For a molecule moving near a single metal surface at equilibrium, following von Oppen and coworkers [N. Bode, S. V. Kusminskiy, R. Egger, and F. von Oppen, Beilstein J. Nanotechnol. 3, 144 (2012)] and using a nonequilibrium Green's-function (NEGF) approach, we derive a very general form of electronic friction that includes non-Condon effects. We then demonstrate that the resulting NEGF friction tensor agrees exactly with the Head-Gordon–Tully model, provided that finite temperature effects are incorporated correctly. The present results are in agreement with our recent claim that there is only one universal electronic friction tensor arising from the Born-Oppenheimer approximation [W. Dou, G. Miao, and J. E. Subotnik, Phys. Rev. Lett. 119, 046001 (2017)].

中文翻译：

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电子摩擦的普遍性：平衡时冯·奥本的非平衡格林函数方法和Head-Gordon-Tully模型的等价性

对于一个在平衡状态下靠近单个金属表面移动的分子，遵循冯·奥本（von Oppen）及其同事[N. Bode，SV Kusminskiy，R.Egger和F.von Oppen，Beilstein J.Nanotechnol 。3，144（2012） ]，并使用非平衡Green's函数（NEGF）的方法，我们得出电子摩擦的一个非常普遍的形式，其包括非康登效果。然后我们证明，只要正确地结合了有限的温度效应，所得的NEGF摩擦张量就与Head-Gordon-Tully模型完全吻合。目前的结果是与我们最近的要求一致认为只有一个普遍的玻恩-奥本海默近似引起的[W.电子摩擦张量 Dou G. Miao和JE Subotnik，物理学。莱特牧师 119，046001（2017） ]。