The Relativistic Two-center Overlap Integrals of Arbitrary Half-Integral Spin Particles

Year 2021, Volume: 11 Issue: 1, 73 - 82, 09.06.2021

Ali Bağcı

Abstract

Supporting Institution

Scientific Research Coordination Unit of Pamukkale University

Project Number

2020BSP011

Thanks

This work is dedicated in memory of Professor Israfil Guseinov who was my PhD thesis advisor. He well adapted his great experience on mathematical analysis for use in quantum chemistry especially when exponential-type orbitals are considered as a basis sets. His works on this field for me in fact, is still a source of inspiration to find an effective and practical solution for a mathematical expression that came to impasse. He unfortunately, passed away in February of last year.

Keyfi Yarım Spinli Parçacıklar için Rölativistik İki-Merkezli Örtme İntegrali

Abstract

The relativistic Ψ^αs-exponential-type spinor orbitals for arbitrary half-integrals spin s, s=1/2,3/2,5/2,… particles is defined. The two-center overlap integrals of spin s=1/2 spinors are generalized to any half-integral spin. They are expressed in terms of non-relativistic Ψ^α-exponential-type orbitals introduced by Guseinov, where α=1,0,-1,-2,-3,…. The relativistic molecular auxiliary functions approximation derived in a previous paper by the author in [Physical Review E 2015; 91(2): 023303] is used for computation of the two-center integrals. The calculations are performed for spin s, s=1/2, s=3/2 and α=1,0,-1,-2,-3,-4,-5 for each value of spin. The coupling feature between lower- and upper-components of Ψ^αs-exponential-type spinor orbitals ensure that the kinetic-balance condition is fulfilled. It is shown that, the suggested relativistic basis spinors in the present study available to be used for algebraic solution of the generalized Dirac equation.

Keywords

Half-integral spin particles, Ψ^α-Exponential-Type Orbitals, Overlap Integrals, Multi-Center Integrals

Project Number

2020BSP011

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