Department of Chemistry, University of California Berkeley, California 94720, USA.
J Chem Phys. 2012 Feb 7;136(5):054113. doi: 10.1063/1.3679658.
Theory and implementation of the analytical nuclear gradient is presented for orbital optimized scaled opposite-spin perturbation theory (O2). Evaluation of the O2 analytical gradient scales with the 4th power of molecular size, like the O2 energy. Since the O2 method permits optimization of the orbitals in the presence of wavefunction-based electron correlation, it is suitable for problems where correlation effects determine the competition between localization and delocalization of an odd electron, or hole. One such problem is the description of a neutral soliton defect on an all-trans polyacetylene chain with an odd number of carbon atoms. We show that the results of the O2 method compare well to benchmark values for small polyenyl radicals. O2 is also efficient enough to be applied to longer chains where benchmark coupled cluster methods are unfeasible. For C(41)H(43), unrestricted orbital O2 calculations yield a soliton length of about 9 carbon atoms, while other unrestricted orbital methods such as Hartree-Fock, and the B3LYP and ωB97X-D density functionals, delocalize the soliton defect over the entire chain. The O2 result is about half the width inferred experimentally.
给出了轨道优化比例相反自旋微扰理论（O2）的分析核梯度的理论和实现。O2 分析梯度的评估与分子尺寸的 4 次方成正比，与 O2 能量相同。由于 O2 方法允许在基于波函数的电子相关存在的情况下优化轨道，因此它适用于关联效应决定奇数电子或空穴的局域化和离域化竞争的问题。这样的问题之一是描述具有奇数个碳原子的全反式聚乙炔链上的中性孤子缺陷。我们表明，O2 方法的结果与小聚烯基自由基的基准值很好地吻合。O2 也足够高效，可以应用于基准耦合簇方法不可行的更长链。对于 C(41)H(43)，非限制轨道 O2 计算得到孤子长度约为 9 个碳原子，而其他非限制轨道方法，如 Hartree-Fock 和 B3LYP 和 ωB97X-D 密度泛函，则将孤子缺陷离域到整个链上。O2 的结果大约是实验推断宽度的一半。
