Graf Nora K, Friese Daniel H, Winter Nina O C, Hättig Christof
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44801 Bochum, Germany.
Centre for Theoretical and Computational Chemistry CTCC, University of Tromsø, N-9037 Tromsø, Norway.
J Chem Phys. 2015 Dec 28;143(24):244108. doi: 10.1063/1.4937944.
We report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D∞). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data.
我们报告了一种针对近似耦合簇单双激发模型CC2的静态和频率相关激发态极化率的实现方法，将其作为激发态准能量拉格朗日量的解析二阶导数。通过为特征向量的归一化和相位纳入适当条件，避免了发散的久期项。这导致在与未微扰特征向量正交的子空间中的响应方程。展示了如何在不存储特征向量的双激发部分的情况下求解这些投影方程。通过利用单位分解近似和数值拉普拉斯变换，可以保持RI - CC2的主内存需求随系统大小的二次缩放。这使得能够在几天内在单个计算节点上对具有近2500个基函数的大分子（例如直至并十苯的线性多并苯）计算激发态极化率。对于一组有测量值作为参考数据的测试分子，我们将轨道弛豫和未弛豫的CC2方法与实验进行比较以验证其准确性。该方法可以很容易地扩展到其他响应方法，特别是CIS(D∞)。在轨道弛豫的情况下，后者给出的结果与CC2值相差在百分之几以内，而耦合簇单激发结果通常与轨道弛豫的CC2和实验参考数据相差约20%。
