Manifold curvature and Ehrenfest forces with a moving basis

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.

SIESTA: recent developments and applications

“…These terms are well known, 86 and their geometrical meaning in terms of the relevant curvature 75 will appear in Ref. 87. They are being tested and should be incorporated shortly to a visible branch in the open source repository, to be later merged into the trunk, and further incorporated into SIESTA releases.…”