma ) of H-, for frequencies below the ionization threshold, have been calculated using accurate, explicitly electron-correlated wavefunctions. The static values are alpha =2.06165*102 au, C=2.5916*103 au, B=-4.843*105 au and gamma =8.03*107 au.

For atoms or molecules of D∞h or higher symmetry, this work gives equations for the long-range, collision-induced changes in the first (Δβ) and second (Δγ) hyperpolarizabilities, complete to order R−7 in the intermolecular separation R for Δβ, and order R−6 for Δγ. The results include nonlinear dipole-induced-dipole (DID) interactions, higher multipole induction, induction due to the nonuniformity of the local fields, back induction, and dispersion. 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 Δβ and Δγ. For dispersion effects, we have derived analytic results in the form of integrals of the dynamic (hyper)polarizabilities over imaginary frequencies, and we have evaluated these numerically for the pairs H...H, H...He, and He...He using the values of the fourth dipole hyperpolarizability ε(−iω; iω, 0, 0, 0, 0) obtained in this work, along with other 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 dispersion effects in terms of static (hyper)polarizabilities and van der Waals energy or polarizability coefficients. Tests of the approximations against accurate results for the pairs H...H, H...He, and He...He show that the root mean square (rms) error in CRA1 is ∼20%–25% for Δβ and Δγ; for CRA2 the error in Δβ is similar, but the rms error in Δγ is less than 4%. At separations ∼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 interactions make the dominant contributions to Δγzzzz (where z is the interatomic axis) and to Δγxxxx, accounting for ∼80%–123% of the total value. Contributions due to higher-multipole induction and the nonuniformity of the local field (Qα terms) may exceed 15%, while dispersion effects contribute ∼4%–9% of the total Δγzzzz and Δγxxxx. For Δγxxzz, the α term is roughly equal to the nonlinear DID term in absolute value, but opposite in sign. Other terms in Δγxxzz are smaller, but they are important in determining its net value because of the near cancellation of the two dominant terms. When Δγ is averaged isotropically over the orientations of the interatomic vector to give Δγ̄, dispersion effects dominate, contributing 76% of the total Δγ̄ (through order R−6) for H...H, 81% for H...He, and 73% for He...He.

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