A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression

We present a new approach to semi-global potential energy surface fitting that uses the least absolute shrinkage and selection operator (LASSO) constrained least squares procedure to exploit an extremely flexible form for the potential function, while at the same time controlling the risk of overfitting and avoiding the introduction of unphysical features such as divergences or high-frequency oscillations. Drawing from a massively redundant set of overlapping distributed multi-dimensional Gaussian functions of inter-atomic separations we build a compact full-dimensional surface for malonaldehyde, fit to explicitly correlated coupled cluster CCSD(T)(F12*) energies with a root mean square deviations accuracy of 0.3%–0.5% up to 25 000 cm⁻¹ above equilibrium. Importance-sampled diffusion Monte Carlo calculations predict zero point energies for malonaldehyde and its deuterated isotopologue of 14 715.4(2) and 13 997.9(2) cm⁻¹ and hydrogen transfer tunnelling splittings of 21.0(4) and 3.2(4) cm⁻¹, respectively, which are in excellent agreement with the experimental values of 21.583 and 2.915(4) cm⁻¹