Adaptive Biasing Force Method: Difference between revisions
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The simplified ABF algorithm (fmode=1) uses the result of the product rule for derivatives applied on Equation 3 leading into the two distinct contributions into the instantaneous collective forces: | The simplified ABF algorithm (fmode=1) uses the result of the product rule for derivatives applied on Equation 3 leading into the two distinct contributions into the instantaneous collective forces: | ||
<center><math>\frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right) \big|_{(t)} = | <center><math>\frac {d} {dt} \left( \bold Z^{-1} \frac{d \boldsymbol \xi} {dt} \right) \big|_{(t)} = \left( \bold Z^{-1}(t) \nabla \boldsymbol \xi (t) \right) \cdot \bold a(t) + \frac{d}{dt} \left( \bold Z^{-1}(t) \nabla \boldsymbol \xi (t)) \right) \cdot \bold v(t) = \bold F_{ICF,pot}(t) + \bold F_{ICF,kin}(t)</math> ... (9)</center> | ||
The potential contribution <math>\bold F_{ICF,pot}(t)</math> employs the accelerations <math>\bold a(t)</math> calculated back from the velocities. This ensures that effect of SHAKE and other constraints on acceleration is properly counted (see [[Molecular_Dynamics_Algorithms|the leap-frog integration algorithm]] for further details): | The potential contribution <math>\bold F_{ICF,pot}(t)</math> employs the accelerations <math>\bold a(t)</math> calculated back from the velocities. This ensures that effect of SHAKE and other constraints on acceleration is properly counted (see [[Molecular_Dynamics_Algorithms|the leap-frog integration algorithm]] for further details): | ||