A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock

Equations which determine the optimum form of paired-electron orbitals are derived. It is shown that for large nuclear separations these equations become the Hartree-Fock equations for appropriate valence states of the separated atoms. An electrostatic interpretation of chemical bonding is developed using optimum paired-electron orbital functions. For these wave functions this simple procedure yields results identical with those obtained by the conventional method of calculation based on the Hamiltonian integral. Numerical computations by the electrostatic method are also discussed.

Download Full-text

Sternheimer Antishielding Functions ß(r) and γ(r) for Rare Earth Atoms

Zeitschrift für Naturforschung A ◽

10.1515/zna-1986-1-208 ◽

1986 ◽

Vol 41 (1-2) ◽

pp. 37-46 ◽

Cited By ~ 2

Author(s):

K. D. Sen ◽

P. C. Schmidt ◽

Alarich Weiss

Keyword(s):

Rare Earth ◽

Valence State ◽

Wave Functions ◽

Electric Field Gradients ◽

Hartree Fock ◽

Field Gradients ◽

Lanthanide Atoms ◽

Hf Wave ◽

Self Consistency ◽

Consistency Effects

The Sternheimer shielding-antishielding functions ß(r) and γ(r) are reported for all the fourteen lanthanide atoms at the uncoupled Hartree-Fock level of theory. Each atom is considered in two valence state configurations, 4fn 5d0 and 4 fn-1 5d1, and the nonrelativistic HF wave functions have been used. The 5d1 configuration leads to a smaller net antishielding than the 4fn configuration by ~ 6-12% in the series. The electron-electron self consistency effects are found to be less than 5% in the series. The importance of the calculated antishielding functions in the antishielding theory of electric field gradients in noncubic metals is discussed.

Download Full-text

A comparison of theory and experiment for photo-ionization cross-sections I. Neon and the elements from boron to neon

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1951.0170 ◽

1951 ◽

Vol 208 (1094) ◽

pp. 408-418 ◽

Cited By ~ 39

Keyword(s):

Cross Sections ◽

General Trend ◽

Wave Functions ◽

Ionization Cross ◽

Hartree Fock ◽

Quantal Theory ◽

Ionization Cross Sections ◽

Photo Ionization ◽

Near Future ◽

Dipole Length

The quantal theory of the continuous photo-electric absorption of radiation is briefly summarized, pàrticular attention being given to the alternative formulae available and to the accuracy to be expected in practical calculations. Detailed calculations are described for the photo-ionization cross-section of neon, a system for which it is understood that experimental data should be available in the near future. The calculation is made using Hartree-Fock wave functions and the two formulae of the dipole length and the dipole velocity. The corresponding cross-sections are found to be 5.8 and 4.4 x 10- 18 cm 2 . at the spectral head and to rise slowly with increasing frequency until a broad maximum is reached for an energy of the ejected electron of about 11 eV. A comparison is made with previous calculations on the elements from boron to neon ; the general trend of the results is discussed and improved estimates for boron and fluorine are given (10 x 10 -18 cm 2 . for boron and 4.3 x 10- 18 cm 2 . for fluorine at the spectral head).

Download Full-text

Studying the x- ray atomic Scattering form Factor and Nuclear Magnetic Shielding Constant for Be atom in its Excited state (1s2 2s 3s) and the Be - like ions

Baghdad Science Journal ◽

10.21123/bsj.12.1.204-209 ◽

2015 ◽

Vol 12 (1) ◽

pp. 204-209

Author(s):

Baghdad Science Journal

Keyword(s):

Form Factor ◽

Excited State ◽

Computer Software ◽

Wave Functions ◽

Magnetic Shielding ◽

Electron Systems ◽

X Ray ◽

Hartree Fock ◽

Atomic Scattering ◽

Nuclear Magnetic

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

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