Chemistry Reference
In-Depth Information
the self-diffusion coefficient is related to the velocity autocorrelation function. On
the other hand, the shear viscosity is associated with the time autocorrelation
function of the off-diagonal elements of the stress tensor. The thermal conductivity
and the electrical conductivity are related to the autocorrelation functions for the
energy and electrical current, respectively.
Beside the Green-Kubo and the Einstein formulations, transport properties
can be calculated by non-equilibrium MD (NEMD) methods. These involve an
externally imposed field that drives the system out of the equilibrium. Similar to
experimental approaches, the transport properties can be extracted from the long-
time response to this imposed perturbation. E.g., shear flow and energy flux
perturbations yield shear viscosity and thermal conductivity, respectively. Numer-
ous NEMD algorithms can be found in the literature, e.g., the Dolls tensor [
221
], the
Sllod algorithm [
222
], or the boundary-driven algorithm [
223
]. A detailed review of
several NEMD approaches can be found, e.g., in [
224
].
The NEMD methods are based on the general expression [
225
]:
h
J
ð
t
Þi
g ¼
lim
F
e
!
0
lim
t!1
;
(34)
F
e
where
is the steady state average of the thermodynamic flux
J
(
t
) perturbed by
the external field
F
e
. Although a methodology for calculating diffusion coefficients
with NEMD is available, such methods are predominantly employed to calculate
the shear viscosity and the thermal conductivity [
226
,
227
]. NEMD methods are
favored when the signal-to-noise ratio is high for long times. There is an extensive
ongoing discussion on whether or not NEMD methods should generally be
preferred over equilibrium MD [
11
,
225
,
228
,
229
].
h
J
(
t
)
i
5.5 Simulation Tools
There are numerous available open source and commercial molecular simulation
codes. Examples for MD codes are CHARMM,
1
DL-POLY [
230
], GROMACS
[
231
], LAMMPS [
232
], MACSIMUS,
2
Moldy [
233
],
ms
2[
234
], NAMD [
235
],
Tinker [
236
], and YASP [
237
]. Some MC simulation codes are BIGMAC,
3
BOSS
[
238
], GCMC,
4
MedeA Gibbs,
5
MCCCS Towhee
6
, and
ms
2[
234
]. These software
packages have been developed for different applications and show large differences
in terms of performance, parallelization paradigm, and handling. Most of them use
1
2
3
4
5
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