A reciprocal-space formulation of mixed quantum–classical dynamics

We derive a formulation of mixed quantum-classical dynamics for describing electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates terms complex variables. A Fourier series over these then yields reciprocal-space coordinates. Evaluating electron-phonon interaction term through Ehrenfest's theorem, arrive at formalism that is equivalent to mean-field real This equivalence numerically verified Holstein and Peierls models, which find Hellmann-Feynman forces involve momentum derivative contributions addition position commonly seen close presenting proof concept inexpensive modeling low-momentum means truncated basis space, not possible within space formulation.