The performance of different approximate algorithms for computing anharmonic features in vibrational spectra is analyzed and compared on model and more realistic systems that present relevant nuclear quantum effects. The methods considered combine approximate sampling of the quantum thermal distribution with classical time propagation and include Matsubara dynamics, path integral dynamics approaches, linearized initial value representation, and the recently introduced adaptive quantum thermal bath. A perturbative analysis of these different methods enables us to account for the observed numerical performance on prototypes for overtones and combination bands and to draw qualitatively correct trends for the numerical results obtained for Fermi resonances. Our results prove that the unequal performances of these approaches often derive from the method employed to sample initial conditions and not, as usually assumed, from the lack of coherence in the time propagation. Furthermore, as confirmed by the analysis reported in Benson and Althorpe, J. Chem. Phys. 130, 194510 (2021), we demonstrate, both via the perturbative approach and numerically, that path integral dynamics methods fail to reproduce the intensities of these anharmonic features and follow purely classical trends with respect to their temperature behavior. Finally, the remarkably accurate performance of the adaptive quantum thermal bath approach is documented and motivated.

中文翻译：

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通过基于轨迹的量子动力学的非谐波光谱特征：动力学和采样之间相互作用的微扰分析

在模型和呈现相关核量子效应的更现实的系统上，分析和比较了用于计算振动谱中非谐特征的不同近似算法的性能。所考虑的方法将量子热分布的近似采样与经典时间传播相结合，包括 Matsubara 动力学、路径积分动力学方法、线性化初始值表示和最近引入的自适应量子热浴。对这些不同方法的微扰分析使我们能够解释在泛音和组合带原型上观察到的数值性能，并为费米共振获得的数值结果绘制定性正确的趋势。我们的结果证明，这些方法的性能不均通常源自用于对初始条件进行采样的方法，而不是通常假设的时间传播缺乏一致性。此外，正如 Benson 和 Althorpe, J. Chem. 所报道的分析所证实的那样。物理。在 130 , 194510 (2021) 中，我们通过微扰方法和数值证明，路径积分动力学方法无法再现这些非谐特征的强度，并且在其温度行为方面完全遵循经典趋势。最后，记录并激发了自适应量子热浴方法的非常准确的性能。