Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here, we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g. replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g. hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyse two different approaches: the QM/MM–MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analysed here, both approaches seem productive although care needs to be exercised when analysing the perturbative corrections.

中文翻译：

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QM/MM 自由能模拟：最新进展和挑战

由于相对于纯分子力学 (MM) 模拟计算成本更高，混合量子力学/分子力学 (QM/MM) 自由能模拟特别需要仔细考虑平衡计算成本和准确性。在这里，我们回顾了与 QM/MM 模拟最相关的自由能方法的最新发展，并使用涉及水中过程的简单但信息丰富的示例讨论了由这些发展激发的几个主题。对于化学反应，我们强调在伞状采样计算中调用增强采样技术（例如副本交换）的价值以及在元动力学模拟中包括集体环境变量（例如水合水平）的价值；我们还说明了弦计算的敏感性，尤其是沿路径的自由能，计算中的各种参数。具有特定热力学循环的炼金术自由能模拟用于探讨在计算溶剂化自由能时将第一个溶剂化壳包含在 QM 区域中的影响。对于需要高级 QM/MM 势函数的情况，我们分析了两种不同的方法：Yang 及其同事的 QM/MM-MFEP 方法和对低级 QM/MM 自由能结果的微扰校正。对于此处分析的示例，尽管在分析微扰校正时需要小心谨慎，但这两种方法似乎都有效。对于需要高级 QM/MM 势函数的情况，我们分析了两种不同的方法：Yang 及其同事的 QM/MM-MFEP 方法和对低级 QM/MM 自由能结果的微扰校正。对于此处分析的示例，尽管在分析微扰校正时需要小心谨慎，但这两种方法似乎都有效。对于需要高级 QM/MM 势函数的情况，我们分析了两种不同的方法：Yang 及其同事的 QM/MM-MFEP 方法和对低级 QM/MM 自由能结果的微扰校正。对于此处分析的示例，尽管在分析微扰校正时需要小心谨慎，但这两种方法似乎都有效。