  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.
