Free Energy Surface (FES) • Educational Schematic View
Target PMF
Bias V(s)
Estimated FES
Particle
CV 1 ($s_1$)
0.000
CV 2 ($s_2$)
0.000
Force Mag
0.000
Gaussians
0
System Status
TRAPPED
Trajectory Trace & Basin Crossings
Controls
Hill Height ($W_0$)
0.20
Hill Width ($\sigma$)
0.10
Pace ($\tau_{\text{dep}}$)
100
Temperature ($k_B T$)
0.50
Sim Speed
1x
Bias Factor (γ)
10.0
PMF vs Est. FES Similarity
RMSE (FES Accuracy)
0.000
Theoretical Background
Collective Variables (CVs):
Enhanced sampling requires mapping the high-dimensional configuration space $\mathbf{R}$ to a set of low-dimensional descriptors $s(\mathbf{R})$. In this explorer, $s_1$ and $s_2$ represent the spatial coordinates.
Metadynamics (MetaD):
A history-dependent bias potential $V(s, t)$ is constructed by depositing Gaussians at the current CV position $\mathbf{s}_t$:
$$V(s, t) = \sum_{t' < t} W_0 \exp\left(-\frac{|\mathbf{s} - \mathbf{s}_{t'}|^2}{2\sigma^2}\right)$$
In Well-Tempered Metadynamics, the hill height is scaled: $W = W_0 \exp\left(-\frac{V(s,t)}{k_B \Delta T}\right)$.
On-the-fly Probability Enhanced Sampling (OPES):
OPES targets a specific distribution by adaptively estimating the bias. The probability $P(s)$ is refined as:
$$V(s, t) = (1 - 1/\gamma) k_B T \ln\left(\frac{P(s, t)}{Z} + \epsilon\right)$$
Free Energy Surface (FES):
The goal is to conduct reweighting to obtain the FES, $G(s) = -k_B T \ln P(s)$. As $t \to \infty$, $G(s) \approx -V(s, t) \frac{\gamma}{\gamma - 1}$.