Coherence as an analytic tool of 2D electronic photon-echo spectroscopy: application to vibronic coupling

我们在计算上探索了一种新的二维（2D）光子回波（PE）光谱分析工具-即所谓的跳动图-以便根据这些实验观测值来表征和分类振动耦合。只要在二维PE实验中使用激光脉冲导致所研究的分子系统中相干振荡的激发和检测，就可以用跳动图进行分析。振荡携带激发态性质的信息，而跳动图能够对这些信息进行有效和可靠的分析。与传统的二维PE信号相比，跳动图的主要优点是它们的选择性（每个图选择一个特定的振荡）和灵敏度，即使是非常弱的光学跃迁。该方法显著降低了传统二维PE信号中的增宽和峰重叠，获得了更精确、更详细的信息。在这个项目中，我们使用跳动图来探测振动耦合的起源。振动耦合，即电子自由度和核自由度之间的耦合，可能具有非常不同的物理性质和表现。最著名的例子是势能面交叉和玻恩-奥本海默近似的破坏。电子和核运动的不可分离性可能导致电子和核构型在同一时间尺度上的变化，并且通常负责反应动力学以及电子转移和光保护等基本过程。有许多完善的模型描述了州际交叉。在这里，我们将讨论避免交叉的模型以及通常用于描述锥形交叉点动力学的振动-哈密顿模型。此外，我们还将考虑低聚物中最简单的振动耦合模型：振动二聚体。低聚物中的振动效应对激子输运效率起着重要的作用。在这些系统中，振动运动可能与离域电子激励耦合。该项目的主要思想是根据与光学耦合电子态有关的系统本征态之间的偶极子跃迁强度来表达所考虑的模型系统的特性。这些偶极子直接促成了热图的形成。因此，我们期望观察到所考虑的每种振动耦合模型的典型模式。该项目为利用振动图对振动相互作用进行分类提供了依据。所有考虑的模型都可以进一步扩展和参数化以适应特定的应用。目前，只有很少的实验小组意识到节拍图分析的潜力。我们设想这项研究将鼓励进一步的实验实现。

We explore computationally a new analytic tool of two-dimensional (2D) photon-echo (PE) spectroscopy - so called beating maps - in order to characterize and classify vibronic coupling in terms of these experimental observables. The analysis by means of beating maps is possible whenever the laser pulses employed in a 2D PE experiment lead to excitation and detection of coherent oscillations in a molecular system under study. The oscillations carry information on the nature of the excited states, and the beating maps enable an efficient and reliable analysis of this information. The main advantage of the beating maps as compared to the conventional 2D PE signal is their selectivity (each map selects one particular oscillation) and sensitivity even to very weak optical transitions.As the result, broadening and peak overlaps present in conventional 2D PE signals are significantly reduced, and more precise and detailed information can be obtained.In this project, we employ the beating maps to probe the origin of vibronic coupling. Vibronic coupling, i.e. the coupling between electronic and nuclear degrees of freedom, may have quite distinct physical nature and manifestations. The most well known case is related to crossings of potential-energy surfaces and breakdown of Born-Oppenheimer approximation. The non-separability of electron and nuclear motion may lead to changes in electron and nuclear configurations at the same timescale and is often responsible for reaction dynamics and such fundamental processes as electron transfer and photoprotection. There is a number of well established models describing the state crossings. Here we will address the model of avoided crossing as well as the vibronic-Hamiltonian model commonly employed to describe dynamics at conical intersections. Further, we will also consider the simplest model of vibronic coupling in oligomers: a vibronic dimer. Vibronic effects in oligomers play an important role in the exciton transport efficiency. In these systems, vibrational motion may be coupled to delocalized electronic excitations.The main idea of the project is to express the properties of the considered model systems in terms of dipole transition strengths between the system eigenstates pertaining to optically coupled electronic states. These dipoles contribute directly to the formation of the beating maps. Therefore, we expect to observe specific patterns typical for each model of the vibronic coupling considered.The project provides a basis for classification of vibronic interactions by means of the beating maps. All the models considered can be further extended and parametrized for specific applications. Currently, only very few experimental groups have realized the potential of the beating-maps analysis.We envision that the research will encourage further experimental realizations.