Steinmann Stephan N, Corminboeuf Clemence
Laboratory for Computational Molecular Design, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
J Chem Theory Comput. 2010 Jul 13;6(7):1990-2001. doi: 10.1021/ct1001494. Epub 2010 Jun 11.
Density functional approximations fail to provide a consistent description of weak molecular interactions arising from small electron density overlaps. A simple remedy to correct for the missing interactions is to add a posteriori an attractive energy term summed over all atom pairs in the system. The density-dependent energy correction, presented herein, is applicable to all elements of the periodic table and is easily combined with any electronic structure method, which lacks the accurate treatment of weak interactions. Dispersion coefficients are computed according to Becke and Johnson's exchange-hole dipole moment (XDM) formalism, thereby depending on the chemical environment of an atom (density, oxidation state). The long-range ∼R(-6) potential is supplemented with higher-order correction terms (∼R(-8) and ∼R(-10)) through the universal damping function of Tang and Toennies. A genuine damping factor depending on (iterative) Hirshfeld (overlap) populations, atomic ionization energies, and two adjustable parameters specifically fitted to a given DFT functional is also introduced. The proposed correction, dDXDM, dramatically improves the performance of popular density functionals. The analysis of 30 (dispersion corrected) density functionals on 145 systems reveals that dDXDM largely reduces the errors of the parent functionals for both inter- and intramolecular interactions. With mean absolute deviations (MADs) of 0.74-0.84 kcal mol(-1), PBE-dDXDM, PBE0-dDXDM, and B3LYP-dDXDM outperform the computationally more demanding and most recent functionals such as M06-2X and B2PLYP-D (MAD of 1.93 and 1.06 kcal mol(-1), respectively).
密度泛函近似无法对由小电子密度重叠产生的弱分子相互作用提供一致的描述。一种纠正缺失相互作用的简单补救方法是事后添加一个吸引力能量项，该项对系统中所有原子对求和。本文提出的密度依赖能量校正适用于元素周期表中的所有元素，并且可以很容易地与任何缺乏对弱相互作用精确处理的电子结构方法相结合。色散系数根据贝克和约翰逊的交换空穴偶极矩（XDM）形式计算，因此取决于原子的化学环境（密度、氧化态）。通过唐和托尼斯的通用阻尼函数，长程R(-6)势被补充了高阶校正项（R(-8)和~R(-10)）。还引入了一个真正的阻尼因子，它取决于（迭代的）赫希菲尔德（重叠）布居、原子电离能以及专门针对给定密度泛函拟合的两个可调参数。所提出的校正方法dDXDM显著提高了流行密度泛函的性能。对145个系统上的30种（色散校正的）密度泛函的分析表明，dDXDM在很大程度上降低了母体泛函在分子间和分子内相互作用方面的误差。PBE - dDXDM、PBE0 - dDXDM和B3LYP - dDXDM的平均绝对偏差（MAD）为0.74 - 0.84 kcal mol(-1)，优于计算要求更高且更新的泛函，如M06 - 2X和B2PLYP - D（MAD分别为1.93和1.06 kcal mol(-1)）。
