Several resonating-valence-bond-type states are being considered as an
approximation of the two-hole ground state of the two-dimensional Hub
bard-Anderson model. These states have been carefully constructed by T
raa and Gaspers with such algebraic properties, as to optimise differe
nt contributions of the Hubbard-Anderson hamiltonian. In this paper, t
he different contributions to their energies are calculated for lattic
es with sizes from 8 x 8 up to 16 x 16 and periodic boundary condition
s, using a variational Monte-Carlo method. We show which state is lowe
st in energy and, more important, why this is so. In accordance with t
he optimal state from this tested set, we propose a bound state. It wi
ll be shown that this state is indeed the most stable state.