MODELING AND SIMULATING REACTIVE MOLECULAR DYNAMICS

USING REAXFF

MARKUS OHLENFORST

REAXFF REACTIVE MD SIMULATION OF A COMBUSTING CHAR STRUCTURE

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CONTENTS 0. Introduction ............................................................................................................................ 3

1. ReaxFF Modeling and Implementation ............................................................................... 4

1.1. Reactive interactions ....................................................................................................... 4

1.1.1. Modeling bond orders .............................................................................................. 4

1.1.2. Equilibrating charges ................................................................................................ 5

1.2. Numerical Aspects ........................................................................................................... 6

1.2.1. The QEq system ........................................................................................................ 6

1.2.2. Solving QEq ............................................................................................................... 7

1.2.3. ILUT-based preconditioning ..................................................................................... 7

1.3. Algorithmic Techniques ................................................................................................... 8

1.3.1 Generating neighbors ................................................................................................ 8

1.3.2. Bonded and non-bonded force computations ......................................................... 9

2. ReaxFF - Simulation based analysis of a new fuel ................................................................ 10

2.1 Simulation details and results ........................................................................................ 10

2.1.1 Mechanisms of initial pyrolysis ............................................................................... 10

2.1.2 Mechanisms of initial combustion .......................................................................... 13

2.2 Output analysis extracting kinetic properties ............................................................. 16

3. Closing remarks .................................................................................................................... 17

Images on cover sheet from:

F. Castro-Marcano, A. M. Kamat, M. F. Russo Jr., A. C. T. van Duin, J. P. Matthews, Combustion of an Illinois No. 6 coal char simulated using

an atomistic char representation and the ReaxFF reactive force field Combustion and Flame, 159 (3), 1272-1285 (2012).

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0. INTRODUCTION

his work was written in the context of the CES-Seminar-class for master students in

Computational Engineering Science at the RWTH Aachen University (WS 12/13). Task

was to write a paper about a current topic of research represented by one or more recent

publications. Prof. Dr. Ismail from the chair for Molecular Simulations and Transformations

gave Reactive Molecular Dynamics as the topic for this work and supervised it as well.

Aforementioned publications for this work were:

[1]: A.C.T. van Duin, S. Dasgupta, F. Lorant, and W.A. Goddard III, ReaxFF: A reactive

force field for hydrocarbons, J. Phys. Chem. A, 105 (2001), pp. 93969409.

[2]: H. M. Aktulga, S. A. Pandit, A. C. T. van Duin, A. Y. Grama, Reactive Molecular

Dynamics: Numerical Methods and Algorithmic Techniques, SIAM J. Sci. Comput.,

34(1), C1C23.

[3]: Liu, Lianchi and Bai, Chen and Sun, Huai and W.A. Goddard III, Mechanism and

Kinetics for the Initial Steps of Pyrolysis and Combustion of 1,6-Dicyclopropane-2,4-

hexyne from ReaxFF Reactive Dynamics, J. Phys. Chem. A, 115 (19). pp. 4941-4950.

In reactive molecular dynamics, ReaxFF (reactive force field) is a force field that can be used

for simulations of the (reactive) behavior of various chemical systems. It was developed by

Adri van Duin, William A. Goddard, III and co-workers at the California Institute of

Technology and published in 2001.

Its advantages in comparison with common techniques in the field of molecular dynamics

are presented and the underlying model, as well as a way to implement it is explained in the

first chapter ReaxFF - Modeling and Implementation. The second chapter, Simulation

based analysis of a new fuel, is about the results of a recent study, in which researchers

applied ReaxFF for the analysis of a new fuel (additive), 1,6-Dicyclopropane-2,4-hexyne.

Aspiration is to help the reader to gain access to the understanding of how to distinguish

ReaxFF from other techniques, what model it relies on, how it can be implemented and

finally, how it is used in practice.

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1. REAXFF MODELING AND IMPLEMENTATION

eaxFF fills the gap between quantum mechanical (QM) and empirical force field (EFF)

based computational chemical methods. Although QM methods can generally be used

for all chemical systems, regardless of their connectivity, they are not practicable for large

systems with sizes in the order of thousands of atoms. Because of the computational

expense QM methods are primarily in use for single point or local energy minimization. High-

temperature molecular dynamics simulations, like the ones presented in this work, are in

general too time-consuming.

