  New ways to treat electron correlation in electronic structure problems are
discussed in the context of many-electron theory. The present work focuses
primarily on static correlation. In related work, a method for including
dynamical correlation effects is described. The overlap density of two basis
functions i, j and the associated density matrix is a signature of bond
formation and can be used to define a local molecular orbital, i + j. The total
electron density \r{ho} can be written in terms of densities derived from these
two-center orbitals and residual one-center terms. In the interaction of total
densities, the self-energy terms resulting from an average field (Hartree-Fock)
Hamiltonian are allowed to respond to an explicit inclusion of electron
repulsion by mixing (i + j)1(i + j)2 +{\lambda}(i - j)1(i - j)2 . The energy
lowering weighted by the density matrix ij approximates this contribution to
the correlation energy of the system. Numerical calculations for a set of 20
molecules representing different bonding environments are reported and results
are compared with configuration interaction calculations using the same
molecular orbital basis. Calculations on chlorin, N4C20H16, are reported as an
example of how the method could be used in an embedding treatment of a large
system.
