Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.
J Chem Phys. 2011 Oct 14;135(14):144116. doi: 10.1063/1.3641642.
An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo̸ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.
描述了一种高效的局部耦合簇方法，该方法具有单激发和双激发算符以及三激发微扰处理[DF-LCCSD(T)]。所有所需的双电子积分都使用密度拟合近似来评估。与标准积分直接法相比，这些近似对精度的影响可以忽略不计，但计算工作量减少了 1-2 个数量级。激发被限制在非正交虚拟轨道的局部子集（域逼近）中。根据距离标准，相关电子对被分类为强、近、弱和非常远的对。只有强对（通常占相关能量的 90%以上）在 LCCSD 处理中进行优化。其余的近对和弱对由 LMP2（局部二阶 Mo̸ller-Plesset 微扰理论）近似；非常远的对被忽略。结果表明，通过在 LCCSD 方程中以及在三激发微扰处理中包含近对 LMP2 幅度，可以显著提高该方案的准确性。使用这种波函数假设，双电子积分的评估和变换与分子大小呈立方关系。如果激活局部密度拟合近似，则将其减少到线性比例。LCCSD 迭代呈二次方比例，但通过忽略一些涉及单激发收缩的项，可以实现线性比例。使用各种近似系统地测试了该方法的准确性和效率，并展示了多达 90 个原子和 2636 个基函数的分子的计算结果。
