The use of biorthogonal valence bond reference functions in evaluating
the correlation energy is investigated. Since the method is not varia
tionally bound some care must be taken in defining the reference state
to ensure that the variational bound is not violated, some discussion
is given to this matter. The procedure adopted here is a matrix eleme
nt driven configuration interaction scheme. To reduce the computationa
l labour involved, a configuration selection criterion is introduced.
The method is tested through its application to the symmetric stretchi
ng of HF, H2O2 (B-2(1)) NH, and the singlet-triplet gap in CH2. Compar
ison is made with other methods, including full CI. The results show t
hat the current method is quite promising.