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

Abstract

The relativistic ??s-exponential-type spinor orbitals are defined for use in algebraic solution of the Dirac equation of particles with arbitrary half-integral spin s, s=1/2,3/2,5/2,… . The analytical expression given for the two-center overlap integrals over Slater-type spinör orbitals of spin s=1/2 particles through the ??s-exponential-type spinor orbitals, is generalized for any half-integral spin. The relativistic two-center overlap integrals are expressed in terms of non-relativistic two-center overlap integrals over the Guseinov’s ??-exponential-type orbitals where ?=1,0,-1,-2,-3,… . In this study, 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 accurate calculation of these integrals. The calculations are performed for spin s, s=1/2, s=3/2 and ?=3,2,1,0,-1,-2,-3 for each value of spin. The coupling feature between lower- and upper-components of ??s-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.