Chemistry Reference
In-Depth Information
5 Computational Methods
In the field of nanoalloys, computer simulation is becoming increasingly important,
both to predict the structures that may form through metal-metal interactions in
bimetallic nanoparticles and to support the interpretation of experimental data.
While high-level ab initio molecular orbital calculations, including electron
correlation, have been carried out for small nanoalloys with up to around ten
atoms [
55
], owing to their computational expense, they rapidly become unfeasible
for larger clusters. DFT calculations [
56
,
57
], which scale much better with cluster
size than ab initio methods, while typically showing good agreement with exper-
iment, have become increasingly popular for studies of NAs with tens or even
hundreds of atoms [
58
,
59
], though rigorous structural searches at the DFT level
(typically combined with genetic algorithm and basin-hopping Monte Carlo
methods) have only been performed for smaller particles with up to around 20-30
atoms [
60
].
For this reason, studies of large NAs have tended to use computationally cheaper
empirical atomistic potential energy functions, which do not explicitly include
electronic effects. There are a variety of empirical atomistic potentials which
have been applied to study the structures, dynamics and thermodynamics of NAs
[
7
,
61
]. These empirical potentials typically have parameters which are fitted to
experimental (or high-level theoretical) data for bulk metals and alloys and some-
times for small clusters. There are several empirical many-body potentials based on
the second moment approximation to tight-binding theory [
62
], the most widely
applied for studying NAs being the Gupta potential [
63
,
64
]. This potential has been
used to study static and dynamic properties of NAs with hundreds or thousands of
atoms [
58
,
65
-
68
].
In the Gupta potential [
63
,
69
], the configuration energy of a system of
N
atoms
is obtained as
X
N
E
i
þ
E
i
E
¼
ð
1
Þ
i
¼
1
where the contribution of each atom,
i
, comprises two terms:
1
X
N
r
ij
r
0
E
i
¼
A
exp
p
ð
2
Þ
j6¼i
t
X
1
N
j6¼i
ξ
r
ij
r
0
E
i
¼
2
exp
2
q
ð
3
Þ
The repulsive term,
E
i
R
, is the pairwise Born-Mayer-type interaction of atom
i
with its neighbours. The binding or cohesive term,
E
i
B
, is proportional to the width
(square root of the second moment) of the d-band of the electron density of states,
