<p>Previously
we proposed the equilibrium and nonequilibrium adaptive alchemical free energy
simulation methods Optimum Bennett’s Acceptance Ratio (OBAR) and Optimum
Crooks’ Equation (OCE). They are based on the statistically optimal
bidirectional reweighting estimator named Bennett’s Acceptance Ratio (BAR) or
Crooks’ Equation (CE). They perform initial sampling in the staging alchemical
transformation and then determine the importance rank of different states via
the time-derivative of the variance (TDV). The method is proven to give
speedups compared with the equal time rule. In the current work, we extended
the time derivative of variance guided adaptive sampling method to the configurational
space, falling in the term of Steered MD (SMD). The SMD approach biasing
physically meaningful collective variable (CV) such as one dihedral or one
distance to pulling the system from one conformational state to another. By
minimizing the variance of the free energy differences along the pathway in an
optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in
the alchemical case, this adaptive sampling method outperforms the traditional
equal-time SMD in nonequilibrium stratification. Also, the method gives much more
efficient calculation of potential of mean force than the selection criterion
based ASMD scheme, which is proven to be more efficient than traditional SMD. The
variance-linearly-dependent minus time derivative of overall variance proposed
for OBAR and OCE criterion is extended to determine the importance rank of the nonequilibrium
pulling in the configurational space. It is shown that the importance rank
given by the standard deviation of the free energy difference is wrong, but by correcting
it with the simulation time we obtain the true importance rank in
nonequilibrium stratification. The OCE workflow is periodicity-of-CV dependent
while ASMD is not. In the non-periodic CV case, the end-state discrimination in
the SD rank is eliminated in the TDV rank, while in the periodic CV case the
correction introduced in the TDV rank is not that significant. The performance is
demonstrated in a dihedral flipping case and two distance pulling cases,
accounting for periodic and non-periodic CVs, respectively. </p>
Efficient computation of free energy of crystal phases due to external potentials by error-biased Bennett acceptance ratio method
