Cembran Alessandro, Song Lingchun, Mo Yirong, Gao Jiali
Department of Chemistry, Digital Technology Center and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455.
J Chem Theory Comput. 2009 Oct 13;5(10):2702-2716. doi: 10.1021/ct9002898.
A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn-Sham determinants and the exchange-correlation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn-Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn-Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of H2+ and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of H2+, the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the S(N)2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three-state model, VBDFT(3), significantly improves the computed barrier heights, which are found to be in accord with accurate results. The BLDFT method is a versatile theory that can be used to analyze conventional DFT results to gain insight into chemical bonding properties, and it is illustrated by examining the intricate energy contributions to the ion-dipole complex stabilization.
描述了一种价键模型框架下的多态密度泛函理论。该方法基于用于构建类价键非绝热电子态的块定域密度泛函理论（BLDFT），适用于电子转移反应的研究以及反应势能面的表示。该方法等同于通过使用密度泛函理论处理定域构型的价键理论（VBDFT）。在VBDFT中，价键态的电子密度和能量由BLDFT确定。利用Kohn-Sham行列式之间的重叠积分以及用跃迁（交换）密度取代基态的交换相关泛函，提出了VB哈密顿量非对角矩阵元的泛函估计。此外，我们描述了一种近似方法，其中非对角矩阵元通过使用块定域Kohn-Sham轨道的波函数理论来计算。关键特征是绝热基态的电子密度不直接计算也不用于获得基态能量；能量由多态价键哈密顿量的对角化确定。这代表了与标准单行列式Kohn-Sham密度泛函理论的不同。通过H₂⁺的键解离以及DBH24数据库中的一组三个亲核取代反应说明了多态VBDFT方法。在H₂⁺的解离中，当两个质子拉伸至无穷远时，VBDFT方法产生正确的渐近行为，而近似泛函则严重失败。对于S(N)2亲核取代反应，杂化泛函B3LYP严重低估了势垒高度，而近似双态VBDFT方法克服了自相互作用误差，并高估了势垒高度。在三态模型VBDFT(3)中包含离子态，显著改善了计算的势垒高度，发现其与精确结果一致。BLDFT方法是一种通用理论，可用于分析传统DFT结果以深入了解化学键性质，并通过研究对离子 - 偶极复合物稳定化的复杂能量贡献进行了说明。
