Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
J Phys Chem A. 2011 Apr 28;115(16):3665-78. doi: 10.1021/jp103536w. Epub 2010 Jun 29.
The improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO-CASCI) method is a simplified CAS self-consistent field (SCF), CASSCF, method. Unlike the CASSCF approach, the IVO-CASCI method does not require iterations beyond an initial SCF calculation, rendering the IVO-CASCI scheme computationally more tractable than the CASSCF method and devoid of the convergence problems that sometimes plague CASSCF calculations as the CAS size increases, while retaining all the essential positive benefits of the CASSCF method. Earlier applications demonstrate that the IVO-CASCI energies are at least as accurate as those from the CASSCF and provide the impetus for our recent development of the analytical derivative procedures that are necessary for a wide applicability of the IVO-CASCI approach. Here we test the ability of the analytic energy gradient IVO-CASCI approach (which can treat both closed- and open-shell molecules of arbitrary spin multiplicity) to compute the equilibrium geometries of four organic radicaloid species, namely, (i) the diradicals trimethylenemethane (TMM), 2,6-pyridyne, and the 2,6-pyridynium cation and (ii) a triradical 1,2,3-tridehydrobenzene (TDB), using various basis sets and different choices for the active space. Although these systems and related molecules have fascinated theoretical chemists for many years, their strong multireference character makes their description quite difficult with most standard many-body approaches. Thus, they provide ideal tests to assess the performance of the IVO-CASCI method. The present work demonstrates consistent agreement with far more expensive benchmark state-of-the-art ab initio calculations and thereby indicates that this new gradient method is able to describe the geometries of various radicaloids very accurately, even when small, but qualitatively correct, reference spaces are used. For example, the IVO-CASCI method leads to a monocyclic structure for the 2,6-isomers of the didehydropyridinium (pyridynium) cation and of didehydropyridine (pyridyne), while SCF and single-reference CCSD computations predict an incorrect bicyclic structure. The IVO-CASCI structures and relative stability for the ground (2)A(1) and excited (2)B(2) states of TDB also accord with the experimentally observed IR spectra and with other highly sophisticated theoretical calculations. The blend of accuracy and reduction in computational cost offered by the present IVO-CASCI analytical gradient method clearly demonstrates that the method provides a practical avenue for studying the geometries of various radicaloid species of different levels of complexity.
改进的虚拟轨道（IVO）完全活性空间（CAS）组态相互作用（IVO-CASCI）方法是一种简化的 CAS 自洽场（SCF）、CASSCF 方法。与 CASSCF 方法不同，IVO-CASCI 方法不需要超出初始 SCF 计算的迭代，使得 IVO-CASCI 方案在计算上比 CASSCF 方法更易于处理，并且没有 CASSCF 计算中有时会出现的收敛问题，因为 CAS 尺寸增加，同时保留了 CASSCF 方法的所有基本积极益处。早期的应用表明，IVO-CASCI 能量至少与 CASSCF 的能量一样准确，并为我们最近开发的分析导数程序提供了动力，这些程序对于广泛应用 IVO-CASCI 方法是必要的。在这里，我们测试了分析能量梯度 IVO-CASCI 方法（可处理任意自旋多重性的闭壳和开壳分子）计算四个有机自由基物种的平衡几何形状的能力，即：（i）双自由基三甲烯甲烷（TMM）、2,6-吡啶和 2,6-吡啶鎓阳离子，以及（ii）三自由基 1,2,3-去氢苯（TDB），使用各种基组和不同的活性空间选择。尽管这些系统和相关分子多年来一直吸引着理论化学家的兴趣，但它们强烈的多参考特征使得用大多数标准多体方法描述它们非常困难。因此，它们提供了评估 IVO-CASCI 方法性能的理想测试。本工作与更昂贵的基准最先进的从头算计算一致，表明这种新的梯度方法能够非常准确地描述各种自由基的几何形状，即使使用较小但定性正确的参考空间也是如此。例如，IVO-CASCI 方法导致 2,6-异构体的二氢吡啶鎓（吡啶鎓）阳离子和二氢吡啶的单环结构，而 SCF 和单参考 CCSD 计算预测了不正确的双环结构。TDB 的基态（2）A（1）和激发态（2）B（2）的 IVO-CASCI 结构和相对稳定性也与实验观察到的 IR 光谱和其他高度复杂的理论计算一致。本研究提供的 IVO-CASCI 分析梯度方法的准确性和计算成本降低的结合，清楚地表明该方法为研究不同复杂程度的各种自由基物种的几何形状提供了一种实用途径。
