Department of Chemistry, University at Buffalo, State University of New York , Buffalo, New York 14260-3000, United States.
Acc Chem Res. 2014 Aug 19;47(8):2592-602. doi: 10.1021/ar500171t. Epub 2014 Jun 26.
Kohn-Sham theory (KST) is the "workhorse" of numerical quantum chemistry. This is particularly true for first-principles calculations of ground- and excited-state properties for larger systems, including electronic spectra, electronic dynamic and static linear and higher order response properties (including nonlinear optical (NLO) properties), conformational or dynamic averaging of spectra and response properties, or properties that are affected by the coupling of electron and nuclear motion. This Account explores the sometimes dramatic impact of the delocalization error (DE) and possible benefits from the use of long-range corrections (LC) and "tuning" of functionals in KST calculations of molecular ground-state and response properties. Tuning refers to a nonempirical molecule-specific determination of adjustable parameters in functionals to satisfy known exact conditions, for instance, that the energy of the highest occupied molecular orbital (HOMO) should be equal to the negative vertical ionization potential (IP) or that the energy as a function of fractional electron numbers should afford straight-line segments. The presentation is given from the viewpoint of a chemist interested in computations of a variety of molecular optical and spectroscopic properties and of a theoretician developing methods for computing such properties with KST. In recent years, the use of LC functionals, functional tuning, and quantifying the DE explicitly have provided valuable insight regarding the performance of KST for molecular properties. We discuss a number of different molecular properties, with examples from recent studies from our laboratory and related literature. The selected properties probe different aspects of molecular electronic structure. Electric field gradients and hyperfine coupling constants can be exquisitely sensitive to the DE because it affects the ground-state electron density and spin density distributions. For π-conjugated molecules, it is shown how the DE manifests itself either in too strong or too weak delocalization of localized molecular orbitals (LMOs). Optical rotation is an electric-magnetic linear response property that is calculated in a similar fashion as the electric polarizability, but it is more sensitive to approximations and can benefit greatly from tuning and small DE. Hyperpolarizabilities of π-conjugated "push-pull" systems are examples of NLO properties that can be greatly improved by tuning of range-separated exchange (RSE) functionals, in part due to improved charge-transfer excitation energies. On-going work on band gap predictions is also mentioned. The findings may provide clues for future improvements of KST because different molecular properties exhibit varying sensitivity to approximations in the electronic structure model. The utility of analyzing molecular properties and the impact of the DE in terms of LMOs, representing "chemist's orbitals" such as individual lone pairs and bonds, is highlighted.
Kohn-Sham 理论（KST）是数值量子化学的“主力军”。对于较大系统的基态和激发态性质的第一性原理计算，特别是对于电子光谱、电子动态和静态线性以及更高阶响应性质（包括非线性光学（NLO）性质）、光谱和响应性质的构象或动态平均，或受电子和核运动耦合影响的性质，更是如此。本专题探讨了在 KST 计算分子基态和响应性质时，离域误差（DE）的影响有时非常显著，以及使用长程校正（LC）和“调谐”泛函的可能益处。调谐是指针对特定分子的非经验确定可调参数，以满足已知的精确条件，例如，最高占据分子轨道（HOMO）的能量应等于负垂直电离势（IP），或者作为分数电子数的函数的能量应提供直线段。本报告从对各种分子光学和光谱性质计算感兴趣的化学家以及开发使用 KST 计算此类性质的方法的理论家的角度给出。近年来，LC 泛函的使用、泛函调谐以及明确量化 DE 为 KST 对分子性质的性能提供了有价值的见解。我们讨论了许多不同的分子性质，其中包括来自我们实验室的最新研究和相关文献的例子。所选性质探测分子电子结构的不同方面。电场梯度和超精细耦合常数可能对 DE 非常敏感，因为它会影响基态电子密度和自旋密度分布。对于π共轭分子，我们展示了 DE 如何表现为局域分子轨道（LMO）的过度离域或离域不足。旋光率是一种电磁线性响应性质，其计算方式与极化率类似，但它对近似的敏感性更高，并且可以从调谐和较小的 DE 中大大受益。π共轭“推挽”系统的超极化率是 NLO 性质的示例，通过调谐范围分离交换（RSE）泛函可以大大提高其性能，部分原因是电荷转移激发能得到了改善。还提到了正在进行的带隙预测工作。不同的分子性质对电子结构模型中的近似表现出不同的敏感性，这一发现可能为未来改进 KST 提供线索。分析分子性质以及 DE 对代表“化学家轨道”（如单个孤对和键）的 LMO 的影响的效用被强调。
