Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.
J Phys Chem A. 2013 Jul 25;117(29):5970-80. doi: 10.1021/jp311668r. Epub 2013 Feb 15.
We present a mixed quantum-classical simulation approach to calculate two-dimensional spectra of coupled two-level electronic model systems. We include the change in potential energy of the classical system due to transitions in the quantum system using the Ehrenfest method. We study how this feedback of the quantum system on the classical system influences the shape of two-dimensional spectra. We show that the feedback leads to the expected Stokes shift of the energy levels in the quantum system. This subsequently leads to changes in the population transfer between quantum sites, which in turn influence the intensities of the peaks in two-dimensional spectra. The obtained spectra are compared with spectra calculated using the Hierarchical Equations of Motion method which is exact. While the spectra match perfectly for short waiting times, clear differences are found for longer waiting times. This is attributed to a violation of detailed balance between the quantum states in the Ehrenfest method. The energy of the total quantum-classical system however does obey a Boltzmann distribution, when coupled to a stochastic heat bath.
我们提出了一种混合量子经典模拟方法来计算耦合双能级电子模型系统的二维谱。我们使用 Ehrenfest 方法包括由于量子系统中的跃迁而导致的经典系统势能的变化。我们研究了量子系统对经典系统的这种反馈如何影响二维谱的形状。我们表明，这种反馈导致量子系统中能级的预期斯托克斯位移。这继而导致量子点之间的粒子数转移的变化，这又反过来影响二维谱中的峰的强度。所得到的谱与使用严格的层次运动方程方法计算的谱进行了比较。虽然在短等待时间下，谱完全匹配，但在较长等待时间下，会发现明显的差异。这归因于 Ehrenfest 方法中量子态之间的详细平衡的违反。然而，当与随机热浴耦合时，总量子经典系统的能量确实服从玻尔兹曼分布。
