Page 204 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

HARTREE-FOCK MODEL TO THE LOWEST SINGLET AND TRIPLET EXCITED STATES 187

Distances in and angles in degrees.

4. Discussions and conclusions
In the present paper, the Half-Projected model is applied to the direct determination
of the lowest singlet and triplet excited states in which just as the usual UHF
method is employed for states in which As examples, the method
is successfully applied to the calculation of some molecular properties of methylene,
methanal, dimethylglyoxal and formic acid, in these excited states.
In the case of methylene, methanal or dimethylglyoxal, in which the excited wave-
function is always orthogonal by symmetry to that of the singlet ground state, the
procedure converges well without any complication. In this case, the HPHF method
could be regarded as an extension of the usual UHF procedure for the states in
which This extension appears to be especially interesting for the direct
determination of the lowest singlet excited states of medium size molecules, for which
no simple and efficient method exists.
In the case of formic acid, in a random conformation, the excited wave-function pos-
sesses the same symmetry as that of the ground state. In the present paper, we
propose to orthogonalize the excited orbital to its companion in order to avoid the
variational collapsing of the excited state into the fundamental one. The procedure
converges more slowly, but procedures for accelerating convergence may be used. No-
tice that the excited wave-function is not necessarily orthogonal to the fundamental
one in this way of proceeding. But, both functions have not to be orthogonal because
the Hamiltonian operators (24) and (37) are not the same. They may expected, how-
ever, to be nearly orthogonal. It may be added here that a complete orthogonalization
will yield probably worst results [15].
It may be concluded thus that the Half-Projected Hartree-Fock model proposed more
than two decades ago for introducing some correlation effects in the ground state
wave-function [1,2], could be employed advantageously for the direct determination
of the lowest triplet and singlet excited states, in which This procedure
could be especially suitable for the singlet excited states of medium size molecules
for which no other efficient procedure exists.

References
1. Y.G. Smeyers, An. Fis. (Madrid), 67, 12 (1971).