Local Elevation Umbrella Sampling Applied to the Calculation of Alchemical Free-Energy Changes via λ-Dynamics: The...

When using molecular dynamics (MD) simulations for the calculation of alchemical free-energy changes, the extended-dynamics method called λ-dynamics (λD) in its currently available implementations does not compare very favorably with thermodynamic integration (TI) in terms of robustness, efficiency, and accuracy, although it is in principle easier to set up, postprocess, and automatize. In the present article, the main shortcomings of the λD approach are carefully analyzed, and possible remedies are proposed. The resulting scheme, called λ-LEUS, involves: (i) the use of a simple noninvertible coordinate transformation ensuring a finite sampling of the two physical end states; (ii) the application of the local elevation umbrella sampling (LEUS) memory-based biasing scheme to enforce homogeneous sampling and overcome barriers along the alchemical coordinate; (iii) recommendations concerning the choice of the mass parameter and of the temperature-coupling scheme for this coordinate; (iv) the use of a second-order splines basis set for the memory-based biasing functions. The λ-LEUS scheme is described and tested considering the perturbation of hydroquinone to benzene in water. The results are compared to those of TI calculations and exhibit a superior accuracy-to-efficiency ratio, presumably because dynamic variations in the alchemical coordinate open up pathways to circumvent orthogonal barriers, these pathways being inaccessible when the coordinate is constrained. Therefore, λ-LEUS combines the practical advantages of λD with the robustness of TI, simultaneously affording a slightly enhanced computational efficiency.