Local Coupled Cluster response for open-shell systems

大分子电子激发态性质的计算在物理、化学、生物等领域有着重要的应用。在上一个项目中，我们成功地在局域CC2响应水平上实现了闭壳分子基态、激发态、单态和三态的解析核能量梯度。这允许在理论水平上对叶绿素-a的大小的系统进行激发态几何优化。此外，我们设计了一系列有效的耦合团簇响应方法来计算电离势(IP)。本项目的目标是将该方法扩展到开壳系统。特别是，我们的目标是大自由基的激发态。这些化合物通常在光化学和光催化过程中作为中间体发挥重要作用，可以通过光谱方法进行检测。在本项目中，我们打算从两个方面来探讨这一目标，即：(I)用传统的基于自旋轨道的开壳耦合团簇响应理论；(Ii)用激发态的耦合响应理论。在后一种情况下，自由基的激发能被计算为两个IP的差值。参考波函数是具有N1电子的闭壳分子的参考波函数，代表自由基态的电离态是纯双重态(没有任何自旋污染)。我们打算实现自由基态和激发态的激发能、跃迁强度、一阶性质和解析核梯度。局部逼近和密度拟合将被用来极大地降低计算成本，从而使该方法适用于大系统。我们认为，在这个项目的过程中开发的程序将对研究光化学反应和光催化反应中的自由基中间体非常有用。

The calculation of properties of electronically excited states of large molecules is of great importance for many applications in physics, chemistry, and biology. In the previous project we successfully implemented analytical nuclear energy gradients for ground and excited singlet and triplet states of closed-shell molecules at the level of local CC2 response. This allows for excited state geometry optimizations at that level of theory for systems of the size of chlorophyllide-a. Furthermore, we devised a hierarchy of efficient coupled cluster response methods for calculating ionization potentials (IPs).The goal of this project continuation is the extension of this methodology to open shell systems. In particular we aim at excited states of large radicals. These often play an important role as intermediates in photochemical and photocatalytical processes and can be detected by means of spectroscopical methods. In the project we intend to approach this goal from two sides, i.e., (i) by traditional spin orbital based open-shell coupled cluster response theory, and (ii) by coupled response theory for IPs. In the latter case the excitation energies of the radical are computed as differences of two IPs. The reference wavefunction is that of the related closed-shell molecule with N+1 electrons, and the ionized states representing the radical are obtained as pure doublet states (without any spin contamination).We intend to implement excitation energies, as well as transition strengths, first-order properties, and analytical nuclear gradients for ground and excited states of radicals. Local approximations and density fitting will be utilized to dramatically reduce the computational cost and, in this way, to make the methods applicable to large systems. We think that the programs developed in the course of this project will be very useful to study radical intermediates in photochemical and photocatalytical reactions.