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Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations.