Iterative variation of charge dependent atomic orbital exponents in approximate molecular all-valence electron linear combination of atomic orbitals (L.C.A.O.) methods

1976 ◽  
Vol 72 ◽  
pp. 715 ◽  
Author(s):  
Hubert P. Figeys ◽  
Paul Geerlings ◽  
Christian Van Alsenoy
Keyword(s):  
Linear Combination ◽  
Valence Electron ◽  
Atomic Orbital ◽  
Atomic Orbitals ◽  
Orbital Exponents

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

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.

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.

scholarly journals A pencil-and-paper method for elucidating halide double perovskite band structures

2019 ◽  
Vol 10 (48) ◽  
pp. 11041-11053 ◽  
Author(s):  
Adam H. Slavney ◽  
Bridget A. Connor ◽  
Linn Leppert ◽  
Hemamala I. Karunadasa
Keyword(s):  
Linear Combination ◽  
Electronic Structures ◽  
Double Perovskite ◽  
Band Structures ◽  
Atomic Orbitals ◽  
Pencil And Paper ◽  
Paper Method

Explaining most known double perovskite electronic structures and predicting new ones using Linear Combination of Atomic Orbitals analysis.

From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

2020 ◽  
pp. 150-187
Author(s):  
Jochen Autschbach
Keyword(s):  
Hydrogen Molecule ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Basis Set ◽  
Orbital Method ◽  
Chemical Bonds ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Generalized Matrix

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

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