Matrix Property of Vibrational Overlap Integrals

Nature ◽  
1968 ◽  
Vol 219 (5150) ◽  
pp. 151-152 ◽  
Author(s):  
R. W. NICHOLLS
Keyword(s):  
Overlap Integrals ◽  
Matrix Property

scholarly journals EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER–MULTIELECTRON INTEGRALS

2009 ◽  
Vol 08 (04) ◽  
pp. 597-602 ◽  
Author(s):  
I. I. GUSEINOV
Keyword(s):  
Exponential Type ◽  
Overlap Integrals ◽  
Charge Densities ◽  
Hartree Fock ◽  
Expansion Formulae ◽  
Multicenter Multielectron Integrals ◽  
Explicitly Correlated ◽  
Explicitly Correlated Methods ◽  
Exponential Type Orbitals ◽  
The One

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETO α = 1,0,-1,-2,…) introduced by the author. Three-center overlap integrals of Ψα appearing in these relations are expressed through the two-center overlap integrals between Ψα-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter–multielectron integrals occurring when the complete orthonormal sets of Ψα-ETO are used as basis functions in the Hartree–Fock–Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter–multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Ψα-orbitals.

A formalism for the indirect Auger effect. II

1976 ◽  
Vol 347 (1651) ◽  
pp. 565-573 ◽  
Keyword(s):  
Band Structure ◽  
Auger Recombination ◽  
Preceding Paper ◽  
Recombination Coefficient ◽  
Overlap Integrals ◽  
Estimated Parameters ◽  
Order Of Magnitude ◽  
Auger Effect ◽  
First Time ◽  
Auger Recombination Rate

The Auger recombination rate in indirect semiconductors with zincblende and diamond lattices is investigated, account being taken, for the first time, the properties of overlap integrals near symmetry points and axes. The effect of using theoretically estimated parameters is a reduction of the recombination coefficient by a factor 10. It is explained that the results, and those of the preceding paper, are still subject to uncertainties arising from the band structure so that only the order of magnitude of these coefficients can so far be regarded as known theoretically.

scholarly journals Use of lined-up auxiliary functions in the evaluation of overlap integrals over integer and non-integer n Slater type orbitals

2019 ◽  
Vol 12 ◽  
pp. 298-301
Author(s):  
Israfil I. Guseinov ◽  
Zekayi Andıç ◽  
Bahtiyar A. Mamedov ◽  
Nurşen Seçkin Görgün
Keyword(s):  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Auxiliary Functions
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