Paradigms and paradoxes how much is out there?: Some thoughts on atomic orbitals and electron densities

Joel F. Liebman; Michelle J. Crockett; Terrance C. Dymski

doi:10.1007/bf00673493

Paradigms and paradoxes how much is out there?: Some thoughts on atomic orbitals and electron densities

Structural Chemistry ◽

10.1007/bf00673493 ◽

1991 ◽

Vol 2 (1) ◽

pp. 81-83

Author(s):

Joel F. Liebman ◽

Michelle J. Crockett ◽

Terrance C. Dymski

Keyword(s):

Electron Densities ◽

Atomic Orbitals

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THE USE OF THE HELLMANN–FEYNMAN THEOREM TO CALCULATE MOLECULAR ENERGIES

Canadian Journal of Chemistry ◽

10.1139/v60-287 ◽

1960 ◽

Vol 38 (11) ◽

pp. 2117-2127 ◽

Cited By ~ 15

Author(s):

Richard F. W. Bader

Keyword(s):

Variational Method ◽

Variational Methods ◽

Present Method ◽

Molecular Orbitals ◽

Internuclear Separation ◽

Electron Densities ◽

Empirical Expression ◽

Atomic Orbitals ◽

Helium Atoms ◽

Feynman Theorem

The Hellmann–Feynman theorem has been employed to calculate the repulsion between two helium atoms and the molecular energies of H2 and H3. The method of molecular orbitals was used to determine the necessary expressions for the electron densities. The screening constants of the atomic orbitals comprising the molecular orbitals were treated as functions of the internuclear separation according to an empirical expression which duplicates very closely the "best" values for these parameters as determined by the variational method. The results of the calculations indicate that the present method is capable of yielding estimates of molecular energies which are comparable to those obtained by the more elaborate and time-consuming variational methods.

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Ab initio band theory approach to electron energy loss near edge structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104595 ◽

1988 ◽

Vol 46 ◽

pp. 506-507

Author(s):

Xudong Weng ◽

O.F. Sankey ◽

Peter Rez

Keyword(s):

Ab Initio ◽

Local Density ◽

Interpolation Method ◽

Atomic Orbital ◽

Plane Waves ◽

Large Set ◽

Theory Approach ◽

Band Theory ◽

Atomic Orbitals ◽

Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

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