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A linear regression correction approach has been developed successfully to account for the electron correlation energy missing in Hartree-Fock calculation and to reduce the calculation errors of density functional theory. The numbers of lone-pair electrons, bonding electrons and inner layer electrons in molecules, and the number of unpaired electrons in the composing atoms in their ground states are chosen to be the most important physical descriptors to determine the correlation energy unaccounted by Hartree-Fock method or to improve the results calculated by B3LYP density functional theory method. As a demonstration, this proposed linear regression correction approach has been applied to evaluate the standard heats of formation DeltaH(f) (Theta) of 180 small-sized to medium-sized organic molecules at 298.15 K. Upon correction, the mean absolute deviation for the 150 molecules in the training set decreases from 351.0 to 4.6 kcal/mol and 360.9 to 4.6 kcal/mol for HF/6-31G(d) and HF/6-311+G(d,p) methods, respectively. For B3LYP method, the mean absolute deviations are reduced from 9.2 and 18.2 kcal/mol to 2.7 and 2.4 kcal/mol for 6-31G(d) and 6-311+G(d,p) basis sets, respectively.

Accurate prediction of heat of formation by combining Hartree–Fock/density functional theory calculation with linear regression correction approach