Local Coupled Cluster response for open-shell systems

计算大分子的电子激发态的性质在物理、化学和生物学的许多应用中是非常重要的。在之前的项目中，我们成功地在局部CC2响应水平上实现了封闭壳分子的基态和激发态和三重态的分析核能梯度。这允许激发态几何优化在理论水平上的系统的叶绿素-a的大小。此外，我们还设计了一种高效耦合簇响应方法来计算电离势（IPs）。本项目延续的目标是将该方法扩展到开放shell系统。我们特别关注大自由基的激发态。它们通常在光化学和光催化过程中作为中间体发挥重要作用，并且可以通过光谱方法检测。在本项目中，我们打算从两个方面来实现这一目标，即(i)通过传统的基于自旋轨道的开壳耦合簇响应理论，以及（ii）通过ip的耦合响应理论。在后一种情况下，自由基的激发能计算为两个IPs的差。参考波函数为具有N+1电子的相关闭壳分子的波函数，表示自由基的电离态为纯重态（没有任何自旋污染）。我们打算实现激发能，以及跃迁强度，一阶性质，和分析核梯度的基态和激发态的自由基。局部近似和密度拟合将被用来大大减少计算成本，并以这种方式使方法适用于大型系统。本课题开发的程序对研究光化学和光催化反应中的自由基中间体具有重要的指导意义。

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.