Journal ArticleDOI
Computation of two-center Coulomb integrals over Slater-type orbitals using elliptical coordinates
TLDR
In this article, a general analytic formula for the two-center Coulomb integrals over Slater-type orbitals in elliptical coordinates is obtained, expressed in terms of a product of the well-known auxiliary functions Ak(p) and Bk(p), and incomplete gamma functions.Abstract:
A general analytic formula is obtained for the two-center Coulomb integrals over Slater-type orbitals in elliptical coordinates. Finite series expansions are used in the evaluation of the radial part of the integrals. The analytic formula is expressed in terms of a product of the well-known auxiliary functions Ak(p) and Bk(p) and incomplete gamma functions. Recursive relations for the computer evaluation of these functions are given as well. The recursive relations are stable and our computer results are in good agreement with the benchmark values given in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003read more
Citations
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Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot
TL;DR: In this paper, the binding energy and optical properties of one-electron quantum dot with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth.
Journal ArticleDOI
Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules
TL;DR: The performances of the algorithms employed in a previously reported program for the calculation of integrals with Slater‐type orbitals are examined and the efficiency of the algorithm selected for each type is analyzed.
A Bibliography of Publications of
TL;DR: A bibliography of publications of Frank E. Harris can be found in this paper, with a focus on cross-reference and cross-word crossreference cross-referencing.
Journal ArticleDOI
Linear and nonlinear optical absorption coefficients of two-electron spherical quantum dot with parabolic potential
TL;DR: Linear and nonlinear absorption coefficients of two-electron spherical quantum dot (QD) with parabolic potential are investigated in this paper, which is a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method.
Journal ArticleDOI
Linear and Nonlinear Optical Properties in Spherical Quantum Dots
TL;DR: In this paper, the energy eigenvalues and the sate functions of one-electron Quantum Dot (QD) were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method.
References
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Journal ArticleDOI
Formulas and Numerical Tables for Overlap Integrals
Abstract: Explicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npσ, and npπ AO's. They are based on approximate AO's of the Slater type, each containing two parameters μ [equal to Z/(n—δ)], and n—δ, where n—δ is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p=½(μa+μb)R/aH , R being the interatomic distance, and t=(μa—μb)/(μa+μb). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=0 (intra‐atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2‐quantum s, p hybrid AO's.Hybrid S values for any desired type of hybrid can be obtained very easily from the tables as simple linear combinations of non‐hybrid S values. It is shown how S values correspondin...
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A Study of Two‐Center Integrals Useful in Calculations on Molecular Structure. I
TL;DR: In this article, explicit formulas for all the integrals arising from the principal quantum numbers 1 and 2, for arbitrary values of the effective nuclear charges and the interatomic distance are given.
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A Study of Two‐Center Integrals Useful in Calculations on Molecular Structure. II. The Two‐Center Exchange Integrals
TL;DR: In this article, the problem of the two-center exchange integrals is solved in the most general way for Slater-type atomic orbitals with integral effective quantum numbers, and the integrals are expressed linearly in terms of certain auxiliary functions.
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Analytical evaluation of two-centre Coulomb, hybrid and one-electron integrals for Slater-type orbitals
TL;DR: In this article, a general formula for the expansion of the product of two normalized associated Legendre polynomials centred on the nuclei a and b was established for the calculation of two-centre integrals with Slater-type orbitals.