Many-Electron Atoms

Abstract

The essential achievements in modern quantum theory are closely connected to the microscopic description of many-electron systems in quantum chemistry, biology and condensed matter physics by using density functional theory (DFT), introduced in pioneering works [1,2]. This approach is used as a basis for ab initio calculations for complex molecular systems and the details of the method are presented in numerous monographs and reviews [3][4][5][6]. The idea of DFT is a use of oneelectron density n e .r/ as a principle dynamic variable defining the state of the system, instead of many-particle wave function « . 1 ; 2 ; : : : ; N /, which depends on the coordinate and spins of all electrons. The exact expression for the density in ground state is determined after the minimization of the density functional F OEn e .r/, and thus the problem is reduced to the construction of the approximation for the functional at certain coordinates of the nuclei of the atoms of system (adiabatic approximation).The most effective and simple way to obtain F OEn e .r/ is based on the local density approximation (LDA) with the use of the model of Thomas-Fermi (MTF) or its modifications [7,8]. The main advantages of this approach are the universal expressions for atomic values depending on nuclear charges Z, and the accurate asymptotic formulas for energy and other physical characteristics of atoms and ions. In the MTF concept, the atom is considered as electron gas with a small gradient of density, and thus one-electron basis is described by quasi-classic wave functions, which are close to plane waves [7]. These functions describe approximately the real localized wave functions of atomic electrons in the region Z 1 only, that results in the disadvantages of MTF: unlimited increase of electron density near atomic nuclei, non-exponential decay at the infinity, the absence of shell effects in atomic characteristics, and asymptotic nature of the corrections to zeroth approximation. As a result, the LDA functional F OEn e .r/ in the basis of MTF describes the distribution of electron density not accurately, especially for the atoms