Samanta Pradipta Kumar, Mukherjee Debashis, Hanauer Matthias, Köhn Andreas
Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700 032, India.
Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany.
J Chem Phys. 2014 Apr 7;140(13):134108. doi: 10.1063/1.4869719.
In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Köhn [J. Chem. Phys. 134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linear-response formalism to the time-averaged ic-MRCC Lagrangian leads to unphysical second-order poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical implementation of the method, we adopt a Tamm-Dancoff-type approximation and neglect these couplings. This approximation is also consistent with an equation-of-motion based derivation, which neglects these couplings right from the start. We have implemented the linear-response approach in the ic-MRCC singles-and-doubles framework and applied our method to calculate excitation energies for a number of molecules ranging from CH2 to p-benzyne and conjugated polyenes (up to octatetraene). The computed excitation energies are found to be very accurate, even for the notoriously difficult case of doubly excited states. The ic-MRCC-LR theory is also applicable to systems with open-shell ground-state wavefunctions and is by construction not biased towards a particular reference determinant. We have also compared the linear-response approach to the computation of energy differences by direct state-specific ic-MRCC calculations. We finally compare to Mk-MRCC-LR theory for which spurious roots have been reported [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044116 (2012)], being due to the use of sufficiency conditions to solve the Mk-MRCC equations. No such problem is present in ic-MRCC-LR theory.
在本文中，我们已经针对Hanauer和Köhn [《化学物理杂志》134, 204211 (2011)] 所描述的内收缩多参考耦合簇（ic-MRCC）理论的变体，制定并实现了线性响应（LR）理论，用于计算相对于具有明显多参考特征的基态的激发能。我们发现，将线性响应形式直接应用于时间平均的ic-MRCC拉格朗日量会导致非物理的二阶极点。然而，只要内收缩近似本身合理，导致这种行为的耦合矩阵元就被证明是可以忽略的。因此，对于该方法的数值实现，我们采用了Tamm-Dancoff型近似并忽略这些耦合。这种近似也与基于运动方程的推导一致，该推导从一开始就忽略了这些耦合。我们已经在ic-MRCC单双激发框架中实现了线性响应方法，并将我们的方法应用于计算从CH₂到对苯炔和共轭多烯（直至八乙烯）等多种分子的激发能。计算得到的激发能被发现非常准确，即使对于双激发态这个 notoriously difficult 的情况也是如此。ic-MRCC-LR理论也适用于具有开壳层基态波函数的系统，并且从构建上就不会偏向于特定的参考行列式。我们还将线性响应方法与通过直接特定状态的ic-MRCC计算能量差的方法进行了比较。我们最终将其与Mk-MRCC-LR理论进行了比较，对于后者已经报道了虚假根 [T.-C. Jagau和J. Gauss，《化学物理杂志》137, 044116 (2012)]，这是由于使用充分条件来求解Mk-MRCC方程所致。在ic-MRCC-LR理论中不存在这样的问题。
