An approximate wave function involving geminals of mixed spin

It has been shown by Kapuy that any alternant molecular orbital wave function is an antisymmetrized product of strongly orthogonal geminals, in which the geminals are of mixed spin. Employing the localized alternant orbitals previously introduced by the author, this fact is used to generate a wave function which is capable of interpolating between the single-parameter AMO wave function and a wave function of the Hurley, Lennard-Jones, and Pople type. The validity of the unprojected form of the least flexible wave function of this type is tested in a model calculation on the hexagonal ring of hydrogen atoms. In the test case, this unprojected wave function is found to do significantly better than the unprojected AMO wave function and almost as well as the projected AMO wave function. It is shown that in the case of an infinite system, this wave function must do better than the projected AMO wave function. Features of the more general wave functions of this type are discussed, and it is mentioned that any of these wave functions may be written as an antisymmetrized geminal powers (AGP) wave function in which the geminal is of mixed spin.