Relativistic Hartree-Fock Computations of Group15 Atoms and Some Diatomic Molecules

Atoms and molecules are the fundamental constituents of materials and they are the main key that can open the door to understand the materials’ structures and dynamics. The goal of a computational atomic and molecular physics is to determine numerical solutions of approximate equations. All measurable properties of the atoms and molecules can be obtained by these solutions.In the present work, accurate treatments for both non-relativistic quantum mechanics and relativistic quantum mechanics have been presented. The treatments were applied for the atoms group15 (in periodic table) that comprises 7N,15P33As,51Sb,83Bi and 115 Uup and for diatomic molecules, such as Li ,N 2 , F 2 and Se . The treatments depended on three essential techniques, which are basis-set, Hamiltonian and type of method. The obtained results, from modified GRASP1.0.0 and DIRAC14.2 programs, were compared with experimental results, non-relativistic C.F.Fischer treatment and relativistic Visscher treatment.2 The first technique depended on approximate 4-component spinors and the expanded spinor into a finite basis set. Each 4-components are a linear combination of scalar basis function (atomic basis set). The scalar basis set was formed by primitive Cartesian Gaussian basis function and subdivided into a large (L) and small (S) components sets, which were used to describe the upper and lower two components of the 4- spinors, respectively. Gaussian basis2 function type Dunning basis set for the non-relativistic treatment and the type Dyall basis set for the case of relativistic treatment have been adopted. The small component Gaussian basis function was derived from the large component Gaussian basis function by using kinetic balance relationship. The second technique depended on the type of Hamiltonian, especially on the potential term. In this technique, two models were utilized to describe the nuclear charge distribution. The first model is called point charge model,whereas the second model is called the Gaussian charge model, which can be combined with Gaussian basis set for the two cases non-relativistic and relativistic treatments to solve the singularity. Accurate calculations for the atoms and molecules required methods that have more flexibility to treat the relativistic and non-relativistic treatments. The third technique depended on two methods. Firstly, Hartree-Fock method, which was used with DunningGaussian basis-set in non-relativistic. Secondly, Dirac-Hartree-Fock method,which was used with Dyall-Gaussain basis-set in relativistic to treat the systems that have many-electrons in atoms and molecules.The results showed that in the case of heavy atoms, such asBiand super heavy atoms, such as 115 Uup the inner spinors s 1were strongly contracted. In addition, the result showed weak singularity. In order to describe the nuclear charge distribution and solve the issue of singularity at the origin for the 1s 1 =2and 2p1=2=2spinors, the Gaussian charge plus Gaussianbasis set model was harnessed. For the atoms, the obtained results, that include the total energy, the energy of each spinor in atoms, the energy of valance configuration, the expectation value of hri, the energy of each molecular orbital, the behavior of the large and small components for closer orbitals and the behavior of the radial overlap density of p1=2and p3for each atomin group15, were better than the C.F.Fischer treatment in non-relativistic and Visscher treatment in relativistic.=251Sb and and p1=283The technique’s accuracy was stemmed from the type of Gaussian basisset,that containens Dunning-Gaussian type (non-relativistic treatment) and Dyall-Gausaaian type (relativistic treatment), which was used to describe the correlation and polarization wave functions for valance orbitals and the Gaussian charge model, which was used to describe the nuclear charge to solve the problem of singularity in closer orbitals.