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The minimum parameterization of the wave function for the many-body electronic Schrödinger equation. I. Theory and ansatz

Year: 2019
Type: preprint
Abstract: The minimum parameterization of the wave function is derived for the time-independent many-body problem. In this parameterization all electrons and electron pairs are indistinguishable which eliminates the exponential scaling with the number of particles plaguing all other correlation methods. An exponential scaling shown to stem from the expansion of the wave function in one-particle basis sets. It is demonstrated that using a geminal basis with a skew-symmetric orthogonal coefficient matrix, which fulfill a Lie algebra, the parameterization of the exact wave function becomes independent of the number of particles and only scale quadratic with the number of basis functions in the optimized basis and quartic in an arbitrary basis. The resulting antisymmetrized geminal power wave function is shown to fulfill the necessary and sufficient conditions for the exact wave function, treat all electrons and electron pairs as indistinguishable and be the most compact representation of the exact wave function possible. The number of parameters in the antisymmetrized geminal power wave function is exactly the same number of parameters as in the two-particle reduced density matrix thereby showing that these representations are equivalent just like the representations for a one-particle Hamiltonian. A detailed discussion of how the most compact wave function can be derived in general is also presented along with different geminal ansatze and sufficient closure relations. Due to the breaking of the scaling wall for the exact wave function it is expected that, if a general set of constraints can be found, even systems of biological relevance can be treated exactly in the future.
Language: English
Open Access status: green
OpenAlex ID: W2981246803
Cites: 75
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Related to: 10