Benchmarking Semiempirical QM Methods for Calculating the Dipole Moment of Organic Molecules

The dipole moment is a simple descriptor of the charge distribution and polarity and is important for understanding and predicting various molecular properties. Semiempirical (SE) methods offer a cost-effective way to calculate dipole moment that can be used in high-throughput screening applications although the accuracy of the methods is still in question. Therefore, we have evaluated AM1, GFN0-xTB, GFN1-xTB, GFN2-xTB, PM3, PM6, PM7, B97-3c, HF-3c, and PBEh-3c SE methods, which cover a variety of SE approximations, to directly assess the performance of SE methods in predicting molecular dipole moments and their directions using 7211 organic molecules contained in the QM7b database. We find that B97-3c and PBEh-3c perform best against coupled-cluster reference values yielding dipole moments with a mean absolute error (MAE) of 0.10 and 0.11 D, respectively, which is similar to the MAE of density functional theory (DFT) methods (∼0.1 D) reported earlier. Analysis of the atomic composition shows that all SE methods show good performance for hydrocarbons for which the spread of error was within 1 D of the reference data, while the worst performances are for sulfur-containing compounds for which only B97-3c and PBEh-3c show acceptable performance. We also evaluate the effect of SE optimized geometry, instead of the benchmark DFT geometry, that shows a dramatic drop in the performance of AM1 and PM3 for which the range of error tripled. Based on our overall findings, we highlight that there is an optimal compromise between accuracy and computational cost using GFN2-xTB (MAE: 0.25 D) that is 3 orders of magnitude faster than B97-3c and PBEh-3c. Thus, we recommend using GFN2-xTB for cost-efficient calculation of the dipole moment of organic molecules containing C, H, O, and N atoms, whereas, for sulfur-containing organic molecules, we suggest PBEh-3c.

偶极矩（dipole moment）是表征电荷分布与分子极性的简洁描述符，对理解和预测各类分子性质具有关键意义。半经验（SE）方法是一类计算成本低廉的偶极矩计算途径，可用于高通量筛选场景，尽管此类方法的精度仍存在争议。为此，我们依托QM7b数据库收录的7211个有机分子，对AM1、GFN0-xTB、GFN1-xTB、GFN2-xTB、PM3、PM6、PM7、B97-3c、HF-3c及PBEh-3c等覆盖多种半经验近似方案的SE方法开展评估，以直接考察半经验方法在预测分子偶极矩及其方向时的性能表现。研究结果表明，B97-3c与PBEh-3c的表现最优，其偶极矩计算结果相较于耦合簇（coupled-cluster）参考值的平均绝对误差（MAE）分别为0.10 D与0.11 D，该精度水平与此前报道的密度泛函理论（DFT）方法（约0.1 D）的平均绝对误差相当。原子组成分析显示，所有SE方法对烃类分子均展现出良好的性能，其误差范围相较于参考数据的波动值在1 D以内；而表现最差的类别为含硫化合物，仅B97-3c与PBEh-3c可达到可接受的精度标准。我们还评估了采用半经验方法优化的几何结构（而非基准DFT几何结构）对计算结果的影响，结果显示AM1与PM3的性能出现显著下滑，其误差范围扩大至原先的三倍。基于整体研究结论，我们发现GFN2-xTB在计算精度与成本之间实现了最优平衡，其平均绝对误差为0.25 D，计算速度较B97-3c与PBEh-3c快三个数量级。因此，我们推荐在计算仅含C、H、O、N原子的有机分子偶极矩时使用GFN2-xTB以实现高效低成本的计算；而针对含硫有机分子，则建议采用PBEh-3c方法。