Kříž Kristian, van Maaren Paul J, van der Spoel David
Department of Cell and Molecular Biology, Uppsala University, Box 596, Uppsala SE-75124, Sweden.
J Chem Theory Comput. 2024 Mar 26;20(6):2362-2376. doi: 10.1021/acs.jctc.3c01257. Epub 2024 Mar 13.
The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., 133-138), or the three-parameter Morse potential (Morse, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σ as and one for the well-depth ϵ as . The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.
由于稀有气体相互作用的基本性质,其体系对于分子建模具有特别的指导意义。它们通常不形成化学键,也不具有(永久)偶极矩,决定其键合/聚集的唯一作用力来自范德华力——色散力和泡利排斥力,这可以通过经验势函数进行建模。对于 Lennard-Jones 12 - 6 势,组合规则(即从相应同二聚体的参数推导异二聚体对势参数的公式)已被深入研究,但对于其他更精确的势则研究得不够详细。在这项工作中,我们研究了九种经验势在重现稀有气体二聚体(He、Ne、Ar、Kr 和 Xe 的同二聚体和异二聚体)量子力学(QM)基准解离曲线方面的有效性,并系统地研究了势的每个参数的不同组合关系排列的功效。我们的 QM 基准包括由几种不同的耦合簇实现以及对称适配微扰理论计算得到的解离曲线。当拟合 QM 解离曲线时,更精细的势明显优于两参数 Lennard-Jones 势,前者的均方根误差(RMSE)低 25 - 30 倍。使用相对简单的四参数甚至三参数势,例如阻尼 14 - 7 势(哈尔格伦,7827 - 7843)、四参数白金汉势(韦尔哈恩等人,133 - 138)或三参数莫尔斯势(莫尔斯,57 - 64),可以很好地拟合 QM 解离曲线。由组合规则生成的异二聚体势的 RMSE 比直接拟合 QM 解离曲线的势高出多达 20 倍。这意味着特别是对于轻原子,RMSE 的大小与势的阱深相当。基于组合规则的系统排列,我们为每个测试的势提出了一个或多个组合规则,这些规则产生相对较低的 RMSE。引入了两个表现良好的新组合规则,一个用于范德华半径 σ,另一个用于阱深 ϵ。在气相中,针对同二聚体和异二聚体的实验第二维里系数评估了 QM 数据和拟合势,后者用于评估组合规则。使用拟合模型进行凝聚相分子动力学模拟,以验证模型预测的纯物质的熔点、熔点时的液体密度和汽化焓。在此发现,由于所使用的理论水平,基准势中的细微差异,特别是阱深,对稀有气体的宏观性质(第二维里系数或模拟中的体相性质)有深远影响。通过在采用最佳对势的分子模拟中明确包含三体色散,我们能够获得准确的熔点以及令人满意的密度和汽化焓。