Constructing Accurate Potential Energy Surfaces with Limited High-Level Data Using Atom-Centered Potentials and Density Functional Theory

We present a general method for the development of a Δ-DFT-type approach for the calculation of accurate potential energy surfaces (PESs) using a minimal amount (hundreds) of high-level wavefunction theory reference data. The method uses a quasirandom (Sobol) approach to sample points on the PES for which reference data are generated. These data are then used to fit atom-centered potentials (ACPs) that improve the accuracy of the PES predicted by a density-functional theory method. The end result is an ACP-augmented DFT method capable of describing a region of the PES for the chosen molecule with approximately the same accuracy as the high-level method, but at approximately the same cost as the DFT method. The effectiveness of the algorithm is demonstrated through its application to the HFCO and uracil molecules. For HFCO, the root-mean-square error (RMSE) using B3LYP/def2-TZVPP in the description of the PES involving energies up to 40000 cm-1 above the global minimum was reduced from 829.2 cm-1 to 56.0 cm-1 with an ACP developed with as few as 272 CCSD(T)-F12/cc-pVTZ-F12 reference data points in the training set. For the more complex uracil molecule treated with B3LYP/6-311++G(2d,2p), the RMSE in the PES up to 7000 cm-1 above the global minimum was reduced from 82.6 cm-1 to 9.9 cm-1 with 404 reference data points in the ACP training set. The quality of the PESs obtained is further demonstrated by comparing the predicted fundamental vibrational frequencies relative to experimental spectroscopic data. The new ACP-based protocol represents a promising tool for generating accurate PESs for molecules of arbitrary size at minimal computational cost, which can then be used in computational quantum dynamics and spectroscopic studies.