Page 192 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

An Application of the Half-Projected Hartree-Fock Model to the Direct
Determination of the Lowest Singlet and Triplet Excited States of
Molecular Systems

1
Y. G. SMEYERS, P. FERNANDEZ-SERRA and M. B. RUIZ
Instituto de Estructura de la Materia, C.S.I.C., c/Serrano, 123, E-28006-Madrid,
Spain

1. Introduction
Among the many ways to go beyond the usual Restricted Hartree-Fock model in
order to introduce some electronic correlation effects into the ground state of an
electronic system, the Half-Projected Hartree-Fock scheme, (HPHF) proposed by
Smeyers [1,2], has the merit of preserving a conceptual simplicity together with a
relatively straigthforward determination. The wave-function is written as a DODS
Slater determinant projected on the spin space with S quantum number even or odd.
As a result, it takes the form of two DODS Slater determinants, in which all the spin
functions are interchanged. The spinorbitals have complete flexibility, and should be
determined from applying the variational principle to the projected determinant.
The difficulty of determining the Half-Projected Hartree-Fock function has somewhat
hampered its utilization [3-10]. Some calculations, however, exist in literature. At
present time, because of the increasing computing facilities, as well as the introduction
of more powerful convergence techniques, the HPHF model is expected to play a more
important role, especially in the field of medium size molecules, in which the use of
more sophisticated procedure are not yet possible [9-10].
In addition, since the HPHF wavefunction exhibits a two-determinantal form, this
model can be used to describe singlet excited states or triplet excited states in which
the projection of the spin momentum The HPHF approximation appears thus
as a simple method for the direct determination of excited states (with such
as the usual Unrestricted Hartree Fock model does for determining triplet excited
states with
In the present paper, we propose the use of the HPHF approximation for the direct
calculation of excited states, in which just as Berthier [11], and Pople and
Nesbet [12] did for the determination of states in which We give some ex-
amples of such calculations, either when the excited state wavefunction is orthogonal
or not by symmetry to that of the ground state.

1
Permanent Address: Departamento de Ingeniería de Circuitos y Sistemas, E.U.I.T. de Teleco-
municacion, Universidad Politécnica de Madrid, E-28031-Madrid, Spain
175
Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 175-188.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.