期刊
JOURNAL OF CHEMICAL PHYSICS
卷 154, 期 22, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/5.0053177
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资金
- International Institute for Nanotechnology at Northwestern University
This study introduces a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space, which is numerically verified to be equivalent to mean-field mixed quantum-classical dynamics in real space. The reciprocal-space Hellmann-Feynman forces for the Holstein and Peierls models are found to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space.
We derive a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. Taking these variables as a Fourier series then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space. To illustrate the advantage of the reciprocal-space formulation, we present a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons using a truncated reciprocal-space basis, which is not possible within a real-space formulation.
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