ReaxFF was developed to simulate the molecular dynamics of large scale chemical systems

(sizes in the order of thousands of atoms) efficiently. Contrary to traditional force fields and

like QM methods, it is able to model chemical reactions. Changing bonds are not a problem,

whereas for traditional force fields, the functional form depends on having all bonds defined

explicitly. ReaxFF replaces explicit bonds by bond orders, which allows continuous bond

forming/breaking. It is developed to be as general as possible and has been parameterized

and tested for hydrocarbon reactions, transition-metal-catalyzed nanotube formation, and

high- energy materials. How the ReaxFF model considers reactive interactions exactly and

how it can be implemented is shown in the following.

1.1. REACTIVE INTERACTIONS

y the reactive force field (ReaxFF) atoms are modeled as separate entities with different

bond structures. These have to be updated at every time-step. In combination with the

therefore necessary charge redistribution (charges on atoms change due to bonding

changes), the dynamic bonding scheme represents the essential part of ReaxFF that

distinguishes the model from classical MD or ab-initio methods. Before going into detail

regarding the numerical and algorithmic aspects when implementing the force field, the

incorporated reactive potentials in ReaxFF are briefly described in this section.

1.1.1. MODELING BOND ORDERS

The strength of the bond between a pair of atoms i and j is described by the bond order

through the number of chemical bonds. ReaxFF models this quantity by a closed form [1]:

(1.1)

R

B

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Here, the bond order depends on the types of atoms i and j and the distance in between.

denotes a - , - or - bond. a and b are parameters belonging to the bond type. is

the length which is optimal for this bond type. Since the actual bond type is unknown during

simulation, the total bond order equals the following sum [1]:

(1.2)

Additionally, the total coordination number of each atom and 13 bond corrections in

valence angles must be considered. This is suggested by the exemplary fact that the bond

length and strength between O and H atoms in OH are different than those in H2O.

Concurrent corrections are employed in ReaxFF by [1]:

(1.3)

stands for the deviation of atom i from its optimal coordination number,

for

the overcoordination correction,

and

for 1 3 bond order

corrections. After bond orders are computed, according charge changes have to be

incorporated. Then, a ReaxFF simulation continues much like a classical MD simulation.

1.1.2. EQUILIBRATING CHARGES

Due to dynamic bonding in ReaxFF atoms underlie different charges for the duration of

simulations. To redistribute charges periodically it would be most accurate to employ

ab-initio methods. Unfavorable is that this would make the ReaxFF method unscalable.

Therefore developers stuck to the QEq method [2]. According to that, the actual problem is

approximated by looking for a set of charges constituting a minimal electrostatic energy of

the system with the same net charge:

(1.4)

i and j represent atom indices and is referred to as the partial charge on atom i. Specifying

the addends in equation 1.4 through physical quantities gives:

(1.5)

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denotes the energy of an isolated neutral atom. is the electronegativity.

stands for

the idem potential or self-Coulomb of i, while corresponds to the Coulomb interaction

between atoms i and j.

1.2. NUMERICAL ASPECTS

hile typical classical MD formulations are based on static charges on atoms,

(re)assigning partial charges to atoms at each time-step constitutes one of the most

computation-intensive parts of a ReaxFF simulation. As seen above, the charge reassignment

problem can be approximated as charge equilibration with the objective of minimizing the

electrostatic energy. One efficient way to solve problem (1.5) of the ReaxFF model

numerically was presented by Aktulga et al. in 2012 [2] and is outlined in the following.

1.2.1. THE QEQ SYSTEM

To get linear systems out of equation 1.5, the method of Lagrange multipliers can be used.

After some computation you acquire:

(1.6)

(1.7)

Here, represents a vector of size N, containing parameters determined based on the types

of atoms in the system. N is the number of incorporated atoms. H represents the QEq N x N

sparse coefficient matrix where the diagonal of H consists of the polarization energies of

atoms, and the off-diagonal elements hold the electrostatic interaction coefficients between

atom pairs. s and t denote fictitious charge vectors of size N. Finally the partial charges are

computed with the help of the fictitious charges:

(1.8)

In fact, a direct solver could give the solution to the linear systems in (1.6) and (1.7).

