Abstract
We conjecture that “Antisymmetrized Geminal Power” wave functions, and, in particular, those of extreme type in Coleman’s terminology (i.e. with all geminal coefficients equal), can always be rewritten as antisymmetrized products of geminals orthogonal to each other. We prove this conjecture in simple cases and provide numerical evidence that it holds true in more complicated examples. Establishing the validity of this conjecture is important as it questions the physical interpretation of AGP wavefunctions.
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Acknowledgements
We acknowledge discussions with Prof. B. Mourrain, and contributions from two former students, T. Perez who performed an extended study of the case \(n=2\) for AGP of extreme type and D. Bergeault who worked on using Hilbert’s Nullstellensatz theorem for proving the conjecture.
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Cassam-Chenaï, P. A conjecture on antisymmetrized geminal power wavefunctions. J Math Chem 62, 222–227 (2024). https://doi.org/10.1007/s10910-023-01522-3
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DOI: https://doi.org/10.1007/s10910-023-01522-3