  In previous research, we tested the wave function format of a linear
combination of several antisymmetrized geminal power states. A numerical
problem in the geminal matrices was noted, which made the total energies of
electronic systems with large numbers of electrons unstable. The underlying
cause was found to be the large cancellation term in the geminal power series.
We have obtained a new format to resolve this problem for the case of total
energies and partly for the first-order derivatives within the antisymmetrized
geminal power states. By using this new formalism, we have calculated the
ground state energies for several electronic systems, including the usage of a
larger chemical basis set. The results are, in some cases, very close to the
exact result, especially for one-dimensional Hubbard systems. Our result for a
water molecule with the Dunning Zeta basis set is better than the CISD energy
and approaches the CCSD energy.
