Larsen Ask Hjorth, De Giovannini Umberto, Rubio Angel
Nano-bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Centro de Física de Materiales CSIC-UPV and DIPC, Universidad del País Vasco UPV/EHU, E-20018, Donostia-San Sebastián, Spain,
Top Curr Chem. 2016;368:219-71. doi: 10.1007/128_2014_616.
We present a review of different computational methods to describe time-dependent phenomena in open quantum systems and their extension to a density-functional framework. We focus the discussion on electron emission processes in atoms and molecules addressing excited-state lifetimes and dissipative processes. Initially we analyze the concept of an electronic resonance, a central concept in spectroscopy associated with a metastable state from which an electron eventually escapes (electronic lifetime). Resonances play a fundamental role in many time-dependent molecular phenomena but can be rationalized from a time-independent context in terms of scattering states. We introduce the method of complex scaling, which is used to capture resonant states as localized states in the spirit of usual bound-state methods, and work on its extension to static and time-dependent density-functional theory. In a time-dependent setting, complex scaling can be used to describe excitations in the continuum as well as wave packet dynamics leading to electron emission. This process can also be treated by using open boundary conditions which allow time-dependent simulations of emission processes without artificial reflections at the boundaries (i.e., borders of the simulation box). We compare in detail different schemes to implement open boundaries, namely transparent boundaries using Green functions, and absorbing boundaries in the form of complex absorbing potentials and mask functions. The last two are regularly used together with time-dependent density-functional theory to describe the electron emission dynamics of atoms and molecules. Finally, we discuss approaches to the calculation of energy and angle-resolved time-dependent pump-probe photoelectron spectroscopy of molecular systems.
我们综述了描述开放量子系统中随时间变化现象的不同计算方法及其向密度泛函框架的扩展。我们将讨论重点放在原子和分子中的电子发射过程，涉及激发态寿命和耗散过程。首先，我们分析电子共振的概念，这是光谱学中的一个核心概念，与电子最终从中逃逸的亚稳态相关（电子寿命）。共振在许多随时间变化的分子现象中起着基本作用，但可以从与散射态相关的与时间无关的角度进行合理化解释。我们介绍复标度方法，该方法用于按照常规束缚态方法的思路将共振态捕获为局域态，并致力于将其扩展到静态和含时密度泛函理论。在含时情况下，复标度可用于描述连续统中的激发以及导致电子发射的波包动力学。这个过程也可以通过使用开放边界条件来处理，该条件允许对发射过程进行含时模拟，而不会在边界（即模拟盒的边界）产生人工反射。我们详细比较实现开放边界的不同方案，即使用格林函数的透明边界以及复吸收势和掩码函数形式的吸收边界。后两者经常与含时密度泛函理论一起用于描述原子和分子的电子发射动力学。最后，我们讨论分子系统能量和角分辨含时泵浦 - 探测光电子能谱的计算方法。
