Fast estimation of standard enthalpy of formation with chemical accuracy by artificial neural network correction of low-level-of-theory ab initio calculations

A methodology for predicting the standard enthalpy of formation of gas-phase molecules with high speed and accuracy has been developed. This includes the development of: (a) a large, diverse database of molecular structures (consisting of H, C, O, N, and S, and up to 23 heavy atoms), computed at the G3MP2B3 level of chemically accurate theory; (b) a 3D, molecule size-independent descriptor, derived from a radial distribution function containing the convolution of weighted interatomic distances up to 8 angstrom; (c) a neural network structure that is capable to decode 3D structural information and use it to correct enthalpy of formation of lower level theory to that of the high-accuracy method; and (d) a method to estimate uncertainty of predictions. The predictions have about 2.5 kJ/mol (0.6 kcal/mol) average deviation from G3MP2B3 level results, at the computational cost of the B3LYP/6-31G* method. The model is able to extrapolate to increased molecular sizes and to different type of hetero-atoms - although with reduced accuracy but still at significant improvements comparing to low-level theory results. Extrapolations with the neural-network based model does not generate spurious results, which may be attributed to the careful selection of a physically and chemically relevant set of inputs. The methodology may be useful for other computational methods, and for computation of other chemical properties in an automated fashion.