Analytic Coulomb approximations for dynamic multipole polarizabilities and dispersion forces

Abstract

This paper presents a comprehensive and unified treatment of atomic multipole oscillator strengths, dynamic multipole polarizabilities, and dispersion force constants in a variety of Coulomb-like approximations. A theoretically and computationally superior modification of the original Bates–Damgaard (BD) procedure, referred to here simply as the Coulomb approximation (CA), is introduced. An analytic expression for the dynamic multipole polarizability is found which contains as special cases this quantity within the CA, the extended Coulomb approximation (ECA) of Adelman and Szabo, and the quantum defect orbital (QDO) method of Simons. This expression contains model-dependent parameters determined from ground and excited state ionization potentials and is derived using a powerful approach based on the sturmian representation of a generalized Coulomb Green’s function. In addition, this result is obtained within the ECA and QDO models through an extension of the novel algebraic procedure previously used in obtaining the static polarizability within the ECA, thus demonstrating the equivalence of the two approaches. Static quadrupole and scalar and tensor dipole polarizabilities for a variety of mono and divalent ground and excited state systems within the CA, ECA, and QDO models are compared, when possible, with recent experimental and accurate theoretical work. Except for quadrupole polarizabilities of light divalent systems, agreement for all models is very good. For ground state systems, best accuracy is obtained using the ECA. Illustrative calculation for the dynamic dipole polarizability at real and imaginary frequencies for the He 11S and 21S systems within the ECA is presented and compared with the definitive results of Glover and Weinhold (GW). For He 11S, despite an 8% error in the predicted static polarizability, scaling the dynamic polarizability to the GW static value shows the frequency dependence to be accurately represented. The analytic nature of the ECA allows a wide variety of dispersion force coefficients to be easily calculated. Extensive, but not exhaustive, tabulations of C6, C8, C10, and D9 (three-body) coefficients are given. C6 coefficients involving the He 11S, 21S, 23S systems are compared with the accurate results of GW and, except for interactions of He 12S, excellent agreement is obtained. The discrepancies for He 11S are removed by a simple scaling procedure utilizing the static polarizability. To facilitate scaling of dispersion coefficients, normalized dispersion coefficients are defined. Normalized dipole and quadrupole dispersion coefficients are given for all alkaline earth–alkaline earth pairs. Accurate results for C6 and C8 coefficients are presented for all alkali–alkali pairs and C6 coefficients for alkali–alkaline earth interactions given. Sample C10 and D9 coefficients are listed for the alkalis and hydrogen. Coupling the ECA dynamic dipole polarizability to available discrete oscillator strength distribution data allows C6 coefficients to be obtained for the interaction of alkali, alkaline earth, and metastable helium atoms with the following systems: He, Ne, Ar, Kr, Xe, N, O, H2, N2, O2, NO, N2O, H2O, NH3, and CH4. Finally, C8 coefficients for He–alkali interactions are presented. A significant number of the dispersion coefficients obtained here are not available in the literature. Based on the success of ECA static multipole polarizability predictions, we feel the results presented here are generally the most reliable to date.