Radial and angular correlation in heliumlike ions

Abstract

ABSTRACT:In the framework of nonrelativistic variational formalism a new type of basis set is proposed, to estimate separately the effect of radial and angular correlations on the ground-state energy for helium isoelectronic sequence H Ϫ to Ar 16ϩ . Effect of radial correlation is incorporated by using multiexponential functions arising from product basis sets suitably formed out of Slater-type one-particle orbitals. The angular correlation can be switched on by incorporating an expansion in terms of basis involving interparticle coordinates. With a set of six-term Slater-type one-particle basis and five-term interparticle expansion, the ground-state energy of helium is estimated as Ϫ2.9037236 (a.u.) compared with the multiterm variational estimates Ϫ2.9037244 (a.u.) due to Pekeris and Thakkar and Smith and Drake. Matrix elements of different operators in the ground state have been calculated and found to be in good agreement with available accurate results.

A new method of solving the many-body Schrödinger equation

“…An increase in the number of nonlinear parameters allowed to reduce the expand length of configuration interaction wave function. Including an explicit dependence of a configuration interaction function on electron separation r 12 leads to a further decrease in the wave function expand length 40,45,46 . Obviously, the application of the theory to solve the Schrödinger equations for He-like ions has a particular importance .…”

Strongly separated pairs of core electrons in computed ground states of small molecules

“…On the other hand, a slightly negative effect of including the 4s orbitals is observed when Thus, the 4s NSOs appear to evaporate out of the core pair's orbital domain as we move up the Be-isoelectronic series from Be to N 3+ . An anonymous referee remarks that this phenomenon probably reflects the fact [37,38,39,40] that the ratio of "radial correlation" to "angular correlation" [41] decreases along the He iso-electronic series, for the core electron pair in a Be-isoelectronic atom is expected to behave much like the two electrons in the corresponding He-isoelectronic atom.…”

An efficient finite difference approach to solutions of Schrödinger equations of atoms in non-linear coordinates

“…The Schrödinger equation is the guiding equation to provide accurate descriptions of atoms [1,2], the solutions of which are further used to account for phenomena occurring in large systems such as solids and chemical reaction systems [3][4][5]. The numerical solution of the Schrödinger equation for many-electron atoms is usually obtained using established methods like hyperspherical coordinates [6][7][8], basis-set methods [9][10][11][12][13], Hartree-Fock [14,15], post Hartree-Fock methods [2,16], density functional theory [17][18][19], momentum space [20][21][22], stabilization method [23][24][25], complex coordinate method [26,27], and the real-space methods [28][29][30][31][32][33][34][35][36][37][38][39][40].…”