Gradient of molecular Hartree–Fock–Bogoliubov energy with a linear combination of atomic orbital quasiparticle wave functions

2014 ◽  
Vol 140 (8) ◽  
pp. 084115 ◽  
Author(s):  
Masato Kobayashi
Keyword(s):  
Linear Combination ◽  
Atomic Orbital ◽  
Wave Functions ◽  
Hartree Fock

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.

Déplacement chimique du proton en résonance magnétique nucléaire. I. Calcul du terme diamagnétique en vue de son utilisation à l'étude de la structure des molécules. Application aux éthers vinyliques

1970 ◽  
Vol 48 (20) ◽  
pp. 3154-3163 ◽  
Author(s):  
François Tonnard ◽  
Simone Odiot ◽  
Maryvonne L. Martin
Keyword(s):  
Carbon Atom ◽  
Linear Combination ◽  
Atomic Orbital ◽  
Ethoxy Group ◽  
Vinyl Ethers ◽  
Résonance Magnétique

A relation between the diamagnetic term for a proton bonded to a carbon atom and the linear combination of atomic orbital charges on C and H is established. Proton diamagnetic terms of some vinyl ethers are calculated, and the conformation of ethoxy group in these molecules studied.

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.

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