Zhang Wenjing, Truhlar Donald G, Tang Mingsheng
The College of Chemistry and Molecular Engineering, Zhengzhou University , Zhengzhou, Henan Province 450001, China.
Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455-0431, United States.
J Chem Theory Comput. 2014 Jun 10;10(6):2399-409. doi: 10.1021/ct500296a.
Vanadium dimer is a notoriously difficult case for Kohn-Sham (KS) density functional theory with currently available approximations to the exchange-correlation (xc) functionals, and many approximate xc functionals yield an exceedingly large error in the calculated bond energy. In this paper, we first test the bond energies estimated by 43 xc functionals and the Hartree-Fock (HF) method. The results further confirm the large errors and show that, with the experimental bond energy being 64.2 kcal/mol, the KS calculations give predictions all over the map with errors ranging from -61.5 to +60.5 kcal/mol, and the HF method performs much worse with an error of -124.4 kcal/mol! The reason for these very large errors is examined in this article by analyzing the atomic and molecular orbital energies calculated by various xc functionals. The results show that the errors in estimates of the bond energy of vanadium dimer can primarily be related to the calculated energy gap between the 4s and 3dz2 atomic orbitals of the vanadium atom and especially to the 3dz2 orbital energy. This interesting relation between the errors in the calculated bond energy and the magnitudes of the single-particle orbital energies provides a constructive alternative to the common but more sterile explanation that it is the static correlation energy due to multicenter left-right correlation that makes the vanadium dimer and many other transition metal compounds so difficult for Kohn-Sham calculations. One of the most important factors in determining the critical atomic orbital energy is the amount of nonlocal HF exchange that is included in the xc functional, but it is still difficult to explain why different local functionals (functionals with no HF exchange) yield quite different results. We conclude that improving calculations of orbital energies of atoms may provide a route to improving the accuracy of theoretical predictions of molecular bond energies for systems containing metal atoms.
对于采用当前可用的交换关联（xc）泛函近似的科恩 - 沈（KS）密度泛函理论而言，钒二聚体是一个极其棘手的案例，许多近似的xc泛函在计算键能时会产生极大的误差。在本文中，我们首先测试了43种xc泛函和哈特里 - 福克（HF）方法所估计的键能。结果进一步证实了这些巨大的误差，表明实验键能为64.2千卡/摩尔时，KS计算结果五花八门，误差范围从 - 61.5到 + 60.5千卡/摩尔，而HF方法的表现更差，误差为 - 124.4千卡/摩尔！本文通过分析各种xc泛函计算出的原子和分子轨道能量，研究了产生这些巨大误差的原因。结果表明，钒二聚体键能估计中的误差主要与钒原子4s和3dz²原子轨道之间计算出的能隙有关，特别是与3dz²轨道能量有关。计算出的键能误差与单粒子轨道能量大小之间的这种有趣关系，为常见但更无成效的解释提供了一种建设性的替代方案，即由于多中心左右关联导致的静态相关能使得钒二聚体和许多其他过渡金属化合物对于KS计算如此困难。决定关键原子轨道能量的最重要因素之一是xc泛函中包含的非局部HF交换量，但仍然难以解释为什么不同的局域泛函（没有HF交换的泛函）会产生截然不同的结果。我们得出结论，改进原子轨道能量的计算可能为提高含金属原子体系分子键能理论预测的准确性提供一条途径。
