Anatomy of a grid-enabled molecular simulation
study: the compressibility of amorphous silica
Andrew M Walker
1
, Martin T Dove
1,2
, Lucy A Sullivan
1
, Kostya Trachenko
1
, Richard
P Bruin
1
, Toby OH White
1
, Peter Murray-Rust
3
, Rik P Tyer
4
, Phillip A Couch
4
, Ilian T
Todorov
1,4
, William Smith
4
, Kerstin Kleese van Dam
4
1. Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ
2. National Institute for Environmental eScience, University of Cambridge, Downing Street, Cambridge
CB2 3EQ
3. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW
4. CCLRC, Daresbury Laboratory, Warrington, Cheshire WA4 4AD
Abstract
We report a case study in grid computing with associated data and metadata management
in which we have used molecular dynamics to investigate the anomalous compressibility
maximum in amorphous silica. The primary advantage of grid computing is that it
enables such an investigation to be performed as a highly-detailed sweep through the
relevant parameter (pressure in this case); this is advantageous when looking for derived
quantities that show unusual behaviour. However, this brings with it certain data
management challenges. In this paper we discuss how we have used grid computing with
data and metadata management tools to obtain new insights into the behaviour of
amorphous silica under pressure.
Introduction
It is now well-established that grid computing
comes into its own in the physical sciences
when it enables simulation studies to be carried
out across a sweep of the input parameters.
Examples might be studies of a system as a
function of external conditions such as
temperature or pressure. Whilst the existence of
a grid of computers facilitates the parallel
running of many separate simulations, to make
effective use of the potential of grid computing
it is essential to have appropriate workflow and
data management tools. In this paper we report
on a case study that has used a set of tools
developed within the eMinerals project.
The particular case concerns a study of the
properties of amorphous silica (SiO
2
) as a
function of pressure. Our interest concerns the
way that volume varies with pressure. In almost
all materials, relative volume changes become
smaller with increasing pressure, which is
equivalent to the statement that most materials
become stiffer under pressure. Usually this can
be explained by the fact that the atoms are being
squeezed closer together, and the closer they are
the stiffer the structure. However, amorphous
silica behaves differently. On increasing
pressure, amorphous silica initially becomes
softer, until it crosses over to normal behaviour
[1]. Formally the stiffness is defined by the
inverse of the compressibility, κ
–1
, where
κ = –V
–1
(∂V/∂P).
Here V is the volume, and P is the pressure. In
most materials, κ decreases on increasing
pressure, but in amorphous silica κ has a
maximum at a pressure of around 2 GPa.
Our approach is to use the classical
molecular dynamics simulation method to study
the pressure-dependence of amorphous silica.
Because we need to calculate a differential, it is
important to obtain a large number of data
points on the volume/pressure graph, and it is in
this regard that grid computing plays an
important role. Using a grid enables the many
separate jobs to be run at the same time,
increasing the throughput by more than an order
of magnitude so that collecting many data
points becomes a viable process.

In this work we make use of the following
technologies:
‣ Methods to create and submit many jobs in
which one or more parameters are varied [2];
‣ Metascheduling within a minigrid compute
environment, with jobs distributed over
clusters and Condor pools [2,3];
‣ Use of the San Diego Storage Resource
Broker (SRB) for data archiving and the
sharing of data files [4];
‣ Use of XML output data and associated tools
to aid data analysis and sharing of the
information between collaborators [5];
‣
Incorporation of workflows within the job
submission procedure to enable analysis to be
performed on the fly [2];
‣ Automatic metadata capture using the
recently-developed RCommands [6].
The purpose of this paper is to describe how
these tools were combined to facilitate a
detailed molecular dynamics simulation study
of the compressibility of amorphous silica using
grid computing.
Science background
Amorphous silica, SiO
2
, is a random network of
corner-linked SiO
4
tetrahedra, Figure 1. We
work with configurations of 512 tetrahedra
generated from initial configurations of
amorphous elemental silicon [7] and tested
against neutron total scattering data [8].
The issue of compressibility concerns the
inherent flexibility of the network of connected
tetrahedra. This is a subtle issue, because
standard engineering methods of counting
constraints and degrees of freedom do not
capture the whole story. We have previously
demonstrated [7] that the silica network has an
inherent network flexibility in which the SiO
4

tetrahedra can rotate and buckle the network
without the tetrahedra themselves needing to
distort. Such motions will cost relatively little
energy; the higher-energy processes are those
that cause the SiO
4
tetrahedra to distort, either
through bending of the O–Si–O bond angles or
stretching of the Si–O bonds. There are two
ways in which buckling of the network of
corner-linked SiO
4
tetrahedra can happen. One
is through fast vibrations, and the other is
through larger jump motions in which several
tetrahedra change their orientations together.
Animations of both processes are available from
references 9 and 10 respectively, and are
surprisingly instructive.
Our approach is to consider the behaviour of
amorphous silica in the two extremes of large
negative and positive pressures in comparison
with intermediate pressures. First we note that
the compressibility, as defined earlier, can also
be defined in terms of the second derivative of
the free energy G:
κ = –V
–1
(∂
2
G/∂P
2
).
Thus compressibility is related to changes in
energy, and our hypothetical extreme end states
are both states in which any changes are
necessarily accompanied by large changes in
energy as compared to the intermediate state. At
large negative pressures (corresponding to
stretching the material) the bonds are
themselves stretched tight and the flexibility of
the network is accordingly reduced. To change
the pressure in this extreme will involve
distorting the SiO
4
tetrahedra – either by
changing bond lengths or bond angles – which
as noted above is quite a high energy process.
At the high-pressure extreme, atoms are pushed
tightly together and further changes in volume
can again only be accomplished by distorting
the SiO
4
tetrahedra. But in the intermediate
region, where there is more flexibility of the
network, volume changes can be accomplished
by crumpling the network without any
distortions of the SiO
4
tetrahedra. Since this is a
low energy process, the compressibility is a lot
higher.
Figure 1. Configuration used in the simulations
described in this paper, with SiO
4
polyhedra
represented as tetrahedra rather than representing
the individual atoms.