  A new method to determine electron correlation energy is described. This
method is based on a better representation of the potential due to interacting
electrons that is obtained by specifying both the average and standard
deviation. The standard deviation is determined from a probabilistic
interpretation of the Coulomb interaction between electrons. This leads to a
better representation of orbital energies as Ei (plus-minus) delta(Ei), where
Ei is the Hartree-Fock orbital energy and delta(Ei), the spread, is an
indicator of the magnitude of correlation energy. This new representation of
the potential when combined with an empirical constant leads naturally to a new
method to determine electron correlation energy. Correlation energy is
determined within the independent electron approximation without any
contribution from higher energy unoccupied states. A consistent physical
interpretation that an electron occupies a given position when other electrons
are farther than on average can be made. It is a general technique that can be
used to determine correlation energy in any system of particles with
inter-particle interaction V(r1, r2) and can be considered to be universal
first step beyond mean-field theory.
