Ryde Ulf
Department of Theoretical Chemistry, Lund University, Chemical Centre , P.O. Box 124, SE-221 00 Lund, Sweden.
J Chem Theory Comput. 2017 Nov 14;13(11):5745-5752. doi: 10.1021/acs.jctc.7b00826. Epub 2017 Oct 26.
Combined quantum mechanical and molecular mechanical (QM/MM) calculations is a popular approach to study enzymatic reactions. They are often based on a set of minimized structures obtained on snapshots from a molecular dynamics simulation to include some dynamics of the enzyme. It has been much discussed how the individual energies should be combined to obtain a final estimate of the energy, but the current consensus seems to be to use an exponential average. Then, the question is how many snapshots are needed to reach a reliable estimate of the energy. In this paper, I show that the question can be easily be answered if it is assumed that the energies follow a Gaussian distribution. Then, the outcome can be simulated based on a single parameter, σ, the standard deviation of the QM/MM energies from the various snapshots, and the number of required snapshots can be estimated once the desired accuracy and confidence of the result has been specified. Results for various parameters are presented, and it is shown that many more snapshots are required than is normally assumed. The number can be reduced by employing a cumulant approximation to second order. It is shown that most convergence criteria work poorly, owing to the very bad conditioning of the exponential average when σ is large (more than ∼7 kJ/mol), because the energies that contribute most to the exponential average have a very low probability. On the other hand, σ serves as an excellent convergence criterion.
量子力学与分子力学相结合（QM/MM）的计算方法是研究酶促反应的一种常用方法。这些计算通常基于从分子动力学模拟的快照中获得的一组最小化结构，以纳入酶的一些动力学信息。关于如何将各个能量组合起来以获得能量的最终估计值，已经有很多讨论，但目前的共识似乎是使用指数平均值。那么，问题是需要多少个快照才能得到可靠的能量估计值。在本文中，我表明，如果假设能量服从高斯分布，这个问题很容易得到答案。然后，可以基于一个参数σ（来自各个快照的QM/MM能量的标准差）模拟结果，一旦指定了所需的结果精度和置信度，就可以估计所需的快照数量。给出了各种参数的结果，结果表明所需的快照数量比通常假设的要多得多。通过采用二阶累积量近似可以减少数量。结果表明，由于当σ较大（超过约7 kJ/mol）时指数平均值的条件非常差，大多数收敛标准的效果都很差，因为对指数平均值贡献最大的能量概率非常低。另一方面，σ是一个很好的收敛标准。
