  Despite of their success, the results of first-principles quantum mechanical
calculations contain inherent numerical errors caused by various
approximations. We propose here a neural-network algorithm to greatly reduce
these inherent errors. As a demonstration, this combined quantum mechanical
calculation and neural-network correction approach is applied to the evaluation
of standard heat of formation $\DelH$ and standard Gibbs energy of formation
$\DelG$ for 180 organic molecules at 298 K. A dramatic reduction of numerical
errors is clearly shown with systematic deviations being eliminated. For
examples, the root--mean--square deviation of the calculated $\DelH$ ($\DelG$)
for the 180 molecules is reduced from 21.4 (22.3) kcal$\cdotp$mol$^{-1}$ to 3.1
(3.3) kcal$\cdotp$mol$^{-1}$ for B3LYP/6-311+G({\it d,p}) and from 12.0 (12.9)
kcal$\cdotp$mol$^{-1}$ to 3.3 (3.4) kcal$\cdotp$mol$^{-1}$ for
B3LYP/6-311+G(3{\it df},2{\it p}) before and after the neural-network
correction.
