To facilitate further development of approximate quantum mechanical methods for condensed phase applications, we present a new benchmark dataset of intermolecular interaction energies in the solution phase for a set of 15 dimers, each containing one charged monomer. The reference interaction energy in solution is computed via a thermodynamic cycle that integrates dimer binding energy in the gas phase at the coupled cluster level and solute-solvent interaction with density functional theory; the estimated uncertainty of such calculated interaction energy is $\pm 1.5$ kcal/mol. The dataset is used to benchmark the performance of a set of semi-empirical quantum mechanical (SQM) methods that include DFTB3-D3, DFTB3/CPE-D3, OM2-D3, PM6-D3, PM6-D3H+, and PM7 as well as the HF-3c method. We find that while all tested SQM methods tend to underestimate binding energies in the gas phase with a root-mean-squared error (RMSE) of 2-5 kcal/mol, they overestimate binding energies in the solution phase with an RMSE of 3-4 kcal/mol, with the exception of DFTB3/CPE-D3 and OM2-D3, for which the systematic deviation is less pronounced. In addition, we find that HF-3c systematically overestimates binding energies in both gas and solution phases. As most approximate QM methods are parametrized and evaluated using data measured or calculated in the gas phase, the dataset represents an important first step toward calibrating QM based methods for application in the condensed phase where polarization and exchange repulsion need to be treated in a balanced fashion.

中文翻译：

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凝聚相中的分子间相互作用：半经验量子力学方法的评估

为了促进凝聚态应用的近似量子力学方法的进一步发展，我们提出了一个新的基准数据集 分子间相互作用 能量 在里面 解决方案 相为一组15个二聚体，每个包含一个带电 单体。 参考资料 相互作用 活力 在 解决方案 通过一个 热力学 整合二聚体结合的循环 活力 在气相中处于团簇水平和溶质溶剂的耦合状态 相互作用 和 密度泛函理论; 估计的不确定性 相互作用 活力 是 $\pm 1.5$千卡/摩尔 该数据集用于对一组半经验量子力学（SQM）方法的性能进行基准测试，这些方法包括DFTB3-D3，DFTB3 / CPE-D3，OM2-D3，PM6-D3，PM6-D3H +和PM7，以及HF-3c方法。我们发现，尽管所有经过测试的SQM方法都倾向于低估绑定能量 在气相中均方根误差（RMSE）为2-5 kcal / mol的气相中，它们高估了结合 能量 在里面 解决方案除了DFTB3 / CPE-D3和OM2-D3之外，它们的均方根误差（RMSE）为3-4 kcal / mol。此外，我们发现HF-3c系统性地高估了结合能量 在气体和 解决方案阶段。由于大多数近似的QM方法是使用气相测量或计算的数据进行参数化和评估的，因此数据集代表了迈向在凝结相中校准基于QM的方法的重要第一步，在凝结相中，极化和交换斥力需要以平衡的方式进行处理。