Metadynamics

Navigation: Documentation / Methods / Metadynamics

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Contents

• MTD:Description
• MTD:Controls
• MTD:Collective variables
• MTD:Post-processing
• MTD:Multiple walkers approach
• MTD:Examples
• MTD:Utilities

Description

Free Energy from Metadynamics Simulations

Metadynamics introduces a history-dependent potential, which is composed of Gaussian functions added in regular intervals. This potential is employed as a bias in molecular dynamics simulation to suppress visiting already sampled regions.

$V_{MTD}(\boldsymbol \xi) = \sum_{t=1}^{T_{MTD}} h_t exp \left( - \frac{1}{2} \frac{(\boldsymbol \xi - \boldsymbol \xi_t)^2}{\boldsymbol \sigma} \right)$ ... (8)

As a result, the system evolves by free diffusions alongside biased collective variables. Moreover, the history-dependent potential converges to the negative value of the free energy in a limit of infinitesimally long metadynamics simulation.

The application of the history dependent potential thus leads to the modified equations of motions:

$m_{i} \frac { d^2 \bold r_i }{dt^2} = \bold F_{pot,i}(\bold r_i) - \bold F_{bias,i}(\bold r_i) = - \frac{\partial V(\bold R)} {\partial \bold r_i} - \frac{\partial G(\boldsymbol \xi)}{\partial \boldsymbol \xi} \frac{\partial \boldsymbol \xi}{\partial \bold r_i}$ ... (8)

where $m_i$ is mass of atom i, $\bold r_i$ is atom position, and $t$ is time.

Since the biasing force is not known prior to the simulation, it is calculated during the simulation and adaptively applied. To accelerate sampling, the biasing force is applied even if an inadequate number of samples is collected in a bin. In this case, the biasing force is scaled in the early stages to avoid artifacts from applications of overestimated biasing forces. The biasing force can also be smoothed to decrease noise in collected data. For further details, see feimode in ABF:Controls.