Neuscamman Eric, Yanai Takeshi, Chan Garnet Kin-Lic
Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14850, USA.
J Chem Phys. 2009 Mar 28;130(12):124102. doi: 10.1063/1.3086932.
Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.
正则变换（CT）理论为多参考系中的动态关联提供了一种严格的尺寸可扩展性描述，其精度优于完全活性空间二阶微扰理论，且成本标度低于该理论。在此，我们通过研究（i）在有效哈密顿量中应用于二次而非线性阶次的对易子近似，以及（ii）在算符和密度矩阵分解中纳入三体约化密度矩阵，来扩展我们之前的理论。当与单行列式参考一起使用时，二次对易子近似提高了CT的精度，弥补了单参考线性CT理论相对于单双激发耦合簇理论之前的形式上的劣势。对BH和HF结合曲线的计算证实了这一改进。在多参考系中，三体约化密度矩阵提高了CT理论的整体精度。对H₂O和N₂结合曲线的测试结果与昂贵的最新多参考方法（如多参考戴维森校正组态相互作用（MRCI+Q）、平均耦合对函数和平均二次耦合簇理论）具有高度竞争力。
