A b i n i t i o effective core potentials including relativistic effects. I. Formalism and applications to the Xe and Au atoms

Abstract

Articles you may be interested inA b i n i t i o effective core potentials including relativistic effects. V. SCF calculations with ω-ω coupling including results for Au2 +, TlH, PbS, and PbSe Relativistic effects in a b i n i t i o effective core potential studies of heavy metal compounds. Application to HgCl2, AuCl, and PtH A b i n i t i o effective core potentials including relativistic effects. IV. Potential energy curves for the ground and several excited states of Au2 A b i n i t i o effective core potentials including relativistic effects. II. Potential energy curves for Xe2, Xe+ 2, and Xe*2 An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials (EP). The EP's are based on numerical Dirac-Hartree-Fock calculations for atoms and on the Phillips-Kleinman transformation with other aspects similar to the treatments of Goddard and Melius and Kahn, Baybutt, and Truhlar. The EP's may be writtenwhere Iljm> is a two-component angular basis function that is a product of a two-component Pauli spinor and spherical harmonics. The numerical functions UIjEP(r) are approximated as expansions in terms of Gaussian or exponential functions. The use of these EP's enables one to use the .ii -coupling scheme for subsequent applications in all-valence-electron calculations on heavy atoms and their molecules. A standard atomic SCF program has been modified to accommodate these EP's and Gaussian and exponential basis sets having the proper j angular dependence. Energy levels for many atomic states of Xe and Au were calculated. The study of Xe excited states indicates that the spin-orbit splittings are reasonably approximated and that the numerical DHF calculations are adequately reproduced. Au has been treated as an atom with I, 11, 17, 19, or 33 valence electrons to investigate the effects of redefinition of the core. P is the momentum operator (-iV). Also, .. (~ ~)with r:r being a Pauli matrix and

Relativistic Pseudopotentional Incorporating Core/Valence Polarization and Nonlocal Effects

“…The REP method is grounded in the fundamental tenet that atomic core and valence electrons can be formally distinguished and, in fact, treated rigorously from first principles as identifiable sets [2]. This subject, generally categorized as pseudopotential theory [3], has been studied for many years since being proposed by Hellmann in the 1930s and has evolved into a rigorous method for the treatment of the electronic structure of polyatomic many-electron systems [4].…”

“…This subject, generally categorized as pseudopotential theory [3], has been studied for many years since being proposed by Hellmann in the 1930s and has evolved into a rigorous method for the treatment of the electronic structure of polyatomic many-electron systems [4]. One type of ab initio REP that accounts for relativistic effects is defined by using shape-consistent nodeless pseudospinors [5] extracted from numerical two-component DF atomic spinors [6] following the procedure of Lee et al [2].…”

“…In the procedure developed by Lee et al [2], this choice is arbitrary. For example, in the case of cesium the most practical REP would correspond to a oneelectron valence space.…”

“…Region (c) accommodates those electrons that lose the knowledge of their atomic parentage in the process of excitation or ionization or as a result of interatomic interactions. Earlier pseudopotential approaches have assumed the existence of the two regions (a) and (c) only [2,13]. Those cases in which changes in the electrons in region (b) are of clear importance were dealt with, as discussed above, by either expanding the region (c) or by adding a CVPP [8,9,14].…”

“…The REP represents the interaction of the core orbitals with the orbitals comprising the outercore (designated by U i REP ) and the valence (designated by U i' REP ). The use of such an REP to represent these interactions is well understood [2]. The energy of the outercore and valence electrons relative to the energy of the core may then be expressed by…”