Umbrella sampling

Initial structures for each umbrella window were obtained from TMD trajectories by selecting snapshots with 0.2 Å RMSD between adjacent windows. To equilibrate each structure in each window, initial simulations were run with a higher biasing force constant of 200 kcal/mol/Ų for 20 ps. The force constant was gradually reduced to 10 kcal/mol/Ų over the course of 80 ps, after which additional equilibration was performed for 50 ps using this force constant. Finally, each umbrella sampling window was sampled for 3 ns. After obtaining biased probability distributions from the resulting trajectories, WHAM (42, 43) was used to unbias the distributions and to obtain the PMF profile. Equilibrium averages of the dipole-moment z-component, μ_z, were calculated from umbrella sampling simulations after unbiasing according to Eq. 7.