Nevertheless Krylov subspace methods are much cheaper for moderate to large sized

systems. A closer look at how the system above can be solved in a highly efficient way is

given in the next section.

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1.2.2. SOLVING QEQ

H is a sparse matrix because the number of non-zeros in H is only on the order of a few

hundred entries per row, and thats independent of the system size. Reason is, non-bonded

interactions in ReaxFF are computed within the cut-off radius only. However, Krylov

subspace solvers are iterative methods depending upon a costly sparse matrix-vector

multiplication at each iteration. Therefore, a preconditioning technique can be employed to

convert the linear system into an equivalent one that has improved spectral properties.

Furthermore, computing linear, quadratic, or higher order extrapolations on the solutions

from previous steps makes sense since individual time-steps in reactive MD simulations have

to be much shorter than those in typical classical MD methods. Consequently, good initial

guesses can be made and are even more favorable.

1.2.3. ILUT-BASED PRECONDITIONIN G

Incomplete LU factorization (ILU) proved to be a useful basis for preconditioning. This

technique is effective and broadly used in the context of solving sparse linear systems since

it helps in reducing the iteration counts. Even though, calculating the ILU factors and putting

them in use as preconditioners frequently is computationally expensive, especially when

solving the QEq problem at each step of a ReaxFF simulation.

Indeed, the simulation environment evolves slowly in a ReaxFF simulation. That indicates

that the QEq coefficient matrix H, as well as the ILU factors L and U evolves slowly, too. For

that reason, analogue to the reuse of the solution from the previous step as initial guess, the

same factors L and U can be assumed effectively as preconditioners over several steps. It is

possible to use the same preconditioner over tens to thousands of time-steps with only a

slight increase in the iteration count. Of course, that depends on the displacement rate of

atoms in the system and the specified accuracy of the solution.

In the sPuReMD-implementation of ReaxFF by Aktulga et al. [2], factors from such an ILU

factorization of the H matrix are employed with a threshold (ILUT). That means, that all

entries in the L and U factors with values less than the specified threshold are set to zero for

optimization reasons. By reducing the threshold, the factors L and U can be turned into

higher quality preconditioners. Disadvantageous is that factorization and application of the

preconditioner takes considerably longer. An optimal threshold value has to be found

empirically depending on the type of the experiment to be simulated.

Concerning the PGMRES (Generalized Minimal Residual Method with Preconditioning) and

PCG (Conjugate Gradients with Preconditioning) solvers (both Krylov subspace methods) for

solving the system (1.6)-(1.8), the following can be said: PGMRES doesnt only perform

better, but shows the higher longevity of preconditioners as well [2]. sPuReMD employs

PGMRES as the default solver.

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1.3. ALGORITHMIC TECHNIQUES

s shown in Algorithm 1, the high-level structure of the sPuReMD-implementation of

ReaxFF looks like one of a classical MD code. Still, due to dynamic bonding and charge

equilibration requirements, each of the listed components entails a significantly higher

complexity compared to a nonreactive classical MD implementation.

In the following, the algorithmic techniques and optimizations applied in sPuReMD are dealt

with. The developers objective was to deliver excellent per time-step performance and

linear time scaling in system size.

1.3.1 GENERATING NEIGHBORS

Both bonded and non-bonded interactions between atoms are truncated after a certain

cut-off distance in ReaxFF. They account for 45 for bonded interactions and 1012 for

non-bonded ones. To gain the relevant neighbors of each atom sPuReMD applies a

procedure called binning or link-cell method [2]. First, a three-dimensional grid structure

is created by partitioning the specified geometry of the simulation into small cubic cells.

Hereafter, atoms are binned into these cells depending on their spatial coordinates.

Obviously, potential neighbors of an atom are either in the same cell or in neighboring cells

within the cut-off distance measured from its own cell. One can achieve O(k) neighbor

generation complexity for each atom with k being the number of neighbors, averaged over

all atoms. However, depending on the applied method and the specified cell size, k can be

considerably high.

