Caldeweyher Eike, Ehlert Sebastian, Hansen Andreas, Neugebauer Hagen, Spicher Sebastian, Bannwarth Christoph, Grimme Stefan
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn, Beringstr. 4, D-53115 Bonn, Germany.
J Chem Phys. 2019 Apr 21;150(15):154122. doi: 10.1063/1.5090222.
The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.
所谓的D4模型用于在密度泛函理论近似（DFT-D4）中精确计算伦敦色散相互作用，一般也适用于原子模型方法。作为DFT-D3模型的后续版本，基于可从各种来源获取的原子部分电荷，对原子配位相关的偶极极化率进行了缩放。为此，设计了一种新的电荷相关参数经济缩放函数。经典电荷通过原子电负性均衡程序获得，并针对核位置开发了高效的解析导数。然后，通过分子中原子动态极化率的数值卡西米尔-波德积分得到与电荷和几何结构相关的偶极-偶极色散系数。与D3模型类似，动态极化率通过含时密度泛函理论预先计算，涵盖了直至氡（Z = 86）的所有元素。两体色散能表达式具有常见的原子对求和形式，包括偶极-偶极以及偶极-四极相互作用。对于一组包含1225个分子偶极-偶极色散系数的基准数据集，D4模型实现了前所未有的精度，平均相对偏差为3.8%，而D3为4.7%。除了两体部分，三体效应由Axilrod-Teller-Muto项描述。对一种常见的多体色散展开进行了广泛测试，发现基于D4极化率的能量校正对更大的系统具有优势。确定了超过60种常见密度泛函的DFT-D4的Becke-Johnson型阻尼参数。对于各种标准能量基准数据集，DFT-D4略微但始终优于DFT-D3。特别是对于含金属系统，引入的色散系数对电荷的依赖性改善了热化学性质。我们建议将（DFT-）D4作为一种物理上改进且更复杂的色散模型，在DFT计算以及其他低成本方法（如半经验模型）中取代DFT-D3。
