CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
2002 American Institute of Physics 0-7354-0068-7
AB INITIO MOLECULAR DYNAMICS SIMULATIONS OF
MOLECULAR COLLISIONS OF NITROMETHANE
Dongqing Wei% Fan Zhangb, Tom K. Wooc>*
"Centre de Recherche en Calcul Applique. 5160 Boul Decarie, suite 400, Montreal, Quebec H3X2H9, Canada.
b
Defense Research Establishment Sujfield, Box 4000 Stn Main, Medicine Hat, Alberta TIB 8K6, Canada
c
Department of Chemistry, University of Western Ontario, London, Ontario N6A 5B7, Canada.
Abstract. Ab initio molecular dynamics simulations of bimolecular collisions of nitromethane, and
collisions of one nitromethane molecule into a cluster of 12 nitromethane molecules have been performed.
For the bimolecular simulations we have examined a variety of collision orientations and collision
velocities between 6.5 and 12.0 km/s. The lowest dissociation threshold velocity found was 7.0 km/s for an
anti-parallel collision orientation. For all low velocity collision simulations, only C-N bond cleavage is
observed. The bimolecular collision simulations only show new fragmentation patterns at high collision
velocities of 11.0 km/s or higher. The multimolecular collision simulations show a much wider variety of
fragmentation patterns, including reactions involving three molecules and initial C-H bond scission.
Our current interest lies in liquid NM under
shocked conditions, where chemical decomposition
is believed to occur. A detailed atomic level
understanding of the decomposition mechanism of
liquid NM under these conditions is not yet clear.
Unimolecular C-N bond scission has often been
implicated as a dominant pathway since the C-N
bond is the weakest in NM. However, some high
pressure studies do not support this mechanism [4,
5], There are other unimolecular mechanisms, such
as, NM rearrangement to methyl nitrite and
formation of nitromethyl aci-anion. Several
bimolecular mechanisms proposed in [4] have also
been suggested by Haskins and Cook [6] as well as
by Bardo [7].
Through simulation, we hope to shed light on
the possible decomposition mechanisms of liquid
NM under shock conditions. Here we report our
results of ab initio MD simulations of bimolecular
collisions, multimolecular collisions and liquid NM.
COMPUTATIONAL DETAILS
In this study, we have utilized Kohn-Sham
density functional theory (KS-DFT) [8] at the
gradient corrected level with Becke's 1988 exchange
functional [9] and Perdew's 1986 correlation
functional (BP86) [10]. For all molecular dynamics
simulations the CPMD package of Parrinello has
INTRODUCTION
Shock-induced chemical decomposition of
molecular liquids and the high-pressure equation of
state have been topics of long-standing interest for
energetic materials. Nitromethane (NM) is a
prototypical energetic molecule, which due to its
small size has been the subject of numerous
theoretical
simulations.
Classical molecular
dynamics (MD) simulations of liquid NM under
ambient and shocked conditions have been
performed with empirically derived potentials.
However, the simulation of the chemical
decomposition of the molecular liquids is
problematic with traditional MD, due to the
limitations of the parameterized potentials.
Recently, it has become possible to perform
practical ab initio MD simulations of small
molecules in both the gas and liquid phase.
Bimolecular collisions of NM in the gas phase have
been simulated at the density functional level (DFT)
in order to examine possible decomposition
pathways. Tuckerman and Klein have performed ab
initio MD simulations of solid NM [1]. Recently,
Kress and coworkers have calculated the equationof-state properties of compressed liquid nitrogen and
deuterium, based on ab initio MD simulations [2, 3].
407
with a rms deviation of 40.0 cm"1 (CPMD to exp.).
The zero-point energy corrected dissociation energy
for the unimolecular decomposition of NM was
determined to 54.9 kcal/mol using the BP86
functional. This value is comparable with the results
ranging from 49.9 to 53.8 kcal/mol calculated at the
MCSCF and DFT levels by Manaa and Fried [15].