Its possible to generate neighbor lists in linear time. Though, this part belongs to the most

computationally expensive components of an MD simulation, which suggests lowering the

large constant associated. Therefore, different optimizations are implemented in sPuReMD.

Two important ones deal with the cell dimensions and the atom list respectively.

On the one hand reducing cell dimensions comes along with a reduced search space per

atom, which helps to lower the neighbor search time to a certain extent. On the other hand

ongoing reduction (shape of the search space approximating a sphere) involves an overhead

ALGORITHM 1 GENERAL STRUCTURE OF AN ATOMISTIC MODELING CODE.

Read geometry, force field parameters, user control file Initialize data structure for t=0 to nsteps do Generate neighbors Compute energy and forces Evolve the system Output system info end for

A

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associated with managing the increased number of cells. For normally sparse and crowded

cells 1/2 should work as a near-optimal value.

Atoms that fall into the same cell are regrouped in the atom list. This allows a better

neighbor search performance because of the better use of the cache.

1.3.2. BONDED AND NON-BONDED FORCE COMPUTATIONS

There are four major steps involved in the computation of forces in ReaxFF: system wide

calculation of the bond orders between atom pairs, determination of the forces due to the

given bonds, assignment of the partial charges on each atom and computation of the non-

bonded forces in the system.

ELIMINATING BOND ORDER DERIVATIVES LIST

For the most part, bonded potentials are determined by the strength of the bonds between

the atoms involved. A closer look at (1.3) reveals that relies on all the uncorrected bond

orders of both atoms i and j. This indicates that when regarding the force due to the i-j bond,

the term is non-zero for all atoms k that share a bond with atom i or j.

Since a single bond might contribute by this means to various bonded interactions, the

evaluation of could be necessary multiple times over a single time-step. Instead

of storing the bond order derivatives for frequent lookups to the physical memory, sPuReMD

postpones their computation until the end of a time-step. Then, when the bonded

interactions are calculated, the needed s are computed and added with the pre-

evaluated according coefficients to the net force on atom k. This way, simulations of much

larger systems are affordable on a single processor due to the saving of abundant memory.

Moreover, it reduces the time for computing forces.

LOOKUP-TABLES FOR NON-BONDED INTERACTIONS

Also the modeling of non-bonded interactions is more complex in ReaxFF than in the

classical counterparts. The application of a lookup table and interpolation to approximate

complex expressions is common for optimizing MD simulations. sPuReMD employs cubic

spline interpolation in combination with a compact lookup table for accurate approximations

of non-bonded energies and forces [2]. Considerable performance improvements justify an

acceptable loss in terms of accuracy.

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2. REAXFF - SIMULATION BASED ANALYSIS OF A NEW FUEL

o show exemplary, how useful results are generated and extracted from simulation

outputs in the field of modern reactive molecular dynamics, the essence of an early

research work is outlined in this section.

In 2010, Liu et al. used the ReaxFF force field successfully for the analysis of a new fuel

material (1,6-dicyclopropane-2,4-hexyne) [3]. Since it has immense heats of pyrolysis and

combustion, this fuel material promised to be a potential high-energy fuel or fuel additive

suitable for rockets and marine vessels. It was assumed that by igniting the main fuel more

easily, 1,6-dicyclopropane-2,4-hexyne would provide more energy in the ignition process.

For the time being, the researchers directed their attention to the initial mechanism and

kinetic analysis for both pyrolysis and combustion. That should help to understand whether

the new material was stable enough in the preheating/injection process and how it would

help the ignition.

Since the objective was to follow the important initial chemical processes in a relatively large

reactive system over a range of temperatures for periods of time of at least 10 ns, the choice

fell onto ReaxFF instead of a quantum mechanics calculation program. Initial pyrolysis and

combustion were analyzed by simulating unimolecular and multimolecular systems for both

processes. The resulting important reaction steps of all unimolecular simulations were

compared with results from quantum mechanics (QM) for validation purposes.

