Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.
J Chem Phys. 2017 Mar 28;146(12):124101. doi: 10.1063/1.4978581.
Vibrational configuration interaction theory is a common method for calculating vibrational levels and associated IR and Raman spectra of small and medium-sized molecules. When combined with appropriate configuration selection procedures, the method allows the treatment of configuration spaces with up to 10 configurations. In general, this approach pursues the construction of the eigenstates with significant contributions of physically relevant configurations. The corresponding eigenfunctions are evaluated in the subspace of selected configurations. However, it can easily reach the dimension which is not tractable for conventional eigenvalue solvers. Although Davidson and Lanczos methods are the methods of choice for calculating exterior eigenvalues, they usually fall into stagnation when applied to interior states. The latter are commonly treated by the Jacobi-Davidson method. This approach in conjunction with matrix factorization for solving the correction equation (CE) is prohibitive for larger problems, and it has limited efficiency if the solution of the CE is based on Krylov's subspace algorithms. We propose an iterative subspace method that targets the eigenvectors with significant contributions to a given reference vector and is based on the optimality condition for the residual norm corresponding to the error in the solution vector. The subspace extraction and expansion are modified according to these principles which allow very efficient calculation of interior vibrational states with a strong multireference character in different vibrational structure problems. The convergence behavior of the method and its performance in comparison with the aforementioned algorithms are investigated in a set of benchmark calculations.
振动组态相互作用理论是计算中小分子振动能级和相关红外和拉曼光谱的常用方法。当与适当的组态选择程序结合使用时，该方法允许处理多达 10 个组态的组态空间。通常，这种方法旨在构建具有物理相关组态显著贡献的本征态。相应的本征函数在选定组态的子空间中进行评估。然而，它很容易达到常规特征值求解器难以处理的维度。尽管戴维森和兰茨方法是计算外特征值的首选方法，但它们在应用于内部状态时通常会陷入停滞。后者通常通过雅可比-戴维森方法进行处理。对于较大的问题，这种结合矩阵分解求解校正方程 (CE) 的方法是不可行的，如果 CE 的解基于克里洛夫子空间算法，则其效率有限。我们提出了一种迭代子空间方法，该方法针对给定参考向量具有显著贡献的特征向量，并基于对应于解向量误差的残差范数的最优性条件。根据这些原则对子空间提取和扩展进行修改，从而可以在不同的振动结构问题中非常有效地计算具有强多参考特征的内部振动状态。在一组基准计算中研究了该方法的收敛行为及其与上述算法的性能比较。
