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We develop a bivariational principle for an antisymmetric product ofnonorthogonal geminals. Special cases reduce to the antisymmetric product ofstrongly-orthogonal geminals (APSG), the generalized valence bond-perfectpairing (GVB-PP), and the antisymmetrized geminal power (AGP) wavefunctions.The presented method employs wavefunctions of the same type asRichardson-Gaudin (RG) states, but which are not eigenvectors of a modelHamiltonian which would allow for more freedom in the mean-field. The generalidea is to work with the same state in a primal picture in terms of pairs, andin a dual picture in terms of pair-holes. This leads to an asymmetric energyexpression which may be optimized bivariationally, and is strictly variationalwhen the two representations are consistent. The general approach may be usefulin other contexts, such as for computationally feasible variationalcoupled-cluster methods.

Bivariational Principle for an Antisymmetrized Product of Nonorthogonal Geminals Appropriate for Strong Electron Correlation