## Evaluating FES Free energy surface could be more complicated, since it includes the effect of entropy. And free energy is directly related to the probability of an event $\implies$ determines the distribution. Therefore, for low probability regions, the statistics would be very bad. Hence, we apply advanced sampling, or say "importance sampling" or "non-Boltzmann" sampling. The idea of advanced sampling is applying different probability distributions, so we can explore those rarely find regions, make sampling more efficient. We actually saw them in [[Reweighting and enhanced sampling techniques]]. Here brief intro will be given. - Umbrella sampling Add a bias potential to a particular value of the reaction coordinate. For umbrella sampling, $V = \frac{1}{2} k ({ \xi (x) - \xi_i })^2$. then reweight, the assigned weight, or probability factor is $W'(q) \propto W(q) \exp \left( -\frac{k(\xi(q) - \xi_i)^2}{2k_B T} \right)$ - Metadynamics Free energy wells are filled with a history-dependent potential with accumulating Gaussian term, so the sample would be encouraged to visit points/conformations it visited. For a given transition from A to B, rate $v_{A→B}$ would be $v_0 \exp \left( \frac{-\Delta F}{RT} \right)$, $\Delta F$ is a function of $s$. So the idea is to add a bias potential depending on $S$. On the original one to increase the probability $\rightarrow$ add a penalty term to already visited state. The best estimation of bias is $-F(s)$, but we don’t know the landscape, that’s why we use metadynamics. Advances of metadynamics: - discourage the exploration of the already visited states in the CV space. - provide an immediate estimate for the underlying [[Free energy surface|F.E. surface]]. - Gaussians are added (i.e., umbrella P) to the potential to the explored states, so revising discouraged. - done in low-dimensional space. - has reasonable chance to explore several times the same value $S$ (may correspond to different config $q$) - ratio of frequency of drop and height of the Gaussian is $w = \frac{w_0}{T_g}$, known as deposition rate. >[!Note] >For MD (molecular dynamics), we typically select collective variables (CV) to analyze instead of the 6N dimensional matrix directly. The free energy depends on this CV (we call $s$).