  Traditional multiconfiguration Hartree-Fock (MCHF) and configuration
interaction (CI) methods are based on a single orthonormal orbital basis (OB).
For atoms with complicated shell structures, a large OB is needed to saturate
all the electron correlation effects. The large OB leads to massive
configuration state function (CSF) expansions that are difficult to handle. We
show that it is possible to relax the orthonormality restriction on the OB and
break down the originally large calculations to a set of smaller ones 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 mixing
coefficients of the PCFs are fixed from a small generalized eigenvalue problem.
The required matrices are computed using a biorthonormal transformation
technique. The new method, called partitioned correlation function interaction
(PCFI), converges rapidly and gives total energies that are lower than the
ordinary ones (MCHF and CI). Considering Li I, we show that by dedicating a PCF
to the single excitations from the core highly improves the convergence
patterns of the hyperfine parameters. Collecting the 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. These constraints
lead to small off-sets in computed properties other than total energy, with
respect to the correct values. By (partially) deconstraining the mixing
coefficients one converges to the correct limits and keeps the important
advantage in the convergence rates. Reducing ultimately each PCF to a single
CSF with its own OB leads to a non-orthogonal CI approach. Various perspectives
of the new method are given.
