Alfè D, Bartók A P, Csányi G, Gillan M J
Department of Earth Sciences, UCL, London WC1E 6BT, United Kingdom.
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom.
J Chem Phys. 2014 Jul 7;141(1):014104. doi: 10.1063/1.4885440.
We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm(3) where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE(h) ≃ 15 meV/monomer for the liquid and the clusters.
我们报告了一项关于压缩水系统密度泛函理论（DFT）近似误差的广泛研究。所研究的近似基于广泛使用的PBE和BLYP交换关联泛函，我们在对一体和二体误差进行校正前后对其误差进行了表征，校正是使用高斯近似势方法进行的。针对两种相关类型的水系统研究了未校正和校正近似的误差：第一，温度为420 K、密度为1.245 g/cm³的压缩液体，其实验压力为15千巴；第二，从三聚体到27聚体的压缩水团簇的热样本。对于液体，我们报告了四个第一性原理分子动力学模拟，两个是用未校正的PBE和BLYP近似生成的，另外两个是用其一体和二体校正后的对应近似生成的。通过与压力的实验数据、三个径向分布函数的中子衍射数据以及周期性边界条件下液体构型集能量的量子蒙特卡罗（QMC）基准进行比较，对模拟误差进行了表征。使用QMC基准计算压缩水团簇构型样本的DFT误差。我们发现液体中的二体及二体以上误差与团簇表现出的类似误差密切相关。对于液体和团簇，DFT的二体以上误差对总误差有很大贡献，因此对一体和二体误差进行校正不足以给出令人满意的描述。对于BLYP，Medders、Babin和Paesani [《化学理论计算杂志》9, 1103 (2013)] 最近提出的三体能量表示给出了一种合理的校正二体以上误差的方法，在此之后，液体和团簇的剩余误差通常为0.5 mE(h) ≃ 15 meV/单体。
