A partitioned correlation function interaction approach for describing electron correlation in atoms

S Verdebout1, P Rynkun2,PJonsson ¨ 3, G Gaigalas4, C Froese Fischer5 and M Godefroid1


 1 Chimie Quantique et Photophysique, CP160/09, Universite Libre de Bruxelles, Av FD Roosevelt 50, ´ B-1050 Brussels, Belgium

2 Lithuanian University of Educational Sciences, Student u 39, Vilnius, LT-08106, Lithuania

3 Group for Materials Science and Applied Mathematics, Malmo University, 20506 Malm ¨ o, Sweden ¨

4 Vilnius University Research Institute of Theoretical Physics and Astronomy, A Gostauto 12, LT-01108 ˇ Vilnius, Lithuania

5 Department of Computer Science, Vanderbilt University, Nashville, TN 37235, USA

E-mail: mrgodef@ulb.ac.be 

Received 4 January 2013, in final form 28 February 2013

Published 4 April 2013


Abstract

The traditional multiconfiguration Hartree–Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis. For atoms with many closed core shells, or complicated shell structures, a large orbital basis is needed to saturate the different electron correlation effects such as valence, core–valence and correlation within the core shells. The large orbital basis leads to massive configuration state function (CSF) expansions that are difficult to handle, even on large computer systems. We show that it is possible to relax the orthonormality restriction on the orbital basis and break down the originally very large calculations into a series of smaller calculations that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The expansion coefficients of the PCFs are determined from a low dimensional generalized eigenvalue problem. The interaction and overlap matrices are computed using a biorthonormal transformation technique (Verdebout et al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitioned correlation function interaction (PCFI), converges rapidly with respect to the orbital basis and gives total energies that are lower than the ones from ordinary MCHF and CI calculations. The PCFI method is also very flexible when it comes to targeting different electron correlation effects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to the single excitations from the core, spin- and orbital-polarization effects can be captured very efficiently, leading to highly improved convergence patterns for hyperfine parameters compared with MCHF calculations based on a single orthogonal radial orbital basis. By collecting separately optimized PCFs to correct the MR function, the variational degrees of freedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. The constraints on the mixing coefficients lead to small off-sets in computed properties such as hyperfine structure, isotope shift and transition rates, with respect to the correct values. By (partially) deconstraining the mixing coefficients one converges to the correct limits and keeps the tremendous advantage of improved convergence rates that comes from the use of several orbital sets. Reducing ultimately each PCF to a single CSF with its own orbital basis leads to a non-orthogonal CI approach. Various perspectives of the new method are given.


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