Adaptive Biasing Force Method: Difference between revisions
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==Description== | ==Description== | ||
===Free Energy from Unconstrained MD Simulations=== | ===Free Energy from Unconstrained MD Simulations=== | ||
The Adaptive Biasing Force (ABF) | The Adaptive Biasing Force (ABF) nethod calculates the free energy as a function of selected collective variables from unconstrained molecular dynamics (MD) simulations. The method does not provide the free energy directly, but instead, it provides the free energy gradient <math>\frac{\partial G(\boldsymbol \xi)}{\partial \boldsymbol \xi}</math>, which must be integrated to get the free energy: | ||
<center><math>\Delta G = G(\boldsymbol \xi_2) - G(\boldsymbol \xi_1) = \int_{\boldsymbol \xi_1}^{\boldsymbol \xi_2} \frac{\partial G(\boldsymbol \xi)} {\partial \boldsymbol \xi} \boldsymbol d \xi </math> ... (1)</center> | <center><math>\Delta G = G(\boldsymbol \xi_2) - G(\boldsymbol \xi_1) = \int_{\boldsymbol \xi_1}^{\boldsymbol \xi_2} \frac{\partial G(\boldsymbol \xi)} {\partial \boldsymbol \xi} \boldsymbol d \xi </math> ... (1)</center> | ||
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===Instanteous Collective Forces=== | ===Instanteous Collective Forces=== | ||
PMFLib implements two approaches to calculate Equation 3. | |||
====Simplified Algorithm==== | |||
====Original ABF Algorithm==== | |||
<center><math>\frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right) = \frac{1}{2} \left( \frac{\bold p^+_{\xi}(t+dt) - \bold p^+_{\xi}(t) } {dt} + \frac{\bold p^-_{\xi}(t+dt) - \bold p^-_{\xi}(t) } {dt} \right)</math> ... (11)</center> | |||
where | |||
<center><math>\frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right) = \frac{1}{2} \left( \frac{\bold p^+_{\xi}(t+dt) - \bold p^+_{\xi}(t) } {dt} + \frac{\bold p^-_{\xi}(t+dt) - \bold p^-_{\xi}(t) } {dt} \right)</math> ... (11)</center> | |||
==References== | ==References== | ||
<references /> | <references /> | ||