λ-Meta Dynamics Approach To Compute Absolute Solvation Free Energy.

We present a new approach to combine λ dynamics with meta-dynamics (named λ-meta dynamics) to compute free energy surface with respect to λ. Particularly, the λ-meta dynamics method extends meta-dynamics to a single virtual variable λ, i.e., the coupling parameter between solute and solvent, to compute absolute solvation free energy as an exemplary application. We demonstrate that λ-meta dynamics simulations can recover the accurate potential of mean force surface with respect to λ compared to the benchmark results from traditional λ-dynamics with umbrella sampling. The solvation free energy results for five small organic molecules from λ-meta dynamics simulations using the same filling scheme show that the statistical errors are within ±0.5 kcal/mol. The new λ-meta dynamics method is general and other variables such as order parameters to describe conformational changes can be easily combined with λ-meta dynamics. This should allow for efficient samplings on high-dimension free energy landscapes.