Bimolecular Collision Simulations
Bimolecular collisions of molecules serve as a
simplified model for shock induced dissociation in
bulk liquid. For this reason, collisions of two NM
molecules has been studied in the past [6]. Previous
MD simulations of the bimolecular collision of NM,
have been performed at the semi-empirical, HartreeFock and density functional theory levels. Haskins
and Cook [6] have examined the bimolecular
collision of two NM molecules at the DFT level
employing the Becke three parameter hybrid
exchange functional with the Perdew-Wang 1991
correlation functional. For a head-to-tail orientation,
they found a threshold velocity, where C-N bond
been utilizedfll] where the valence orbitals were
expanded in the basis of plane waves with a kinetic
energy cutoff of between 50 and 70 Ry. The nonlocal norm-conserving pseudo-potentials of Trouileer
and Martins [12] have been applied to represent the
ionic cores for O, N and C. The Car-Parrinello [13]
dynamics scheme was used with a time step of 0.14
fs. All simulations were performed in the spin
unrestricted formalism unless stated.
For comparison, the conventional all-electron
Gaussian basis set deMon package of Salahub [14]
was used with a double-zeta quality basis set which
includes polarization functions.
RESULTS AND DISCUSSION
Gas-phase Monomer Properties
There have been a number of theoretical studies
that have examined the gas-phase properties of NM
at the DFT and ab initio levels [6, 15, 16]. In
general, DFT results for the equilibrium geometry
and vibrational frequencies are in good agreement
with high level ab initio calculations and available
experimental data. We have benchmarked our planewave pseudopotential DFT calculations (BP86-
scission occurs, to be 8.5 km/s.
ay
CPMD) to that of conventional all-electron localized
basis set method (BP86-deMon), high level ab initio
calculations and experimental data.
p,
TABLE I. Comparison of Single Molecule Ground State
Properties of Nitromethane.
BP86
BP86
CPMDa
deMon
MCSCFb
Exp.c
C-N (A)
1.507
1.508
1.489
1.509
1.242
N-O (A)
1.224
1.240
1.197
C-N-O (°)
117.8
117.3
117.3
117.8
dipole (D)
3.41
3.53
3.57d
3.67
HH
perpendicular
(8.0 km/s)
head-to-tail
(8.5 km/s)
anti-parallel
(10.5 km/s)
H
offset anti-parallel
(7.0 km/s)
Figure 1. Orientations examined for bimolecular collision.
Shown in parenthesis are the observed threshold velocities.
We have performed bimolecular collision
simulations with the ab initio molecular dynamics
approach. Additional effort was made to examine
the dependence of the threshold velocity on the
initial orientation of the molecules. An orthorhomic
simulation cell of dimensions 16x12x12 A was used
with a plane wave cut-off of 60 Ryd. At time zero,
one molecule is set to a hyper-velocity of between
6.5 to 12.0 km/s (6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0,
11.0 and 12.0 km/s), towards the second, stationary
NM molecule. Typical simulations times were 250
fs. Shown in Figure 1 are the initial orientations that
have been examined. Two sets of "perpendicular"
and "offset anti-parallel" orientations were
examined. Parenthetic values in Figure 1, are the
observed threshold impact velocities where
dissociation is observed. Of the six collision
a
A FCC cell with a cell length of 17 A and a plane wave cut-off of
70 Ry was used. "MCSCF from ref. [15] with 6-311++G(2d,2p)
basis set cref. [17].dref. [18].
Key geometric parameters for gas-phase NM are
shown in Table I. There is exceptional agreement
between the all-electron Gaussian deMon results to
those of the plane wave pseudopotential CPMD
results. There is further excellent agreement in these
properties between MCSCF results[15] and
exerimental data.
The calculated harmonic
vibrational frequencies show a similar agreement,
with a rms deviation of only 15.4 cm"1 between the
CPMD and deMon results. These vibrational
frequencies are also in excellent agreement with the
anharmonic frequencies obtained experimentally
408
orientations that we have studied, one of the offset
anti-parallel collision orientations has the lowest
threshold velocity of 7.0 km/s. For the head-to-tail
collision orientation we have found a threshold
velocity of 8.5 km/s. This in agreement with the 8.5
km/s threshold velocity that Haskins and Cook found
for their head-to-tail bimolecular collisions at the
DFT level.
