skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} for alkaline-earth dimers

Abstract

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.

Authors:
 [1];  [2]
  1. Russian Academy of Sciences, Petersburg Nuclear Physics Institute (Russian Federation), E-mail: porsev@thd.pnpi.spb.ru
  2. University of Nevada, Physics Department (United States)
Publication Date:
OSTI Identifier:
21067746
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 102; Journal Issue: 2; Other Information: DOI: 10.1134/S1063776106020014; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BARIUM; BERYLLIUM; CALCIUM; DIMERS; ELECTRIC DIPOLES; GROUND STATES; MAGNESIUM; OCTUPOLES; POLARIZABILITY; QUADRUPOLES; STRONTIUM; VAN DER WAALS FORCES

Citation Formats

Porsev, S. G., and Derevianko, A. High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} for alkaline-earth dimers. United States: N. p., 2006. Web. doi:10.1134/S1063776106020014.
Porsev, S. G., & Derevianko, A. High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} for alkaline-earth dimers. United States. doi:10.1134/S1063776106020014.
Porsev, S. G., and Derevianko, A. Wed . "High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} for alkaline-earth dimers". United States. doi:10.1134/S1063776106020014.
@article{osti_21067746,
title = {High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} for alkaline-earth dimers},
author = {Porsev, S. G. and Derevianko, A.},
abstractNote = {The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C{sub 6}, C{sub 8}, and C{sub 10} of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.},
doi = {10.1134/S1063776106020014},
journal = {Journal of Experimental and Theoretical Physics},
number = 2,
volume = 102,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • The van der Waals C{sub 6} coefficients of fullerenes are shown to exhibit an anomalous dependence on the number of carbon atoms N such that C{sub 6} ∝ N{sup 2.2} as predicted using state-of-the-art quantum mechanical calculations based on fullerenes with small sizes, and N{sup 2.75} as predicted using a classical-metallic spherical-shell approximation of the fullerenes. We use an atomistic electrodynamics model where each carbon atom is described by a polarizable object to extend the quantum mechanical calculations to larger fullerenes. The parameters of this model are optimized to describe accurately the static and complex polarizabilities of the fullerenes bymore » fitting against accurate ab initio calculations. This model shows that C{sub 6} ∝ N{sup 2.8}, which is supportive of the classical-metallic spherical-shell approximation. Additionally, we show that the anomalous dependence of the polarizability on N is attributed to the electric charge term, while the dipole–dipole term scales almost linearly with the number of carbon atoms.« less
  • The authors have determined the dynamic dipole ([alpha][sub 1]), quadrupole ([alpha][sub 3]), and dipole-dipole-quadrupole (B) polarizabilities and the second hyperpolarizability tensor ([gamma]) for the helium atom in its lowest triplet state (2[sup 3]S). They have done so for both real and imaginary frequencies: in the former case, for a range of frequencies ([omega]) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss-Legendre grid running from zero to [Dirac h][omega] = 20 E[sub h]. They have also determined the dispersion-energy coefficients C[sub 6], C[sub 8], and C[sub 10] for the systems H(1[sup 2]S)-He(2[sup 3]X),more » He(1[sup 1]S)-He(2[sup 3]S), and He(2[sup 3]S)-He(2[sup 3]S) and the C[sub 6][sup 0], C[sub 6][sup 2], C[sub 8][sup 0], C[sub 8][sup 4] coefficients for the interaction He(2[sup 3]S)-H[sub 2](X[sup 1][Sigma][sub g][sup +]). Their values of the higher-order multipolar polarizabilities and of [gamma] for the 2[sup 3]S state of helium are, they believe, the first to be published. 14 refs., 5 tabs.« less
  • The authors have calculated certain dynamic polarizabilities (for both real and imaginary frequencies) for H, He, and H[sub 2] and the dispersion-energy coefficients for long-range interactions between them. This was done so in a sum-over-states formalism with explicitly electron-correlated wave functions to describe the states. To be precise, the authors have determined the dipole ([alpha][sub 1]), quadrupole ([alpha][sub 2]), and octupole ([alpha][sub 3]) polarizabilities of H and He for real frequencies ([omega]) in a range between zero and the first electronic-transition frequency and for imaginary frequencies (i[omega]) on a 32-point Gauss-Legendre grid running from zero to h[omega] = 20 E[submore » h], and for H[sub 2], the authors found the dipole ([alpha]), quadrupole (C), and dipole-octupole (E) polarizability tensors for the same real and imaginary frequencies. The dispersion-energy coefficients, obtained by combining the sum-over-states formalism for the polarizabilities with analytic integration over [omega], gave values of C[sub 6], C[sub 8], and C[sub 10] for the atom-atom systems; C[sup 0][sub 6], C[sup 2][sub 6], C[sup 0][sup 8], C[sup 2][sub 8], and C[sup 4][sub 8] for the atom-diatom systems; and C[sub 6], C[sup [prime]][sub 6], and C[sup [double prime]][sub 6] for the H[sub 2]-H[sub 2] system. Nearly all the results are considered to be more reliable than those hitherto published and some have been obtained for the first time, e.g., C(i[omega]), and E(i[omega]) for H[sub 2] and C[sup 0][sub 8] and C[sup 4][sub 8] for the H-H[sub 2] system. 9 tabs.« less
  • A quantum chemistry study of the ground-state structures and binding energies of the van der Waals dimers of benzene, naphthalene, and anthracene has been made at the MP2/6-31G and MP2/6-31+G levels of theory. For naphthalene and anthracene, the calculations yield two low energy dimers of very similar energies: D{sub 2d} (crossed) and C{sub 2h} (parallel-displaced). Conformers, analogous to the T-shaped dimer of benzene, are less stable than the crossed and the parallel-displaced dimers. BSSE-corrected MP2/6-31+G/MP2/6-31G binding energies of the crossed and the parallel-displaced dimers are, respectively, 15.77 and 15.65 kJ/mol for naphthalene and 36.40 and 31.84 kJ/mol for anthracene. Themore » fully optimized MP2/6-31G structures of the parallel-displaced dimer of naphthalene has a horizontal displacement of 1.5 {angstrom} along the short axes of the monomers and a vertical displacement of 3.5 {angstrom}. The corresponding horizontal and vertical separations for the parallel-displaced (PD) dimer of anthracene are 1.1 and 3.6 {angstrom}, respectively. for the crossed dimers, the vertical separation of the aromatic rings is 3.6 {angstrom} for naphthalene and 3.3 {angstrom} for anthracene. The greater binding energy and the shorter horizontal displacement of the anthracene PD dimer relative to the naphthalene PD dimer are consistent with the stronger dispersion interactions expected of a larger dimer. The greater stability and smaller vertical separation of the crossed dimer of anthracene relative to that of naphthalene can also be attributed to the disparity in the dispersion interactions.« less