Laboratory of Computational Science and Modeling, Institut des Matériaux , École Polytechnique Fédérale de Lausanne , 1015 Lausanne , Switzerland.
Fritz Haber Institute of the Max Planck Society , Faradayweg 4-6 , 14195 Berlin , Germany.
J Chem Theory Comput. 2019 Nov 12;15(11):5845-5857. doi: 10.1021/acs.jctc.9b00596. Epub 2019 Oct 8.
Quantitative evaluation of the thermodynamic properties of materials-most notably their stability, as measured by the free energy-must take into account the role of thermal and zero-point energy fluctuations. While these effects can easily be estimated within a harmonic approximation, corrections arising from the anharmonic nature of the interatomic potential are often crucial and require computationally costly path integral simulations to obtain results that are essentially exact for a given potential. Consequently, different approximate frameworks for computing affordable estimates of the anharmonic free energies have been developed over the years. Understanding which of the approximations involved are justified for a given system, and therefore choosing the most suitable method, is complicated by the lack of comparative benchmarks. To facilitate this choice we assess the accuracy and efficiency of some of the most commonly used approximate methods: the independent mode framework, the vibrational self-consistent field, and self-consistent phonons. We compare the anharmonic correction to the Helmholtz free energy against reference path integral calculations. These benchmarks are performed for a diverse set of systems, ranging from simple weakly anharmonic solids to flexible molecular crystals with freely rotating units. The results suggest that, for simple solids such as allotropes of carbon, these methods yield results that are in excellent agreement with the reference calculations, at a considerably lower computational cost. For more complex molecular systems such as polymorphs of ice and paracetamol the methods do not consistently provide a reliable approximation of the anharmonic correction. Despite substantial cancellation of errors when comparing the stability of different phases, we do not observe a systematic improvement over the harmonic approximation even for relative free energies. We conclude that, at least for the classes of materials considered here, efforts toward obtaining computationally feasible anharmonic free energies should therefore be directed toward reducing the expense of path integral methods.
材料热力学性质的定量评估——尤其是用自由能衡量的稳定性——必须考虑热和零点能涨落的作用。虽然这些效应在简谐近似中很容易估计，但来自原子间势的非谐性质的修正通常是至关重要的，需要计算成本高昂的路径积分模拟才能获得给定势的基本精确结果。因此，多年来已经开发了不同的近似框架来计算负担得起的非谐自由能估计值。了解涉及的近似哪些对于给定的系统是合理的，因此选择最合适的方法，这是复杂的，因为缺乏比较基准。为了便于做出这种选择，我们评估了一些最常用的近似方法的准确性和效率：独立模式框架、振动自洽场和自洽声子。我们将亥姆霍兹自由能的非谐修正与参考路径积分计算进行比较。这些基准是针对各种系统进行的，范围从简单的弱非谐固体到具有自由旋转单元的柔性分子晶体。结果表明，对于简单的固体，如碳的同素异形体，这些方法在计算成本显著降低的情况下，与参考计算结果非常吻合。对于更复杂的分子系统，如冰和扑热息痛的多晶型物，这些方法并不总是能可靠地逼近非谐修正。尽管在比较不同相的稳定性时，错误的大量抵消，但即使对于相对自由能，我们也没有观察到系统地优于简谐近似。我们得出结论，至少对于这里考虑的材料类别，努力获得计算上可行的非谐自由能应该指向降低路径积分方法的费用。
