非绝热分子动力学的量子路径模拟

基于近期发展的经典-量子混合模拟非绝热分子动力学的量子路径方案,本文对5个典型势能面模型进行了模拟,包括单交叉模型、双交叉模型、拓展耦合模型、哑铃模型以及双弓模型.由于难以在严格意义上得到退相干速率,数值模拟中,我们比较了三个不同的退相干速率公式,包括冻结高斯波包近似退相干速率、能量分辨速率以及力分辨速率.在模拟过程中,我们恰当地处理了势能面跳跃时的能量守恒和力的反向问题.通过与全量子动力学模拟的精确结果进行对比发现,对于结构较简单的势能面模型,三种退相干速率都能得到较好的结果;然而对于较复杂的势能面模型,由于复杂量子干涉的原因,与其他混合经典-量子动力学方案类似,量子路径方案仍然难以得到较准确的结果.如何发展更加有效的混合经典-量子模拟方案,是未来研究的重要课题.

Quantum trajectory simulation for nonadiabatic molecular dynamics

The mixed quantum-classical (MQC) molecular dynamics (MD) approaches are extremely important in practice since, with the increase of atomic degrees of freedom, a full quantum mechanical evaluation for molecular dynamics would quickly become intractable. Moreover, in some cases, the nonadiabatic effects are of crucial importance in the proximity of conical intersection of potential energy surfaces (PESs), where the energy separation between different PESs becomes comparable to the nonadiabatic coupling. In the past decades, there has been great interest in developing and improving various nonadiabatic MQC-MD protocols. The widely known nonadiabatic MD proposals include the so-called “Ehrenfest” or “time-dependent-Hartree mean-field” approach, the “trajectory surface-hopping” method, and their mixed scheme. Among the trajectory-based surface hopping methods, the most popular one is Tully's fewest switches surface hopping approach. In this approach, the nonadiabatic dynamics is treated by allowing hops from one PES to another, with the hopping probability determined by a certain artificial hopping algorithm. In our present work, we extend the study of a recent work on the nonadiabatic MQC-MD scheme, which is based on a view that the nonadiabatic MQC-MD actually implies an effective quantum measurement on the electronic states by the classical motion of atoms. The new protocol, say, the quantum trajectory (QT) approach, provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also connects two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. In our present study, we implement further the QT approach to simulate several typical potential-surface models, i.e., including the single avoided crossing, dual avoided crossing, extended coupling, dumbbell and double arch potentials. In particular, we simulate and compare three decoherence rates, which are from different physical considerations, i.e., the frozen Gaussian approximation, energy discrimination and force discrimination. We also design simulation algorithms to properly account for the energy conservation and force direction change associated with the surface hopping. In most cases, we find that the QT results are in good agreement with those from the full quantum dynamics, which is insensitive to the specific form of the decoherence rate. But for the model involving strong quantum interference, like other nonadiabatic MQC-MD schemes, the QT approach cannot give desirable results. Developing better method should be useful for future investigations in this research area.