  Free energy profile (FE Profile) is an essential quantity for the estimation
of reaction rate and the validation of reaction mechanism. For chemical
reactions in condensed phase or enzymatic reactions, the computation of FE
profile at ab initio (ai) quantum mechanical/molecular mechanics (QM/MM) level
is still far too expensive. Semiempirical (SE) method can be hundreds or
thousands of times faster than the ai methods. However, the accuracy of SE
methods is often unsatisfactory, due to the approximations that have been
adopted in these methods. In this work, we proposed a new method termed
MBAR+wTP, in which the ai QM/MM free energy profile is computed by a weighted
thermodynamic perturbation (TP) correction to the SE profile generated by the
multistate Bennett acceptance ratio (MBAR) analysis of the trajectories from
umbrella samplings (US). The weight factors used in the TP calculations are a
byproduct of the MBAR analysis in the post-processing of the US trajectories,
which are often discarded after the free energy calculations. The results show
that this approach can enhance the efficiency of ai FE profile calculations by
several orders of magnitude.
