Phillip R. Certain

Upper and lower bounds of two‐ and three‐body dipole, quadrupole, and octupole van der Waals coefficients for hydrogen, noble gas, and alkali atom interactions

Upper and lower bounds of the multipole van der Waals coefficients C6, C8, and C10 for hydrogen, noble gas, and alkali atoms are established. Nonadditive three‐body coefficients involving dipole, quadrupole, and octupole interactions are also determined. For the dipole polarizabilities a three‐term, two‐point Pade approximant is used to obtain the upper bound and a two‐term Pade approximant is used to obtain the lower bound. For the quadrupole and octupole polarizabilities a one‐term approximation of the dynamic polarizability is used, except for the helium quadrupole polarizability, where extended approximations are possible.

Calculation of matrix elements for one- dimensional quantum-mechanical problems.

A simple method proposed by Harris et al. using the techniques of transformation theory for the generation of the matrix elements of one‐dimensional potential functions in a discrete, orthonormal basis is shown to be equivalent to Gaussian quadratures when the basis is constructed of orthogonal polynomials. The basis exp(inθ) on (− π, π) is also discussed.

Resonance properties of complex-rotated hamiltonians

The fundamental work of Balslev, Combes, and Simon has provided a mathematical foundation for the description of atomic and molecular resonances by the complex-rotation method. In the present paper we discuss some formal properties of the complex-rotated hamiltonian operators and the variational criteria for the approximation of their resonance eigenvalues. These criteria are employed in numerical studies of the complex-rotation method, which is illustrated and compared with various stabilization procedures in an application to a simple model potential. We propose a virial-scaling procedure for determining variationally optimal estimates of the resonance position and lifetime and apply the technique to the helium (2s)2 auto-ionizing resonance. Our results lend support to the idea that resonance features in the continuous spectrum can be successfully described by techniques similar to those employed for bound states.

Bounds to two- and three-body long-range interaction coefficients for S-state atoms

New upper and lower bounds to the van der Waals C6, C8, and C10 coefficients for hydrogen, noble gas, alkali, and alkaline earth atoms are determined by using Pade approximants to bound the dynamic multipole polarizabilities. Also, the nonadditive, three‐body coefficients involving dipole, quadrupole, and octupole interactions are bounded.

Extended diatomics in molecules calculations

The diatomics in molecules method of estimating polyatomic energy surfaces is extended to include valence bond configuration interaction. The results are applied to H3, using a basis of covalent and ionic functions. The method is found to be stable to the addition of the ionic functions, but it is found to be necessary to assume that the overlap between orbitals centered on different atoms vanishes.

Cusps, θ trajectories, and the complex virial theorem

The conditions are discussed under which cusps in ϑ trajectories of complex resonance energies correspond to eigenvalues which satisfy the complex virial theorem. (AIP)

Long‐Range Polarizability of the Helium Diatom

The coefficients A6∥ and A6⊥ of R−6 in the long‐range expansion of the helium diatom polarizability tensor have been computed with the result A6∥ = 60.09 a.u. and A6⊥ = 28.43 a.u.

New Partitioning Perturbation Theory. I. General Formalism

By the use of partitioning techniques, a general formalism is developed for considering degenerate, almost‐degenerate, and electron‐exchange perturbation problems. In effect, we generalize the Van Vleck–Kirtman approach to arbitrary orders and arbitrary normalization and obtain three types of approximations: In the modified Kirtman treatment the functions through the Nth order are fully normalized and the energies are obtained as the roots of the secular equation. The DE–FOP–VIM approximation is the same except that the normalization of the functions is energy optimized. The Kirtman approximation uses the same functions as the modified Kirtman but the energies are obtained as the roots of a much simpler secular equation which results from a factorization of the original secular equation (except for terms of order 2N + 2). The Kirtman energies are not upper bounds. Lowdins formalism is equivalent to the Modified Kirtman with the exception that Lowdin uses intermediate normalization. Electron exchange prob...

Exchange and Coulomb Energy of H2 Determined by Various Perturbation Methods

Four different types of perturbation theories for the exchange forces between two atoms are applied to the ground and first excited state of the hydrogen molecule at internuclear separations R = 4,6,8a0. The energy through second order and the expectation value of the Hamiltonian using the wavefunction accurate through first order are calculated to compare the theories. The results for the Hirschfelder–Silbey procedure are satisfactory. The Murrell–Shaw or Musher–Amos results are equally good with the exception of the Hamiltonian expectation values for both states at R = 6 and 8a0, which are bad. The Eisenschitz–London, van der Avoird, or Hirschfelder (HAV) results are good at small separations but at large separations they give a second‐order energy which appears to be about one‐half the correct dispersion energy. The Rayleigh–Schrodinger treatment using a Sternheimer type of zeroth‐order Hamiltonian gave the best energy for the ground state but not very good energy for the excited state. At the separati...

Dielectric properties of helium: The polarizability of diatomic helium

Self‐consistent field calculations of the dipole polarizability tensor of diatomic helium at four internuclear separations between 4a0 and 6a0 are reported. For larger separations, the calculations are shown to reduce to the point‐dipole model of long‐range polarizabilities. The computed polarizability is used in a companion paper to obtain estimates of the second dielectric constant virial coefficient, the Kerr constant virial, and the spectral moments for Raman scattering.