Orthogonal effective atomic orbitais in the topological theory of atoms

1996 ◽  
Vol 74 (6) ◽  
pp. 939-942 ◽  
Author(s):  
I. Mayer
Keyword(s):  
Large Scale ◽  
Atomic Orbital ◽  
Molecular Fragment ◽  
Wave Functions ◽  
Actual State ◽  
Topological Theory ◽  
Hartree Fock ◽  
Maximal Weight ◽  
Simple Formalism ◽  
The Given

A simple formalism has been developed permitting us to extract, from the molecular wave functions, the effective orthogonal atomic orbitais characterizing the actual state of the atom in the molecule within the framework of Bader's topological theory of atoms. This may give important conceptual connections between the SCF wave functions obtained in the large-scale ab initio calculations, or even at the Hartree–Fock limit, and the traditional atomic orbital picture. The method is based on some partial orthogonality properties of the non-orthogonal localized molecular orbitais constructed by requiring a maximal weight in the given atomic domain, or in another selected molecular fragment. (The use of such localized orbitais may also be of independent interest.) Key words: effective atomic orbitais, atomic orbitais from molecular wave functions, non-orthogonal localized orbitais, topological theory of atoms, Bader's theory of atoms in molecules.

The electrostatic calculation of molecular energies - IV. Optimum paired-electron orbitals and the electrostatic method

1956 ◽  
Vol 235 (1201) ◽  
pp. 224-234 ◽  
Keyword(s):  
Simple Procedure ◽  
Wave Functions ◽  
Optimum Form ◽  
Method Of Calculation ◽  
Hartree Fock ◽  
Electron Orbital ◽  
Electrostatic Method ◽  
Valence States ◽  
Paired Electron ◽  
Electrostatic Interpretation

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.

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

1986 ◽  
Vol 41 (1-2) ◽  
pp. 37-46 ◽  
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.

Large- Scale ab initio Simulations of Fe-doped SrTiO3 Perovskites

2002 ◽  
Vol 731 ◽  
Author(s):  
R.A. Evarestov ◽  
R.I. Eglitis ◽  
S. Piskunov ◽  
E. A. Kotomin ◽  
G. Borstel
Keyword(s):  
Energy Level ◽  
Ab Initio ◽  
High Spin ◽  
Spin State ◽  
Large Scale ◽  
Covalent Bonding ◽  
Hartree Fock ◽  
Ab Initio Simulations ◽  
Displacement Mode ◽  
Jahn Teller

AbstractUsing the Unrestricted Hartree-Fock method and supercells containing up to 160 atoms, we calculated the energy level positions in the gap and atomic geometry for the Fe4+ impurity substituting for a host Ti atom in SrTiO3. In agreement with experiment, the high spin (S=2) state is much lower in energy than the zero-spin state. The energy level positions strongly depend on the asymmetric displacement mode of the six nearest O ions which is a combination of the Jahn-Teller and breathing modes. A considerable covalent bonding between the Fe ion and four nearest O ions takes place.

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

1951 ◽  
Vol 208 (1094) ◽  
pp. 408-418 ◽  
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).

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