The X1 method for accurate and efficient prediction of heats of formation

We propose the X1 method which combines the density functional theory method with a neural network (NN) correction for an accurate yet efficient prediction of heats of formation. It calculates the final energy by using B3LYP∕6-311+G(3df,2p) at the B3LYP∕6-311+G(d,p) optimized geometry to obtain the B3LYP standard heats of formation at 298K with the unscaled zero-point energy and thermal corrections at the latter basis set. The NN parameters cover 15 elements of H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, and Cl. The performance of X1 is close to the Gn theories, giving a mean absolute deviation of 1.43kcal∕mol for the G3∕99 set of 223molecules up to 10 nonhydrogen atoms and 1.48kcal∕mol for the X1∕07 set of 393molecules up to 32 nonhydrogen atoms.