Adaptive Biasing Force Method: Difference between revisions
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===Adaptive Bias=== | ===Adaptive Bias=== | ||
ABF introduces an adaptive bias, which improves the sampling of rare events. The bias removes barriers or higher free energy regions in the space described by predefined collective variables <math>\boldsymbol \xi</math>. As a result, the system evolves alongside these collective variables | ABF introduces an adaptive bias, which improves the sampling of rare events. The bias removes barriers or higher free energy regions in the space described by predefined collective variables <math>\boldsymbol \xi</math>. As a result, the system evolves by free diffusions alongside these collective variables. The bias is derived from the free energy, which is projected in the form of biasing force <math>\bold F_{bias}</math> to the Cartesian space and removed from force <math>\bold F_{pot}</math> originated from interatomic interaction potential <math>V(\bold R)</math>. The application of the bias thus leads to the modified equations of motions: | ||
<center><math>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}</math> ... (8)</center> | <center><math>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}</math> ... (8)</center> | ||
where <math>m_i</math> is mass of atom i, <math>\bold r_i</math> is atom position, and <math>t</math> is time. | where <math>m_i</math> is mass of atom i, <math>\bold r_i</math> is atom position, and <math>t</math> 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]]. | |||
===Instanteous Collective Forces=== | ===Instanteous Collective Forces=== | ||