Bias-exchange metadynamics

Bias-exchange metadynamics is an enhanced sampling method for MD simulations, specifically a form of parallel-tempering metadynamics intended for systems with a large number of collective variables (CVs). Unlike traditional metadynamics where all CVs are treated in combination, bias-exchange metadynamics runs one independent simulation per CV and swaps them randomly after a predetermined number of steps according to the Metropolis rule, similar to Replica-exchange molecular dynamics.

Details

The swapping probability is:

$$\min \left(1,\exp \left(\beta \left(V_G^a(X^a,t)+V_G^a(X^b,t)-V_G^a(X^b,t)-V_G^a(X^a,t)\right)\right)\right)$$

where $x^a$ and $x^b$ are coordinates of replicas $a$ and $b$, $V_G^{a(b)}(x,t)$ is the metadynamics potential acting on replica $a(b)$, and $\beta$ is the inverse temperature. If the swap would decrease the biasing potential, it is accepted; otherwise, it is accepted under the Metropolis criterion.