密度拟合近似下变分双电子约化密度矩阵方法的能量梯度分析
Analytic energy gradients for variational two-electron reduced-density matrix methods within the density-fitting approximation
摘要：
采用密度拟合（DF）方法对双电子排斥积分进行近似，得到了变分双电子约化密度矩阵驱动的完全活性空间自洽场（v2 RDM-CASSCF）的能量梯度解析解. DF近似显著降低了v2 RDM-CASSCF梯度评估的计算成本，在浮点运算数量和内存需求方面，使几何优化能够在比以前在该理论水平上考虑的大得多的化学系统上进行[E. Maradzike等人，化学理论计算杂志，2017，13，4113-4122]。使用一组25个封闭和开放壳层小分子评估v2 RDM-CASSCF计算平衡几何形状和谐波振动频率的功效。从v2 RDM-CASSCF的平衡键长不同于从组态相互作用驱动的CASSCF（CI-CASSCF）获得的0.62 pm和0.05 pm，取决于是否从v2 RDM-CASSCF的最佳约化密度矩阵满足两粒子N-可表示性条件（PQG）或PQG加部分三粒子条件（PQG+T2），分别。谐波振动频率，这是通过有限差分的v2 RDM-CASSCF分析能量梯度，同样表明，v2 RDM-和CI-CASSCF之间的定量协议需要考虑部分三粒子N-可表示性条件。最后，优化的几何形状得到的最低能量的单重态和三重态的线性多并苯系列高达十二并苯（C50 H28），在这种情况下，活性空间是由50个电子在50个轨道。外推到无限长线性并苯分子的v2 RDM-CASSCF单重态-三重态能隙为7.8 kcal/mol
英文摘要：
Analytic energy gradients are presented for a variational two-electron reduced-density-matrix-driven complete active space self-consistent field (v2RDM-CASSCF) procedure that employs the density-fitting (DF) approximation to the two-electron repulsion integrals. The DF approximation significantly reduces the computational cost of v2RDM-CASSCF gradient evaluation, in terms of both the number of floating-point operations and memory requirements, enabling geometry optimizations on much larger chemical systems than could previously be considered at the this level of theory [E. Maradzike et al., J. Chem. Theory Comput., 2017, 13, 4113-4122]. The efficacy of v2RDM-CASSCF for computing equilibrium geometries and harmonic vibrational frequencies is assessed using a set of 25 small closed- and open-shell molecules. Equilibrium bond lengths from v2RDM-CASSCF differ from those obtained from configuration-interaction-driven CASSCF (CI-CASSCF) by 0.62 pm and 0.05 pm, depending on whether the optimal reduced-density matrices from v2RDM-CASSCF satisfy two-particle N-representability conditions (PQG) or PQG plus partial three-particle conditions (PQG+T2), respectively. Harmonic vibrational frequencies, which are obtained by finite differences of v2RDM-CASSCF analytic energy gradients, similarly demonstrate that quantitative agreement between v2RDM- and CI-CASSCF requires the consideration of partial three-particle N-representability conditions. Lastly, optimized geometries are obtained for the lowest-energy singlet and triplet states of the linear polyacene series up to dodecacene (C50H28), in which case the active space is comprised of 50 electrons in 50 orbitals. The v2RDM-CASSCF singlet-triplet energy gap extrapolated to an infinitely-long linear acene molecule is found to be 7.8 kcal/mol
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