Benchmarking Vibrational Second‐Order Perturbation Theory Computations of Dipole Moments and Their Correlation With Electronic Density Errors Using Density Functional Theory

The dipole moment is a simple electronic property with widespread experimental and theoretical applications. Using vibrational second-order perturbation theory (VPT2) and density functional theory (DFT), we calculate the dipole moments of 125 small molecules. While it is known that vibrational effects can significantly affect the dipole moments of molecules, there has been no large-scale study that assessed the effectiveness of including vibrational effects in dipole moment calculations using DFT-VPT2. We find that DFT-VPT2 dipole moments calculated with the aug-cc-PVTZ basis set and averaged across a variety of exchange-correlation functionals when compared to DFT dipole moments with no vibrational corrections have an absolute mean error that is lower by 0.003 Debye, a mean absolute error that is lower by 0.005 Debye, a mean percentage error that is lower in units of percentage points by 0.1, and a root mean squared error that is lower by 0.009 Debye relative to experiment for a test set of 125 small molecules. Calculated dipole moments are also often used as a proxy for the accuracy of the electronic density distribution. We investigate the correlation between dipole moments and electronic densities using a measure of the electron density error based on density profiles computed in a previous study (J. Phys. Chem. Lett. 2017 8 (15) 3488). We find that the correlation between the accuracy of the calculated dipole moment and the electronic density error is weak (all R² values are less than 0.5), suggesting that dipole moments are an inadequate metric for assessing electronic density errors. Based on the results in this study, we find it unnecessary to include VPT2 vibrational effects when using DFT to compute dipole moments, as any increase in accuracy is limited.