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Metadynamics
In metadynamics [76,73], the bias potential
that acts on a selected number of geometric parameters (collective variables)
is constructed onthefly during the simulation.
The Hamiltonian for the metadynamics
can be written as:

(6.17) 
where is the Hamiltonian for the original
(unbiased) system, and
is the
timedependent bias potential. The latter term
is usually defined as a sum of Gaussian hills with
height and width :

(6.18) 
In practice,
is updated by adding a new Gaussian
with a time increment , which is typically one or two orders of magnitude greater
than the time step used in the MD simulation.
In the limit of infinite simulation time, the bias potential is related
to the free energy [76,73] via:

(6.19) 
Practical hints as how to adjust the parameters used in metadynamics
(, , ) are described in Refs. [69,77].
The error estimation in freeenergy calculations with metadynamics
is discussed in Ref. [77].
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