University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Structure function S(Q)
This equation can be used to calculate
the structure function from an atomic
configuration.
∑∑
=<
+
=
N
j
N
j
i
ij
ij
Qr
Qr
N
Q
S
1
)
sin(
2
1
)
(
The calculations, however, involve the summation over all pairs of
atoms in the system, leading to the quadratic dependence of the
computational cost on the number of atoms and making the calculations
expensive for large systems.
=>
−
=
N
j
N
j
i
ρ
π
Nr
1
ij
0
2
)
r
δ
(r
2
1
g(r)
An alternative approach to calculation of S(Q) is to substitute the double
summation over atomic positions by integration over pair distribution
function
[2]
The expression for the structure function can be now reduced to the
integration over r (equivalent to Fourier of g(r) ):
The calculation of
g(r)
still involves
N
2
/2 evaluations of interatomic
distances
r
ij
, but it can be done much more efficiently than the direct
calculation of
S(Q)
, which requires evaluation of the sine function and
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 Fall '11
 Zhigilei
 Atomistic Simulations, rmax, Leonid Zhigilei, structure function, fs laser pulse

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