Chemistry Reference
In-Depth Information
• The physical problem is translated into an analogous probabilistic or
statistical model.
• The probabilistic model is solved by a numerical stochastic sam-
pling experiment.
• The obtained data are analyzed by using statistical methods.
Athwart MD which provides information for nonequilibrium as well
as equilibrium properties, MC gives only the information on equilibrium
properties (e.g., free energy, phase equilibrium). In a NVT ensemble with
N atoms, new formation the change in the system
Hamiltonian
(ΔH) by
randomly or systematically moving one atom from position
i→j
can cal-
culated.
ΔH = H(j)-H(i)
(11)
Where
H(i)
and
H(j)
are the
Hamiltonian
associated with the original and
new configuration, respectively.
The
ΔH<
0
shows the state of lower energy for system. So, the move-
ment is accepted and the new position is stable place for atom.
For Δ
H
≥0 the move to new position is accepted only with a certain
probability P which is given by
(12)
is the Boltzmann constant.
According to
Metropolis
method, a random number ζ between 0 and 1
could be generated and determine the new configuration according to the
following rule:
For
the move is accepted;
(13)
For
the move is not accepted.
(14)
If the new configuration is rejected, repeats the process by using other
random chosen atoms.