We note that C-N bond scission of the incoming
NM molecule is observed for virtually all collision
simulations. Only for the off-set anti-parallel
orientation at a collision velocity of 11.0 km/s or
higher is a different decomposition pathway
observed. In those high velocity simulations, there is
initial O-N bond cleavage of the stationary NM
molecule and transfer of this oxygen to the incoming
CH3 fragment. The oxygen transfer is accompanied
by C-N bond scission of the incoming NM molecule
and transfer of a oxygen back to the CH3NO
fragment of the station molecule to reform NM. The
products of this simulation are NM, NO and OCH3.
Multiple Molecule Collision Simulations
Bimolecular collision simulations serve as a
reasonable first approximation for shock-induced
reactions. However, it is obvious that these
simulations can not take into account the role of
neighboring molecules, particularly the further
reaction of molecular fragments after initial, say, CN bond cleavage. To investigate this issue, we have
carried out multi-molecular collision simulations
such that one NM molecule is projected into a cluster
of 12 molecules.
For the multi-molecule collision simulations, the
CPMD program was utilized with a plane wave cutoff of 50 Ryd. 13 NM molecules were placed in a
orthorhombic simulation cell of dimensions
19.0x14.2x14.2 A. 12 NM molecules were on one
side of the simulation cell. These molecules were
randomly oriented possessing a local density of 1.14
g/cm3, corresponding to the density of liquid NM at
room temperature and ambient pressure. One
molecule was placed on the other end of the
simulation cell. Approximately 1 ps or 7000 time
steps were performed for each simulation.
Figure 2 shows snap shots from a
multimolecular simulation with a collision velocity
of 12.0 km/s. Frames a and b reveals that there is
initial head-to-tail impact resulting in C-H bond
cleavage instead of C-N bond scission. We note, that
t = 52 f s
i
t = 78 fs
t = 99 fs
t = 305 fs
Figure 2. Snapshots from a multimolecular collision simulation.
Spectator molecules have been removed for clarity.
409
intend to compute equation-of-state properties and
molecular collision mechanisms in liquid NM
simulations under initial conditions of high-pressure
compression. A preliminary CPMD simulation of
liquid NM at ambient pressure in a cubic cell of
14.174 A with 32 molecules has been performed.
Our initial results after 10,000 time steps of
equilibration show that vibrational frequencies at
300 K are in good agreement with experiment.
ACKNOWLEDGMENTS
We would like to thank Professor D. Salahub for
allowing us use of the deMon package, and CERCA
for the RQCHP supercomputing facilities. Funding
from NSERC of Canada is gratefully acknowledged.
this is due to the influence of the spectator NM
molecules. We have checked this, by repeating the
simulation under identical starting conditions, except
that the 11 spectator molecules are removed. In this
simulation, C-N bond scission of the incoming
molecule occurs.
Another interesting observation from this
simulation is that a spectator molecule reacts with
the products of the initial collision. Thus, three NM
molecules are involved in this fragmentation
pathway - the incoming molecule, the molecule it
initially collides with and a third spectator NM
molecule.
We have also performed 3 spin restricted multimolecular collision simulations, one with an impact
velocity of 8.0 km/s and two at 12.0 km/s. The 8.0
km/s simulation resulted in no decomposition. For
the first 12.0 km/s simulation, the final
decomposition products were OCH2, NO, CH4 and
NO2 while for the second 12.0 km/s simulation, the
molecule that is initially hit, fragments into NO and
OCH3. For both the spin restricted 12.0 km/s
simulations, only the incoming NM molecule and the
molecule it first collides with, reacted.
Whereas only C-N bond scission is observed
with the bimolecular collisions, the multi-molecular
collisions show a wider range of fragmentation
patterns, including initial C-H bond breakage instead
of C-N bond scission.
More multimolecular
simulations need to be performed in order to
determine if these fragmentation patterns also occur
at lower impact velocities.
CONCLUSIONS
Simulations of bimolecular and multimolecular
collision of NM have been performed at the density
functional level. For the bimolecular collision
simulations, the lowest threshold velocity was found
to be 7.0 km/s for an offset anti-parallel collision
orientation. In almost all bimolecular simulations, if
decomposition occurs, it is via C-N bond scission.
Only for very high collision velocities are new
fragmentation patterns observed. Simulations where
one NM molecule is collided at high velocity into a
cluster of 12 molecules show new fragmentation
patterns, including trimolecular reactions.
In future, we intend to perform more
multimolecular collision simulations to study
possible decomposition pathways of nitromethane
under shock compression conditions. We further
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