Sharir-Ivry Avital, Shurki Avital
Department of Medicinal Chemistry and Natural Products, The Lise Meitner-Minerva Center for Computational Quantum Chemistry, School of Pharmacy, The Hebrew University of Jerusalem, Jerusalem, Israel.
J Phys Chem B. 2008 Oct 2;112(39):12491-7. doi: 10.1021/jp802667y. Epub 2008 Sep 4.
Two recently developed methods, VB/MM and density embedded VB/MM (DE-VB/MM), are compared, and their respective approximations are examined. The two methods combine valence-bond (VB) calculations with molecular mechanics (MM) and aim to allow VB analysis of reactions in large biological environments. Furthermore, the two methods utilize two major approximations regarding both the overlap and the reduced resonance integral between the various VB configurations. The difference between the two methods, however, is that VB/MM employs these approximations for the overall interaction of the reacting fragments with their surrounding, whereas DE-VB/MM employs the approximations only with regards to the van der Waals (VdW) interactions whereas the electrostatic interactions are calculated rigorously at the quantum level. The approximations that lay the grounds for the two methods involve the assumption that the overlap between the VB configurations and the respective reduced resonance integral are both invariant to the environment. Similar approximations are utilized in several other VB-based QM/MM methods. However, although extensively used, these approximations were never rigorously proved. Here, we exploit the development of the DE-VB/MM method to numerically examine the approximations by calculating the accurate as well as the approximated values of overlap and reduced resonance integral for systems where the environment involves only electrostatic interactions. The quality of the approximations is examined together with their effect on the absolute energies, the wave function, and the overall energetics. Three test cases are chosen, the dissociation of CH 3F and LiF and the identity S N2 reaction. It is shown that the approximations are usually good with the exception of cases where extreme changes are expected in the wave function. Furthermore, the impact of the approximations on the overall wave function and the overall energetics is found to be quite small. It is concluded that VB/MM, where the approximations are used more extensively, can serve as the first method of choice.
对最近开发的两种方法，即价键/分子力学（VB/MM）和密度嵌入价键/分子力学（DE-VB/MM）进行了比较，并研究了它们各自的近似方法。这两种方法将价键（VB）计算与分子力学（MM）相结合，旨在对大型生物环境中的反应进行VB分析。此外，这两种方法在各种VB构型之间的重叠和简化共振积分方面采用了两个主要近似。然而，这两种方法的区别在于，VB/MM将这些近似用于反应片段与其周围环境的整体相互作用，而DE-VB/MM仅对价层范德华（VdW）相互作用采用这些近似，而静电相互作用则在量子水平上进行严格计算。这两种方法所基于的近似涉及这样的假设，即VB构型之间的重叠和相应的简化共振积分对环境都是不变的。其他几种基于VB的量子力学/分子力学方法也采用了类似的近似。然而，尽管这些近似被广泛使用，但从未得到严格证明。在这里，我们利用DE-VB/MM方法的发展，通过计算环境仅涉及静电相互作用的系统的重叠和简化共振积分的精确值和近似值，对这些近似进行数值检验。研究了近似的质量及其对绝对能量、波函数和整体能量学的影响。选择了三个测试案例，即CH₃F和LiF的解离以及相同的SN2反应。结果表明，除了预期波函数会发生极端变化的情况外，这些近似通常是良好的。此外，发现这些近似对整体波函数和整体能量学的影响相当小。得出的结论是，更广泛使用这些近似的VB/MM可以作为首选方法。
