Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
J Chem Phys. 2011 Jan 21;134(3):034111. doi: 10.1063/1.3526298.
Photoexcited radical reactions are critical to processes in both nature and materials, and yet they can be challenging for electronic structure methods due to the presence of strong electron correlation. Reduced-density-matrix (RDM) methods, based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) for the two-electron RDM (2-RDM), are examined for studying the strongly correlated mechanisms of these reactions with application to the electrocyclic interconversion of allyl and cyclopropyl radicals. We combine recent extensions of the ACSE to excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary spin states [A. E. Rothman, J. J. Foley IV, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. The ACSE predicts that the ground-state ring closure of the allyl radical has a high 52.5 kcal/mol activation energy that is consistent with experimental data, while the closure of an excited allyl radical can occur by disrotatory and conrotatory pathways whose transition states are essentially barrierless. Comparisons are made with multireference second- and third-order perturbation theories and multireference configuration interaction. While predicted energy differences do not vary greatly between methods, the ACSE appears to improve these differences when they involve a strongly and a weakly correlated radical by capturing a greater share of single-reference correlation that increases the stability of the weakly correlated radicals. For example, the ACSE predicts a -39.6 kcal/mol conversion of the excited allyl radical to the ground-state cyclopropyl radical in comparison to the -32.6 to -37.3 kcal/mol conversions predicted by multireference methods. In addition, the ACSE reduces the computational scaling with the number of strongly correlated orbitals from exponential (traditional multireference methods) to quadratic. Computed ground- and excited-state 2-RDMs are nearly N-representable.
光激发自由基反应对自然和材料过程至关重要，但由于存在强电子相关，它们可能对电子结构方法具有挑战性。基于求解双电子密度矩阵（2-RDM）的反厄米特约化薛定谔方程（ACSE）的约化密度矩阵（RDM）方法，用于研究这些反应的强关联机制，并应用于烯丙基和环丙基自由基的电环化互变。我们结合了最近对激发态的 ACSE 扩展[G. Gidofalvi 和 D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)]和任意自旋态[A. E. Rothman, J. J. Foley IV, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]。ACSE 预测，烯丙基自由基的基态环闭具有高达 52.5 kcal/mol 的高活化能，这与实验数据一致，而激发态烯丙基自由基的环闭可以通过反式和顺式途径发生，其过渡态基本上是无势垒的。与多参考二阶和三阶微扰理论和多参考组态相互作用进行了比较。虽然预测的能量差异在方法之间没有很大差异，但 ACSE 似乎通过捕获更大比例的单参考相关来改善涉及强相关和弱相关自由基的差异，从而增加弱相关自由基的稳定性。例如，ACSE 预测激发态烯丙基自由基转化为基态环丙基自由基的能量为-39.6 kcal/mol，而多参考方法预测的转化率为-32.6 至-37.3 kcal/mol。此外，ACSE 将与强相关轨道数量的计算缩放从指数（传统多参考方法）降低到二次。计算的基态和激发态 2-RDM 几乎是 N 可表示的。
