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Quantum Chemistry
Ab-initio Quantum Chemistry Through Computer Algebra
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Authors: Ichio Kikuchi, Akihito Kikuchi
Year
2022
Paper ID
11884
Status
Peer-reviewed
Abstract Read
~2 min
Abstract Words
98
Citations
N/A
Abstract
In this article, we demonstrate the first-principles computation of quantum chemistry through symbolic computation, using computational algebraic geometry. We generate symbolic formulas of one- and twoelectron integrals. The approximations of those integrals by multivariate polynomials yield the set of equations required by quantum chemistry. We solve these equations in hybrid ways where numeric and symbolic computations are intertwined. Thereby polynomials are converted into the Gronber basis; and it is decomposed to the primary ideals (each of which represents a quantum state). The primary ideals are equipped with triangular forms, which allows us to evaluate the roots robustly.
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- This paper contributes to the Quantum Chemistry research area in the Quantum Articles archive.
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- In this article, we demonstrate the first-principles computation of quantum chemistry through symbolic computation, using computational algebraic geometry.
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