2.1 SIMULATION DETAILS AND RESULTS

otential functions and parameters from a prior ReaxFF analysis of the initiation

mechanisms and kinetics of pyrolysis and combustion of the JP-10 hydrocarbon Jet Fuel

were adopted for the analysis of 1,6-dicyclopropane-2,4-hexyne. These parameters were

trained and validated against results from quantum mechanics. The RD simulations ran

subject to the conditions of a constant number of atoms, constant volume and constant

temperature (NVT ensemble). Additionally, periodic boundary conditions (PBC) were

applied. The temperature was controlled with the help of a Berendsen thermostat. QM

calculations were performed by the TURBOMOLE 5.8 package.

2.1.1 MECHANISMS OF INITIAL PYROLYSIS

For the unimolecular pyrolysis simulations, a single fuel molecule was examined in a cubic

cell with 16.29 sides. In the first place, the system was equilibrated at 300 K for 10 ps with

0.1 fs time steps. After that it was heated up to 2500 K steadily over a time of 10 ps. Then

simulation was accomplished for another 1 ns at 2500 K. The resulting pressure accounted

for 84 MPa which is realistic for the preheat/injection phase in engines. For the sake of

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P

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proper statistical sampling and to gain a variety of likely mechanisms ten independent

simulations of the unimolecular pyrolysis were performed. The researchers have noticed two

different initial decomposition reactions when examining the results, see table 1.

TABLE 1: INITIAL REACTIONS FROM REAXFF UNIMOLECULAR PYROLYSIS SIMULATION [3]

INITA: The ring of the cyclopropyl structures breaks to create the two stable molecules

ethylene and 1,3,5-hexatriyne.

INITB: The fuel molecule is isomerized, which causes a biradical intermediate to form, that

then transfers a hydrogen atom to form more stable intermediates.

TABLE 2: SPECIFIC REACTIONS FR OM UNIMOLECULAR PYROLYSIS SIMULATIONS [3]

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Following these two initial reactions, there are many other reactions in the unimolecular

pyrolysis, see table 2. You can derive the lead initial reaction from the name of each

elementary reaction. All in all, it can be seen that most ReaxFF energies are close to the QM

calculations. Only the energies of some radical decomposition reactions and radical-radical

reactions are undervalued. It is assumed that the reason for this was ReaxFF

underestimating the energy of radicals [3]. Otherwise, the trends in the total energy are in

good agreement with the QM calculations which confirms the accuracy of the ReaxFF force

calculation. The researchers categorized the observed reactions and put them into two

groups including different types, see markings in table 2 and corresponding legend

underneath.

NORAD: Reactions with no radicals involved in reactants.

YESRAD: Reactions that involve radicals in the reactants.

While dissociation reaction energies for NoRad are computed positive (endothermic), what

induces less active species, but with entropy release getting crucial in pyrolysis, reaction

energies for the radical-radical and molecule-radical reactions of the YesRad group are

negative (exothermic), what induces reactive radicals leading to a variety of pyrolysis.

Figure 1 visualizes the energetics of the unimolecular pyrolysis for three of the ten pyrolysis

simulations. It can be seen that the unimolecular pyrolysis reaction behavior is endothermic.

Clearly entropy has a certain weight in this process.

FIGURE 1: RELATIVE ENERGIES (KCAL/MOL) OF THE THREE PATHWAYS OBSERVED IN REAXFF UNIMOLECULAR PYROLYSIS [3]

The thermal conditions for the multimolecular pyrolysis simulations were the same as for

the unimolecular ones. To get the same density as in the unimolecular structure, a periodic

cubic box with 60 sides was taken and filled with 50 fuel molecules. Again, the system was

equilibrated in the first place (300 K, 50 ps, 0.1 fs time step) and then heated to 2500 K

steadily (10 ps time step). Finally RD simulation was performed for another 100 ps (2500 K,

0.25 fs time step). Figure 2 shows the fragment distributions and potential energy profiles

with time for pyrolysis of the multimolecular system at 2500 K.

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FIGURE 2: FRAGMENT DISTRIBUTIONS AND POTENTIAL ENERGY PROFILE OF MULTIMOLECULAR PYROLYSIS [3]

A large number of different radicals can be observed in the middle. Here, C4H, C2H, C2H3,

C2 and C4H2 represent the major species. On the one hand the initial steps of

multimolecular are mainly the same as the ones of the unimolecular pyrolysis. The fuel

molecules mostly decompose to ethylene and 1,3,5-hexatriyne because of the initial

reaction InitA. On the other hand the following reactions after this initial decomposition

were considerably different for the multimolecular system. Much more complex species and

the existence of many radicals lead to the conclusion that intermolecular radical reactions

are crucial in the pyrolysis. Furthermore, the multimolecular pyrolysis proceeds faster than

the unimolecular one. This is a result of the additional radical reactions in the multimolecular

pyrolysis.

