Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, Budapest H-1521, Hungary.
J Chem Phys. 2010 Feb 21;132(7):074103. doi: 10.1063/1.3310288.
The state-specific multireference coupled-cluster (SS-MRCC) ansatz developed by Mukherjee and co-workers [J. Chem. Phys. 110, 6171 (1999)] has been implemented by means of string-based techniques. The implementation is general and allows for using arbitrary complete active spaces of any spin multiplicity and arbitrarily high excitations in the cluster operators. Several test calculations have been performed for single- and multiple-bond dissociations of molecular systems. Our experience shows that convergence problems are encountered when solving the working equations of the SS-MRCC in the case the weight of one or more reference functions tends to take on very small values. This is system specific and cannot yet be handled in a black-box fashion. The problem can be obviated by either dropping all the cluster amplitudes from the corresponding model functions with coefficients below a threshold or by a regularization procedure suggested by Tikhonov or a combination of both. In the current formulation the SS-MRCC is not invariant with respect to transformation of active orbitals among themselves. This feature has been extensively explored to test the degree of accuracy of the computed energies with both pseudocanonical and localized active orbitals. The performance of the method is assessed by comparing the results with the corresponding full configuration interaction (CI) values with the same set of orbitals (correlated and frozen). Relative efficacies of CI methods such as MRCI singles and doubles with the same active space and size-extensivity corrected ones such as MR averaged coupled pair functional and MR averaged quadratic CC have also been studied. Allied full-fledged CC methods have also been employed to see their relative performance vis-à-vis the SS-MRCC. These latter methods are the complete-active-space-inspired single-reference (SR) CC based SS theory and the single-root MR Brillouin-Wigner CC. Our benchmark results indicate that the performance of the SS-MRCC is generally quite good for localized active orbitals. The performance with the pseudocanonical orbitals, however, is sometimes not as satisfactory as for the localized orbitals.
由 Mukherjee 及其同事开发的特定州多参考耦合簇 (SS-MRCC) 假设 [J. Chem. Phys. 110, 6171 (1999)] 已通过基于字符串的技术实现。该实现是通用的，并允许在集群运算符中使用任意自旋多重性的任意完整活动空间和任意高激发。已经针对分子系统的单键和多键离解进行了多次测试计算。我们的经验表明，当在 SS-MRCC 的工作方程求解中，一个或多个参考函数的权重趋于取非常小的值时，会遇到收敛问题。这是特定于系统的，目前无法以黑盒方式处理。可以通过从具有低于阈值的系数的对应模型函数中删除所有集群幅度，或者通过 Tikhonov 建议的正则化过程或两者的组合来避免该问题。在当前的公式中，SS-MRCC 对于自身的活性轨道之间的转换不具有不变性。已经广泛探索了这一特性，以测试用伪规范和本地化的活性轨道计算出的能量的准确性程度。通过将结果与相同轨道（相关和冻结）的相应完全组态相互作用（CI）值进行比较来评估方法的性能。还研究了具有相同活动空间和大小扩展性校正的 CI 方法（如 MRCI 单和双）以及 MR 平均耦合对函数和 MR 平均二次 CC 的相对功效。还使用了 Allied 全功能 CC 方法来观察它们相对于 SS-MRCC 的相对性能。这些后一种方法是基于完整活性空间的单参考（SR）CC 的 SS 理论和单根 MR Brillouin-Wigner CC。我们的基准测试结果表明，对于本地化的活性轨道，SS-MRCC 的性能通常非常好。然而，对于伪规范轨道，性能有时不如本地化轨道令人满意。
