Chemistry Reference
In-Depth Information
need not concern ourselves with; we will call MD a deterministic method, but
we know this is only approximately true. Other simulation methods exist that
are part stochastic and part deterministic, and these are becoming increasingly
useful to compute properties of complex systems.
The trajectories generated using MD or MC will be consistent with the
energetic model imposed on the system. If the methods have been implemen-
ted correctly, the trajectories will also be consistent with the limiting
probability distribution of the particular statistical mechanical ensemble
under which the simulations were run. Atomic positions are all that is needed
to, at least in principle, compute all the thermodynamic properties of the
model system. If the velocities are also available (i.e., if an MD simulation
was run), then time-dependent properties may also be computed. Assuming
the simulations have been carried out properly, the resulting trajectories pro-
vide an
exact
solution for the model system. Therefore, the degree to which
the simulation results agree with experimental data for the ''real'' system tells
us how good the model is at representing the real system. This is how simula-
tions are often used, and one can think of them as a ''theoretical'' result.
Alternatively, if we use simulation methods to model a theoretical system
for which an approximate analytical solution exists, the level of agreement
between the simulation and theory tells us how accurate the theoretical
approximation is. Used in this manner, simulations are like a computational
''experiment'' against which theory can be tested. Both approaches have been
used for ionic liquids, though the former method is far more common and will
be the focus of this review.
The above comments emphasize the fact that a great deal of attention
must be paid to the model used to represent the atomic species and their
energetic interactions if quantitative property predictions are desired.
Much of the early work on ionic liquid simulations has focused on this,
and so we will need to discuss this in some detail if we are to understand
how simulations are used for these systems. The place to start discussing
potential models for ionic liquids is with the early work on molten alkali
halides. Even though these materials do not fall under our definition of ionic
liquids, almost all the current simulation approaches to ionic liquids
have their roots in these early studies. In what follows, the shorthand term
force field
will be used to represent a set of analytic equations that approx-
imate the energetic interactions among atoms in a system. We know that
these interactions take many forms, from strong forces characteristic of cova-
lent bonds to weaker forces representative of van der Waals interactions, and
long-range electrostatic interactions.
One of the earliest functional forms used to model alkali halides is due to
Huggins and Mayer.
16
They modeled the electrostatic interactions between
ions by placing formal charges
q
i
on each atom center. Short-range repulsive
interactions were modeled with an exponential function, and long-range
attractive interactions with two terms representing dipole-dipole and dipole-
