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using Gaussian distribution at a low temperature, usually around 100K.
The system is then heated up to the desired temperature using various
techniques (e.g. scaling of the velocities, equilibration with a heat bath)
and equilibrated to allow energy redistribution. After all of these steps,
the equilibrated system can be studied and the production dynamics
started.
3.2. Thermodynamic Ensembles
Newton's equation (6), where
F
i
represent interatomic forces, describes
the evolution of an isolated system. The associated integrator [Eq. (9)]
generates trajectories at a fixed energy
E
determined by the initial condi-
tions. Let the Hamiltonian function
2
p
m
Â
i
Hr p
(, )
=
+
Vr
()
2
i
1
represent the instantaneous energy of the system. We say that the
Newtonian dynamics (or the equivalent Hamiltonian dynamics)
generates the NVE or microcanonical ensemble. This means that
allowed system conformations (
r, p
) in phase space are restricted to a
hypersurface of constant energy
E
, described by the microcanonical
density of states
r
NVE
(, )
rp
µ
d
[ (
Hr p E
-
-
)].
However, many laboratory experiments are conducted in solution,
where the system is thermally coupled to its environment. In this case,
the temperature of the system not its energy, is fixed. This corresponds
to the NVT or canonical ensemble. A fundamental reason to study
systems coupled to heat baths is that isolated systems cannot display any
dissipative behavior. For the system to be able to relax to a state
of maximum entropy, as the second law of thermodynamics describes for
all macroscopic systems, there has to be a way to exchange energy with
