Chemistry Reference
In-Depth Information
Initial coordinates
R
(
X
, Y,
Z
)
Set initial conditions
r
i
(
t
0
) and
v
i
(
t
0
)
Random displacement
of
i
Get new forces
F
i
(
r
i
)
th
atom in
R
to get
R
¢
(
X
¢
, Y
¢
, Z
¢
)
Solve the equations of motions
numerically over a short step
Δ
t
Calculate
Δ
u
=
u
¢
−
u
r
i
(t
)
r
i
(
t
n
+1
)
n
v
i
(t
)
r
i
(
t
n
+1
)
n
YES
t
=
t
+
Δ
t
Is
Δ
u
> 0?
Set
R
=
R
¢
Get desired physical quantities
NO
Get Random Number
RAN
in [0, 1]
NO
Is
t
>
t
max
?
NO
YES
-
Δ
u
/
kT
<
Is
e
RAN
?
YES
Calculate results and finish
Fig. 4 Simplified Metropolis Monte Carlo and molecular dynamics scheme
After equilibrium is achieved, equilibrium properties can be calculated by an
appropriate sampling of the ensemble. As only about a few hundred or thousand
particles are used in a simulation box, many particles are close to the wall. This creates
special wall effects which have to be avoided. This can be overcome by implementing
periodic boundary conditions.
MC techniques can also be used for solving the Schr
€
odinger equation (quantum
MC) [
82
,
83
]. QMC differs from other post-HF approaches in that it is a fully
correlated method from the outset, rather than building on a mean-field approach.
All QMC methods are presently computationally very demanding. Details of the
MC approach can be found in the books [
23
-
25
].
The accuracy of MC and MD calculations depends primarily on proper force
fields. General force fields for molecular systems are not of sufficient quality for
universal use. As they were adapted to specific interactions, the terms are not
transferable to any other application. Nevertheless, one can formulate some require-
ments force fields should satisfy. They should be robust, that means they should be
valid in varying environments. For example, phase behaviour can only be des-
cribed correctly if the same model represents all phases of the same quality. Other
requirements are accuracy, simplicity and transferability. The accuracy of a force
field should be such that experimental data can be reproduced with the required
precision. Transferability means that the underlying principles of constructing the
model and the parameters obtained should be applicable for various molecular
problems. It is often the non-additivity of constituent terms, and the omission of
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