Slater determinants wave function analysis

The results obtained by MBPT serve as a decisive basis for the selection of suitable orbital spaces in high-level ab initio calculations in order to account for the dominant contributions. The MBPT analysis applies equally well to four-component theory where a single configuration wave function built from Slater determinants of Dirac spinors is used as the reference wave function. In the following we will briefly outline the various theoretical approaches for relativistic atomic hfs calculations. 

Abstract This work reports the formulation of Shannon entropy indices in terms of seniority numbers of the Slater determinants expanding an A-electron wave fimc-tion. Numerical determinations of those indices prove that they provide a suitable quantitative procedure to evaluate compactness of wave functions and to describe their configurational structures. An analysis of the results, calculated for full configuration interaction wave functions in selected atomic and molecular systems, allows one to compare and to discuss the behavior of several types of molecular orbital basis sets in order to achieve more compact wave... 

This article has been organized as follows. Section 2 summarizes the notation and formulation of the main concepts used in this work it also reports the formulation of the Shannon entropy indices in terms of the seniority numbers of the Slater determinants. In Sect. 3, we present numerical values of those indices for wave functions of selected atomic and molecular systems these values allow one to characterize the compactness of the wave function expansions. The calculation level and the computational details are also indicated in this section. An analysis and discussion of these results are reported in Sect. 4. Finally, in the last section, we highlight the main conclusions and perspectives of this work. 

Accurate distance determinations depend critically on the accurate determination of phase shifts. There are two general approaches to this problem theoretical and empirical determination. The main approaches to the theoretical calculation of phase shifts are based on the Hartree-Fock (HF) and Hartree-Fock-Slater (HFS) methods. However, both of these are too involved for general use. Teo and Lee used the theoretical approach of Lee and Beni to calculate and tabulate theoretical phase shifts for the majority of elements. Use of these theoretical phase shifts requires the use of an adjustable q in the data analysis (vide supra). Most recently, McKale and co-workers performed ab initio calculations of amplitude and phase functions using a curved wave formalism for the range of k values 2 < k < 20. 

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