Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, Göttingen 37077, Germany.
J Chem Theory Comput. 2020 Jun 9;16(6):3504-3512. doi: 10.1021/acs.jctc.0c00106. Epub 2020 May 28.
Free-energy calculations based on atomistic Hamiltonians and sampling are key to a first-principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the free-energy perturbation method and derive nonlinear Hamiltonian transformation sequences yielding free-energy estimates with minimal mean squared error with respect to the exact values. Our variational approach applies to finite sampling and holds for any finite number of intermediate states. We show that our sequences are also optimal for the Bennett acceptance ratio (BAR) method, thereby generalizing BAR to small sampling sizes and non-Gaussian error distributions.
基于原子哈密顿量和采样的自由能计算是从第一性原理理解生物分子过程、材料性质和大分子化学的关键。在这里，我们推广了自由能微扰方法，并推导出了非线性哈密顿变换序列，这些序列可以以最小的均方误差得到与精确值相对应的自由能估计。我们的变分方法适用于有限的采样，并且适用于任何有限数量的中间状态。我们表明，我们的序列对于 Bennett 接受比（BAR）方法也是最优的，从而将 BAR 推广到小采样尺寸和非高斯误差分布。
