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

We present a general method for developing a Δ-DFT-type approach that enables the generation of energies with complete basis set CCSD(T)-level accuracy on the potential energy surfaces (PESs) of molecules of arbitrary size, while requiring only a minimal set (hundreds) of high-level wave function theory reference data points for fitting. 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 predicting the energies on the PES for the chosen molecule with approximately the same accuracy as the high-level reference 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 to predict the energies on the PES up to 40,000 cm –1 above the global minimum was reduced from 829.2 to 56.0 cm –1 with an ACP trained on as few as 272 CCSD(T)-F12/cc-pVTZ-F12 reference data points. For the more complex uracil molecule treated with B3LYP/6–311++G(2d,2p), the RMSE of the energies on the PES up to 7000 cm –1 above the global minimum was reduced from 82.6 to 9.9 cm –1 with an ACP trained on 404 data points. The quality of the ACP-corrected PESs obtained is further demonstrated by comparing the predicted fundamental vibrational frequencies relative to experimental spectroscopic data. The comparison shows that the approach generates CCSD(T)-quality data in the vicinity of PES minima at the cost of DFT, which can then be used in vibrational second-order perturbation theory calculations (equivalent to fitting a quartic force field). The new ACP-based protocol represents a promising tool for generating PES energy data with wavenumber accuracy relative to CCSD(T) for molecules of arbitrary size at minimal computational cost. These data can be used in computational quantum dynamics and spectroscopic studies and for the development of energy data sets required for analytical representations and/or machine learning models of PESs.

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