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Manifold curvature and Ehrenfest forces with a moving basis

Jessica F. K. Halliday, Emilio Artacho

SciPost Phys. 12, 020 (2022) · published 13 January 2022

Abstract

Known force terms arising in the Ehrenfest dynamics of quantum electrons and classical nuclei, due to a moving basis set for the former, can be understood in terms of the curvature of the manifold hosting the quantum states of the electronic subsystem. Namely, the velocity-dependent terms appearing in the Ehrenfest forces on the nuclei acquire a geometrical meaning in terms of the intrinsic curvature of the manifold, while Pulay terms relate to its extrinsic curvature.


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