Electron-density delocalization in many-electron atoms confined by penetrable walls: A Hartree-Fock study

The standard D-G-2D pattern of Raman spectra of sp2 amorphous carbons is considered from the viewpoint of graphene domains presenting their basic structure units (BSUs) in terms of molecular spectroscopy. The molecular approximation allows connecting the characteristic D-G doublet spectra image of one-phonon spectra with a considerable dispersion of the C=C bond lengths within graphene domains, governed by size, heteroatom necklace of BSUs as well as BSUs packing. The interpretation of 2D two-phonon spectra reveals a particular role of electrical anharmonicity in the spectra formation and attributes this effect to a high degree of the electron density delocalization in graphene domains. A size-stimulated transition from molecular to quasi-particle phonon consideration of Raman spectra was experimentally traced, which allowed evaluation of a free path of optical phonons in graphene crystal.

Download Full-text

The dependence of the hyperfine interaction on the cellular potential in Na and K. II

Canadian Journal of Physics ◽

10.1139/p69-170 ◽

1969 ◽

Vol 47 (13) ◽

pp. 1331-1336 ◽

Cited By ~ 11

Author(s):

R. A. Moore ◽

S. H. Vosko

Keyword(s):

Fermi Surface ◽

Electron Density ◽

Wave Functions ◽

Electron Wave ◽

Surface Electron ◽

Conduction Electrons ◽

Hartree Fock ◽

A Value ◽

Dependent Potential ◽

Conduction Electron Density

The dependence of the Fermi surface electron wave functions in Na and K on (i) an L-dependent effective local cellular potential constructed to simulate Hartree-Fock theory and (ii) the inclusion of the Hartree field due to the conduction electrons in the cellular potential is investigated. All calculations are performed using the Wigner–Seitz spherical cellular approximation and the Schrödinger equation is solved by the Kohn variational method. It is found that to ensure a value of the Fermi surface electron density at the nucleus accurate to ~5%, it is necessary to use the L-dependent potential along with the Hartree field due to a realistic conduction electron density.

Download Full-text

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

Australian Journal of Chemistry ◽

10.1071/ch17624 ◽

2018 ◽

Vol 71 (4) ◽

pp. 295 ◽

Cited By ~ 1

Author(s):

Dylan Jayatilaka ◽

Kunal K. Jha ◽

Parthapratim Munshi

Keyword(s):

Density Matrix ◽

Electron Density ◽

Ground State ◽

Density Functional ◽

Particle Density ◽

Density Matrices ◽

Hartree Fock ◽

Electron Density Matrix ◽

Ground State Electron ◽

Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

Download Full-text