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

摘要

Multiconfiguration expansions frequently target valence correlation andcorrelation between valence electrons and the outermost core electrons.Correlation within the core is often neglected. A large orbital basis is neededto saturate both the valence and core-valence correlation effects. This in turnleads to huge numbers of CSFs, many of which are unimportant. To avoid theproblems inherent to the use of a single common orthonormal orbital basis forall correlation effects in the MCHF method, we propose to optimize independentMCHF pair-correlation functions (PCFs), bringing their own orthonormalone-electron basis. Each PCF is generated by allowing single- and double-excitations from a multireference (MR) function. This computational scheme hasthe advantage of using targeted and optimally localized orbital sets for eachPCF. These pair-correlation functions are coupled together and with eachcomponent of the MR space through a low dimension generalized eigenvalueproblem. Nonorthogonal orbital sets being involved, the interaction and overlapmatrices are built using biorthonormal transformation of the coupled basis setsfollowed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energiesthat are lower than the ones from traditional CAS-MCHF calculations using largeorbital active sets. It is fair to say that we now have the possibility toaccount for, in a balanced way, correlation deep down in the atomic core invariational calculations.