arXiv subjects

A. Bağcı

Publications and source records attributed to A. Bağcı.

3 recordsLinked to original sources

arXiv2023

Solution of the Dirac-Coulomb equation using the Rayleigh-Ritz method. Results for He-like atoms

The Dirac-Coulomb equation for helium-like ions is solved using the iterative self-consistent field method, with Slater-type spinor orbitals as the basis. These orbitals inherently satisfy the kinetic-balance condition due to their coupling for both large- and small-components. The $1/r_{12}$ Coulomb interaction is treated without constraints. Computations are carried out for total energies of atoms with nuclear charges up to $Z \leq 80$ using both minimal and extended basis sets. Variationally optimal values for orbital parameters are determined through the Rayleigh-Ritz variational principle. No manifestations related to the Brown-Ravenhall disease are found.

quant-ph↗

arXiv2023

On the Evaluation of the electron repulsion integrals

The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They involve hyper-geometric functions. Due to the non-trivial structure of infinite series that are used to define them the hyper-geometric functions are practically difficult to compute. Convergence of their series are strictly depends on the values of parameters. Computational issues such as cancellation or round-off error emerge. Relationships free from hyper$-$geometric functions for expectation values of Coulomb potential $\left(r_{21}^{-1}\right)$ are derived. These relationships are new and show that the complication coming from two-range nature of Laplace expansion for the Coulomb potential is removed. These integrals also form an initial condition for expectation values of a potential with arbitrary power. The electron repulsion integrals are expressed by finite series of power functions. The methodology given here for evaluation of electron repulsion integrals are adapted to multi-center integrals.

quant-ph↗

arXiv2022

I. Complete and orthonormal sets of exponential-type orbitals with noninteger principal quantum numbers

The definition for the Slater-type orbitals is generalized. Transformation between an orthonormal basis function and the Slater-type orbital with non-integer principal quantum numbers is investigated. Analytical expressions for the linear combination coefficients are derived. In order to test the accuracy of the formulas, the numerical Gram-Schmidt procedure is performed for the non-integer Slater-type orbitals. A closed form expression for the orthogonalized Slater-type orbitals is achieved. It is used to generalize complete orthonormal sets of exponential-type orbitals obtained by Guseinov in [Int. J. Quant. Chem. 90, 114 (2002)] to non-integer values of principal quantum numbers. Riemann-Liouville type fractional calculus operators are considered to be use in atomic and molecular physics. It is shown that the relativistic molecular auxiliary functions and their analytical solutions for positive real values of parameters on arbitrary range are the natural Riemann-Liouville type fractional operators.

physics.chem-ph↗