Half-projected Hartree-Fock model

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

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 Ms = 0. This procedure could be especially suitable for the singlet excited states of medium size molecules for which no other efficient procedure exists. 

An application of the half-projected Hartree-Fock model to the direct... 

THE HALF PROJECTED HARTREE-FOCK MODEL FOR DETERMINING SINGLET EXCITED STATES. 

Keywords DODS functions. Half-projected Hartree-Fock Model, determination of singlet excited states. Core excitations calulations. 

Because this new model is equivalent to a projection on half of the spin space, it is called the Half-Projected Hartree-Fock model (HPHF). The corresponding projection operator can be written easily in the following way J8j ... 

Finally, the applications of the Half-Projected-Hartree-Fock model have not to be limited to the excitations of the valence electron shell. This model can also be used to study core electron excitations. This aspect is especially interesting, since there are very few efficient methods for such calculations in molecular systems [29,30). 

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]. 

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