An Optimisation on the Grassmannian with Applications toQuantum Chemistry

Yuri Alexandre Aoto, Márcio Fabiano da Silva

Resumo


In this work we propose an algorithm to find critical points of the inner product betweenan element of the Grassmannian and a fixed point of the projective space of the exterior algebrawhere the Grassmannian is embedded. This has interesting applications to electronic structuretheory, where the wave functions are represented by elements of the exterior algebra. This methodis exemplified for a Grassmannian that is a model for the hydrogen molecule, H2.

Palavras-chave


Grassmannian; differential geometry; exterior algebra; quantum chemistry

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Referências


Absil, P.-A. and Mahony, R. and Sepulchre, R. Riemannian Geometry of Grassmann Mani-folds with a View on Algorithmic Computation,Acta Appl. Math., 2004, 80, 199–220, DOI:10.1023/B:ACAP.0000013855.14971.91.

Aoto, Y. A and da Silva M. F. Calculating the distance from an electronic wave function tothe manifold of Slater determinants through the geometry of Grassmannians,Phys. Rev. A,2020, 102, 052803, DOI: 10.1103/PhysRevA.102.052803.

Bowen, R. M. and Wand, C.-C.Introduction to Vectors & Tensors. Dover, 2008.

Griffiths, P. and Harris, J.Principles of Algebraic Geometry. Wiley, 1978.

Helgaker, T. and Jørgensen, P. and Olsen, J.Molecular Electronic Structure Theory. Wiley,2000.

Lischka H.et. al. Multireference Approaches for Excited States of Molecules,Chem. Rev.,2018, 118, 7293, DOI: 10.1021/acs.chemrev.8b00244.

Messiah, A.Quantum Mechanics. Dover, 1999.

Mundim, K. C Anticommuting space: an alternative formulation of the wavefunction antisym-metry description,J. Phys. France, 1989, 50, 11–17, DOI: 10.1051/jphys:0198900500101100.

Mundim, K. C and Mundim, M. S. P. ́Algebra de Grassmann e a Teoria Quˆantica,RevistaBrasileira de Ensino de F ́ısica, 1997, 19, 209–233.




DOI: https://doi.org/10.5540/03.2021.008.01.0356

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