Classical molecular simulation methods
Collaborators: Donald W. Noid and Bobby G. Sumpter, Chemical and
Analytical Sciences Division, Oak Ridge National Laboratory
Polymer, biological, and other systems treated by molecular dynamics (MD),
molecular mechanics (MM), normal coordinate analysis (NCA), and Monte
Carlo (MC) methods consist of highly connected bond networks. The
potential energy surfaces used to model these systems contain
manybody chemically bonded interactions (stretch, bend,
proper and improper torsion, and so on). The most expensive
portion of the above methods is the computation of
internal coordinates and their first and second derivatives;
this has been an active area of research for us in the last several years.
Developments over the last several years include:

An approach for computing internal coordinates and first and second
derivatives of three and fourbody interactions in terms of two
and threebody interactions contained therein. Because of the way
it is programmed, we have named this the geometric statement
function approach. Interaction types treated in this manner include
bend,
torsion (the cosine, sine, and the angle itself),
improper torsion, and inplane and outofplane bend (angles and
heights).

A switching function approach for overcoming bend angle singularities
that occur in torsional interactions accompanied by dissociation.

Formulas for gradient dot products and Laplacians used in the
internal coordinate quantum Monte Carlo method. The Laplacians are
also useful for economizing the computation of second derivatives
required in NCA and some MM calculations.

The general bond network method,
a method of automating the
bookkeeping for chemically bonded
internal coordinates and derivatives for
any bond network. Software for molecular simulation, especially at
the research level, is
often optimized for particular applications. For example, it makes
sense to segregate the atoms in a carbon nanotube by rings, a polyethylene
chain by its monomer units, and so on. However, programming for specific
applications can be a tedious, errorprone process.
General bond network code for chemically bonded internal coordinates
and derivatives
can be ported to completely different applications with no
modification and with no loss of computational efficiency.
Current developments include:

Continual efforts to improve formulas for internal coordinates and their
derivatives.

A repeating general bond network method. The general bond network
method requires a lot of memory. In systems with composed of identical
or nearly identical pieces (for example, carbon nanotubes or diamondoid
bond networks),
the memory usage can be reduced by constructing interaction tables
for each piece type and then tiling together the pieces.

A paper under preparation for submission to Computer Physics Communications
giving the very latest version of our formulas for internal coordinates
and their derivatives, as well as accompanying software. We are in
the process of adapting the software, which we have used successfully
for several years, for more general consumption.