Nonadiabatic mixed quantum–classical (NA-MQC) dynamics methods form a class of computational theoretical approaches in quantum chemistry tailored to investigate the time evolution of nonadiabatic phenomena in molecules and supramolecular assemblies. NA-MQC is characterized by a partition of the molecular system into two subsystems: one to be treated quantum mechanically (usually but not restricted to electrons) and another to be dealt with classically (nuclei). The two subsystems are connected through nonadiabatic couplings terms to enforce self-consistency. A local approximation underlies the classical subsystem, implying that direct dynamics can be simulated, without needing precomputed potential energy surfaces. The NA-MQC split allows reducing computational costs, enabling the treatment of realistic molecular systems in diverse fields. Starting from the three most well-established methods—mean-field Ehrenfest, trajectory surface hopping, and multiple spawning—this review focuses on the NA-MQC dynamics methods and programs developed in the last 10 years. It stresses the relations between approaches and their domains of application. The electronic structure methods most commonly used together with NA-MQC dynamics are reviewed as well. The accuracy and precision of NA-MQC simulations are critically discussed, and general guidelines to choose an adequate method for each application are delivered.

中文翻译：

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非绝热混合量子-经典动力学的最新进展和观点

非绝热混合量子经典（NA-MQC）动力学方法形成了一类量子化学计算理论方法，旨在研究分子和超分子组装物中非绝热现象的时间演化。NA-MQC的特征是将分子系统划分为两个子系统：一个被机械地量子处理（通常但不限于电子），另一个被经典处理（原子核）。这两个子系统通过非绝热耦合项进行连接以增强自洽性。局部逼近是经典子系统的基础，这意味着可以模拟直接动力学，而无需预先计算的势能面。NA-MQC拆分可降低计算成本，从而能够处理各个领域中的实际分子系统。从三种最完善的方法（平均场Ehrenfest，轨迹表面跳变和多重生成）开始，本文着眼于过去10年中开发的NA-MQC动力学方法和程序。它强调了方法及其应用领域之间的关系。还回顾了最常与NA-MQC动力学一起使用的电子结构方法。严格讨论了NA-MQC模拟的准确性和精确性，并提供了针对每种应用选择适当方法的一般准则。还回顾了最常与NA-MQC动力学一起使用的电子结构方法。严格讨论了NA-MQC模拟的准确性和精确性，并提供了针对每种应用选择适当方法的一般准则。还回顾了最常与NA-MQC动力学一起使用的电子结构方法。严格讨论了NA-MQC模拟的准确性和精确性，并提供了针对每种应用选择适当方法的一般准则。