APSG ansatz

An interesting idea was used by Franchini and Vergani [50], who avoided the expensive optimization of geminals, rather they expanded them in a localized MO basis. A notable study was published in early seventies by Robb and Csizmadia [51, 52, 53, 54], entitled The Generalized Separated Electron Pair Model . They have also determined geminals on a localized basis, introduced a multi-configuration APSG ansatz, and considered one- and two-electron transfer terms as well. They performed calculations on NH3 and its isoelectronic series [51, 52, 53] as well as for the CO molecule [54],... 

It is possible to base on the APSG ansatz a rigorous variational procedure, i.e. to minimize with respect to the cot, subject to their strong orthogonality which is equivalent to Eq. (64), and to calculate the optimum cot without introducing further simplifications Applications to some small molecules by K. Ruedenberg et cH. 42,43) have to be mentioned in this context. This is a substantial advantage of this ansatz, but there are also some serious drawbacks. 

Extending the structure of the wave function is not the only way of improving the APSG approximation. In our laboratory [109, 107, 108], we proposed the biorthogonal formulation to take care of intergeminal overlap effects, and derived simple formulae to account for delocalization and dispersion interactions using either perturbation theory or a linearized coupled-cluster-type ansatz with the APSG reference state. 

Since our wave function is most conveniently written in the form (69), i.e. as an antisymmetrized product of strongly orthogonal geminals i), the name APSG is now commonly used for this ansatz. 

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