EGAS41 - Swansea University

41 st EGAS CP 100 Gdańsk 2009
Description of the Be ground state based on the interaction of
separately optimized pair correlation functions
S. Verdebout 1∗ , C. Froese Fischer 2 , G. Gaigalas 3 , M.R. Godefroid 1 , P. Jönsson 4
1 SCQP, Université Libre de Bruxelles, 1050 Brussels, Belgium
2 National Institute of Standards and Technology, Gaithersburg, USA
3 Institute of Theoretical Physics and Astronomy,Vilnius University, Vilnius, Lithuania
4 Nature, Environment, Society, Malmö University, Malmö, Sweden
∗ Corresponding author: sverdebo@ulb.ac.be
It is well known that variational methods produce one-electron functions placing themselves
for bringing the largest stabilizing contribution to the total energy. It is therefore
possible to target specific correlation by tailoring the configuration expansion. We want
to take advantage of this feature in using independent pair correlation functions (PCF)
obtained by separate multiconfiguration Hartree-Fock (MCHF) calculations [1]. Each
PCF is built to represent a specific correlation effect, i.e. valence, core-valence or core
correlation. The so-optimized separate PCFs are coupled to each other by solving the
associated generalized eigenproblem. But the independent optimization of one-electron
sets of orbitals spanning the different PCFs gives rise to radial non-orthogonalities between
the correlation subspaces. The evaluation of the Hamiltonian and overlap matrix
elements in the PCF basis is realized through biorthonormal orbital transformations and
efficient counter-tranformation of the configuration interaction eigenvectors [2]. The latter
approach has been implemented in atsp2K [1] and has been used successfully for the
treatment of one-body transition operator. The present study constitutes the first robust
tests of this method for the two-body Coulomb operator.
The ground state of Be atom has been used thoroughly for testing various computational
strategies and correlation models [3,4]. For this four electrons system, we show
that the energy convergence is faster with our simple interaction model than with the
usual SD-MCHF method optimizing a common one-electron orbital basis spanning the
complete configuration space. Beryllium is a small system for which basis saturation can
be achieved through complete active space MCHF expansions. But for larger systems,
describing electron correlation in all the space by optimizing a common orthonormal set
becomes hopeless. Moreover, our independent optimization scheme can also be used for
coupling - through any one- or two-body operator - different and independently optimized
physical states, with their own representation. Although looking promising, it
raises many questions, especially related in the choice of the zeroth-order model to be
used when building the interaction matrix. The present study constitutes the very first
step in the current development of a large extension [5] of the atsp2K package that will
adopt the biorthonormal treatment for energies, isotope shifts, hyperfine structures and
transition probabilities.
References
[1] C. Froese Fischer & all, Comp. Phys. Com. 176, 559 8 (2007)
[2] J. Olsen & all, Phys. Rev. E 52, 4499 4 (1995)
[3] C. Froese Fischer, J. Phys. B: At. Mol. Opt. Phys. 26, 855 5 (1993)
[4] I. Lindgren, J. Morrison, Atomic Many-Body Theory (Springer-Verlag, 1982)
[5] P. Jönsson, G. Gaigalas, M. Godefroid, C. Froese Fischer, Comp. Phys. Com.
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