Environmental Engineering Reference
In-Depth Information
TABLE 1.6
Brief Comparison of Three Different Simulation Methods
Merits
Drawbacks
DFT
High accuracy; more details
(electronic states, charge dis-
tribution, molecule orbits)
Limited to static states of small sys-
tems; slow and expensive
MD
Available for large systems;
fast and cheap
Disable in chemical reaction (bond
breaking/forming); empirical poten-
tials are used whichleads to low accu-
racy
CPMD
Combined MD with DFT; a
balance between the time con-
suming andprecision
Limited to dynamic process of small
systems
1.3.2.2 MOLECULAR INTERACTIONS
Molecular dynamics simulation consists of the numerical, step-by-step, solution
of the classical equations of motion, which for a simple atomic system may be
written:

mr
=
f f
=−
U
ii
i i
r
(103)
i
For this purpose we need to be able to calculate the forces fi acting on the atoms,
and these are usually derived from a potential energy U(r N ), wherer N = (r 1 ; r 2 ; : : :
r N ) represents the complete set of 3N atomic coordinates. In this section, we focus
on this function U(r N ), restricting ourselves to an atomic description for simplic-
ity. In simulating soft condensed matter systems, we sometimes wish to consider
non-spherical rigid units, which have rotational degrees of freedom.
1.3.2.3 NON-BONDED INTERACTIONS
The part of the potential energy U non-bonded representing non-bonded interac-
tions between atoms is traditionally split into 1-body, 2-body, 3-body, ... terms:
(
)
(
)
( )
∑∑
N
U
r
=
ur
+
vrr
,
+
(104)
non
bonded
i
i
j
i
i ji
>
The u(r) term represents an externally applied potential eldor the effects of the
container walls; it is usually dropped for fully periodic simulations of bulk sys-
tems. Also, it is usual to concentrate on the pair potential v(ri; i ; r j ) = v(r ij ) and neglect
three-body (and higher order) interactions. There is an extensive literature on the
way these potentials are determined experimentally, or modeled theoretically. In
 
 
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