1. Background
Molecular simulation is a methodology for predicting the collective (in
particular, thermodynamic and transport) properties of systems from
information about how the molecules in the system interact with each
other. That “information” can be obtained on-the-fly from quantum
mechanics but, in most molecular simulations, it is encoded in a
mathematical function, called a force field, that attempts to include
all the intermolecular interactions between molecules (electrostatic
interactions, van der Waals repulsive and attractive interactions) as
well as intramolecular interactions (e.g., bond stretching, bond angle
bending, and torsional interactions). More specifically, a force field
is a representation of the total potential energy associated with
interactions of all the atoms in the system (obtained by summing over
all the molecules), which can be differentiated with respect to the
position of an atom to obtain the force exerted on that atom. Force
fields can be derived from first principles calculations (e.g., quantum
chemistry calculations) and/or experimental data; thus, generally force
fields are semi-empirical. For inhomogenous systems (e.g., a fluid
adsorbed on a surface or into a pore), the force field includes models
for how the molecules interact with atoms in the surfaces or with an
external field. Assuming that the molecular simulation runs long enough
to attain equilibrium, and that the system is large enough or configured
to eliminate unwanted surface effects (through so-called periodic
boundary conditions), for a given force field, molecular simulation can
provide essentially exact information about the properties of the
system, obtained by averaging over the configurations generated in the
simulation. Two major types of molecular simulations are routinely
performed: molecular dynamics (MD), in which Newton’s equations, or a
convenient variation thereof, are solved for the dynamics of each atom
in the system, and Monte Carlo (MC) simulation, in which configurations
of the system are generated via a Markov chain process that
asymptotically are distributed according to the appropriate equilibrium
ensemble probability (e.g., for systems at constant molecule number\(N\), volume \(V\), and temperature \(T\), the Boltzmann distribution,
in which configurations have probability \(\propto e^{-E/k_{B}T}\),
where \(E\) is the energy of the system and \(k_{B}\) is Boltzmann’s
constant). In either case, the raw output of the simulation is
configurations of the system (known as a trajectory) that can then be
analyzed to compute properties. From an MD simulation, the trajectory
will consist of positions and velocities for all atoms in the system
over the course of the simulation; a typical MD simulation will employ a
time step of \(10^{-15}\)s, so that a 10-100 ns trajectory covers\(10^{7}-10^{8}\) steps. For a 100,000-atom simulation (a typical
system size with current computational resources), a trajectory file can
be of the order of terabytes, so that statistical analysis of such files
can be thought of as a particular kind of “big data” problem.
Molecular simulation began in the 1950s with simple systems such as hard
spheres (MC1 and MD2,3) and in the
1960s with the Lennard-Jones fluid (MC4 and
MD5). For such monatomic systems, the force field is
very simple, specifying the interaction energy between spherically
symmetric molecules. Beginning in the 1970s, molecular simulation was
introduced to the field of chemical engineering primarily by Keith
Gubbins, the honoree of this Founders issue of AIChE Journal .
Keith is known and admired internationally and across many disciplines
not only for his contributions in molecular theory (which have been
seminal, such as Gray-Gubbins perturbation theory and the statistical
associating fluid theory, or SAFT, equation of state) but also for his
research in molecular simulation. One of the earliest Gubbins simulation
papers6 from 1979 has been cited almost 1000 times.
[As an aside, his postdoctoral trainee co-author on this paper,
Dominic Tildesley, was for many years a successful academic in the UK
before joining Unilever, where he established one of the world’s premier
industrial molecular modeling groups, eventually rising to Vice
President of Discovery Platforms; Tildesley also co-authored one of the
seminal text books on molecular simulation7.]
Keith’s influence on the field of chemical engineering in relation to
molecular simulation can be measured in programming at AIChE Annual
Meetings (which in the early 1980s had no sessions on molecular
simulation in contrast to today when a whole programming area – the
Computational Molecular Science and Engineering Forum, Area 21 – is
largely focused on molecular simulation) and in papers presented at
Properties and Phase Equilibria for Process and Product Design
conference series established in 1977 (in which the first molecular
simulation paper was presented in 1980, and by 2007 more than half the
presentations involved molecular simulation and/or molecular theory).
Since its early days, molecular simulation has become a workhorse in
science and industry. The promise of being able to predict collective
properties from molecular interactions, and the attendant insight
gained, have made molecular simulation (both MD and MC) an ideal and
indispensable capability in materials science, biology, medicine
(specifically, drug discovery) and engineering. There are commercial
entities that market molecular simulation software (e.g., BIOVIA and
Schrödinger). A 2002 international comparative study on molecular
modeling (of which molecular simulation constitutes a major component)
documented the widespread use of molecular modeling in industry,
including many chemical, drug, and personal care product
companies8.
The authors of this Perspective article are all beneficiaries of the
trail-blazing efforts of Keith Gubbins in establishing molecular
simulation as an accepted and respected subfield of chemical
engineering. Today, molecular simulation is taught in most chemical
engineering departments in the U.S. at the graduate level, and is
increasingly available as an elective at the undergraduate level or even
offered as a first-year seminar to incoming undergraduate students. It
has become one of the major focuses of the educational foundation, CAChE
(Computer Aids for Chemical Engineering Education, cache.org), which
established a molecular modeling task force in 1998. CACHE runs a highly
successful technical conference, Foundations of Molecular Modeling and
Simulation (fomms.org, held every three years since 2000) that has
produced many educational resources to enable chemical engineers to
teach and utilize molecular simulation in the classroom. In 2012, Keith
Gubbins was awarded the FOMMS Medal for his numerous and long-standing
contributions to the molecular simulation community. In addition to
prodigious research contributions, he has authored seminal
textbooks9, including the two-volume definitive
treatise on the theory of molecular fluids10,11 that
is an essential part of the library of any serious statistical
mechanician interested in molecular fluids.
2. Development of molecular simulation tools in the chemical
engineering
community
Although molecular simulation (MD and MC) transcends disciplinary
boundaries as noted above, chemical engineers have been particularly
active in developing algorithms that compute properties of strong
interest to the chemical engineering community (ChEC). One example is
vapor-liquid phase equilibria, which is of enduring interest to the ChEC
due to separation processes. Thus, a molecular simulation methodology
for computing phase equilibrium directly and efficiently, the Gibbs
ensemble MC (GEMC) algorithm, was developed in 1987 within the ChEC by
Panagiotopoulos12. Phase equilibria can involve
differences in densities between phases of several orders of magnitude;
likewise, in chemical manufacturing there can be wide ranges of state
conditions. Hence, along with the development of algorithms, the ChEC
has also been at the forefront of developing force fields that are
accurate over wide ranges of state conditions, such as the TraPPE family
of force fields optimized for vapor-liquid equilibrium (see the
extensive resources at http://trappe.oit.umn.edu) and the Gaussian
charge polarizable model (GCPM) for water13 that
correctly predicts water’s phase equilibria, thermodynamic, transport
and dielectric properties over wide ranges of temperature and pressure.
By contrast, much of the molecular simulation community in other
disciplines is focused on properties at or near ambient conditions
(including ambient conditions for biological systems).