A critical investigation of proposed electrostatic corrections to quantum mechanical volumes: the importance of variation and the irrelevance of imbalance

The crystal density of neutral and ionic molecular crystals is remarkably well approximated by the enclosed volume of molecular surfaces, where these surfaces are defined as regions of constant and small electron density. Several workers have proposed that estimates may be improved if one includes quantities extracted from the electrostatic potential on the surface of the molecule. The variation of the potential and the imbalance of positive and negative values have been considered to be of importance. In this study we demonstrate that whereas variation is important for improving crystal density predictions, imbalance is not. We present a density functional theory study on a set of 44 neutral molecular crystals. Ten-fold cross-validations were performed on models that incorporate variation, imbalance and combinations of both. Geometries were optimised using B3LYP and basis sets of type 6-31G(d). Electron densities and electrostatic potentials were computed with B3LYP and M05. Regardless of functional, models that correct for variation yield a relative decrease of 15%–18% in root-mean-square error of prediction. This correction appears to sharpen the error distribution about zero. Models based on imbalance yield no improvement, and we argue that it plays an insignificant role.

中性与离子型分子晶体的晶体密度，可通过分子表面的包络体积实现极佳近似；此类分子表面被定义为电子密度恒定且较低的区域。已有多位研究者提出，若纳入从分子表面静电势中提取的特征量，可提升密度估算的精度。此前研究认为，静电势的变化以及正负值分布的不均衡性，均对提升估算精度具有重要意义。本研究证实，尽管静电势变化对优化晶体密度预测精度至关重要，但正负值分布的不均衡性并无此类作用。我们针对包含44种中性分子晶体的数据集开展了密度泛函理论 (Density Functional Theory, DFT) 研究。针对纳入静电势变化、正负值不均衡性以及二者组合特征的三类模型，我们开展了十折交叉验证。几何结构优化采用B3LYP泛函与6-31G(d)型基组。电子密度与静电势的计算采用B3LYP与M05泛函。无论采用何种泛函，纳入静电势变化校正的模型，其预测均方根误差可相对降低15%~18%。此类校正可使误差分布向零点附近收窄。基于正负值不均衡性构建的模型则未带来精度提升，因此我们认为该特征对晶体密度预测的影响可忽略不计。