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with the results of Hanke, Prince and Lynden-Bell, 30 who also observed that
their united-atom models tended to give denser systems than their explicit-
atom counterparts. These findings suggest that explicit-atom models are
more accurate than united-atom models possibly because of their greater rea-
lism, although one could tune the united-atom parameters to get as accurate a
result as wanted. Nearly all subsequent simulation studies of ionic liquids have
relied on explicit-atom models.
The simulation times in the Morrow and Maginn 49 study were signifi-
cantly longer than that used in any simulation of an ionic liquid up to that
point. Equilibration times ranged from 700 to 1000 ps, and production runs
of 4 ns were carried out. As foreshadowed by the work of Margulis and co-
workers, 47 long simulations are required if reasonable dynamical properties
are to be obtained with these fluids. This is because ionic liquids tend to exhi-
bit very sluggish dynamical behavior at room temperature, reminiscent of
supercooled liquids. While densities and other static properties appear to
converge within 50-100 ps, rotational time constants were calculated to be
much longer than even the 4-ns simulation run time. The picture that began
to emerge from this and the work of others 47 is that reasonably short simula-
tions suffice for computing static properties (although proper equilibration is
required), but very long simulations might be required if dynamic properties
are being probed.
The group of de Andrade, Boes and Stassen published two studies dur-
ing 2002 in which MD was used to examine imidazolium-based ionic liquids.
The first 51 was a study of 1-ethyl-3-methylimidaziolium tetrachloroalumi-
nate, and the second 52 was a follow-up study in which a force field was
proposed for the 1-ethyl-3-methylimidaziolium and 1-butyl-3-methylimida-
ziolium cations paired with the tetrachloroaluminate and tetrafluoroborate
anions. Their force field was based on the AMBER functional form, 53 which
is similar to that used in the previous works. Derivation of the force field fol-
lowed the same procedure outlined earlier, including gas-phase calculation of
the ions followed by partial charge assignment for each atom by fitting to
reproduce the quantum electrostatic potential. The RESP method within
the package GAMESS 54 was used, but other methods give similar (though
not identical) results. Intramolecular terms as well as nonbond Lennard-Jones
parameters were taken from literature sources for similar compounds. Their
liquid densities were in near perfect agreement with experiment and com-
puted enthalpies of vaporization, once again, suggested that ionic liquids
should have some volatility (3 years later experimentalists made such mea-
surements). Finally, they estimated self-diffusion coefficients, but the short
(200-ps) simulation times lead one to believe that these systems are not yet
in the diffusive regime. One of the most interesting results from their study
is that they were able to compare their computed liquid structure with neu-
tron diffraction data that had just become available; 55 remarkably good
agreement between the computed liquid structure and the neutron diffraction
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