Improving the accuracy of density-functional theory calculation: The statistical correction approach

Recently, a novel, neural-networks-based method, the DFT-NEURON method, was developed to improve the accuracy of first-principles calculations and was applied to correct the systematic deviations of the calculated heats of formation for small-to-medium-sized organic molecules (Hu, L. H.; Wang, X. J.; Wong, L. H.; Chen, G. H. J. Chem. Phys. 2003, 119, 11501). In this work, we examine its theoretical foundation and generalize it to adopt any other statistical correction approaches, in particular, the multiple linear regression method. Both neural-networks-based and multiple-linear-regression-based correction approaches are applied to calculate the Gibbs energies of formation, ionization energies, electron affinities, and absorption energies of small-to-medium-sized molecules and lead to greatly improved calculation results as compared to the conventional first-principles methods. For instance, after the neural networks correction (multiple linear regression correction), the root-mean-square (RMS) deviations of the calculated standard Gibbs energy of formation for 180 organic molecules are reduced from 12.5, 13.8, and 22.3 kcal(.)mol(-1) to 4.7 (5.4), 3.2 (3.5), and 3.0 (3.2) kcal(.)mol(-1) for B3LYP/6-31G(d), B3LYP/6-311+G(3df,2p), and B3LYP/6-311+G(d,p) calculations, respectively, and the RMS deviation of the calculated absorption energies of 60 organic molecules is reduced from 0.33 eV to 0.09 (0.14) eV for the TDDFT/B3LYP/6-31G(d) calculation. In general, the neural networks correction approach leads to better results than the multiple linear regression correction approach. All these demonstrate that the statistical-correction-based first-principles calculations yield excellent results and may be employed routinely as predictive tools in materials research and design.