Analysis of major product distributions at the end of 100 ps RD of pyrolysis as a function of

temperature (not presented here) demonstrate that the H2 concentration apparently grows

with temperature, pointing at the increased importance of H abstractions and activity of H

radicals in the high temperature pyrolysis.

Rsum: The pyrolysis of the fuel seems to begin with unimolecular pyrolysis involving

radicals from secondary decompositions that accelerate the process. Additionally it was

found that the endothermic, entropy-driven abstraction of ethylene from the fuel molecule

is the most important initial step. In parallel, isomerization of the fuel molecule occurs as an

occasional initial reaction (20%). Despite not being the main reaction, the isomerization

creates radicals that influence the multimolecular pyrolysis significantly.

2.1.2 MECHANISMS OF INITIAL COMBUSTION

For the analysis of the initial mechanism of combustion, first, a single fuel molecule (C10H10)

was situated in a cubic periodic box with 20 sides. 13 additional oxygen molecules caused

an equivalent ratio of ca. 1.0. After equilibrating the system at 300 K (10 ps, 0.1 fs time step)

and heating it to 1500 K steadily (10 ps, 0.25 fs time step) with bonding being disabled to

prevent combustion reactions from occurring beforehand, again, 10 parallel independent

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simulations were performed. Three different initial combustion reactions were observed for

the unimolecular model:

INITR1: O2 attack on the cyclopropyl structure, which causes the formation of a five-

membered peroxide ring.

INITR2: O2 attack on the middle C-C bond of the diyne. That cracks to form two C5H5O

radicals.

INITR3: O2 attack on the cyclopropyl structure causes ring-opening and formation of a 7-

membered peroxide ring.

Following these two initial reactions, there are many other reactions in the unimolecular

combustion, see table 3.

TABLE 3: SPECIFIC REACTIONS FR OM UNIMOLECULAR COMBUSTION SIMULATIONS [3]

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Obviously, oxygen attack reactions and radical reactions are the most important subsequent

reactions with the oxygen molecule as a radical acceptor and generator, thus inducing other

radical reactions to accelerate the oxidation.

In Figure 3, relative energies for the three different pathways of unimolecular combustion

are shown.

FIGURE 3: RELATIVE ENERGIES (KCAL/MOL) OF THE THREE PATHWAYS OBSERVED IN REAXFF UNIMOLECULAR COMBUSTION [3]

The combustion processes are all exothermic, which signifies that combustion proceeds

more easily than pyrolysis. Again, the comparison between ReaxFF and QM reaction energy

values verifies the accuracy of the ReaxFF force field. Though, once more the ReaxFF

simulations seem to have underestimated the energies of radicals.

To examine the initial mechanisms of multimolecular combustion, 30 fuel molecules and 390

oxygen molecules were placed in a cubic box with 62.0 sides. Result was a multimolecular

system with an equivalent ratio of ca. 1.0 and the same density as the unimolecular one.

After equilibrating the box at 300 K (10 ps, 0.1 fs time step) and heating it to 1500 K (10 ps,

0.25 fs time step) with bond interactions being turned off, RD simulation was accomplished

at 1500 K for 1 ns using 0.25 fs time steps.

FIGURE 4: FRAGMENT DISTRIBUTIONS AND POTENTIAL ENERGY OF MULTIMOLECULAR COMBUSTION [3]

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During 1 ns of multimolecular combustion simulations, the initial intermediates were

C10H10O2 and C5H5O and the major products were CO2, CO, CH2O and C2H4. Their

distribution, as well as the potential energy profile is shown in figure 4. Also multimolecular

combustion seems to be exothermic. Furthermore, the resulting initial reactions with most

initial intermediates being C10H10O2 and C5H5O are similar to the unimolecular system.

Still, multimolecular combustion generates many more radical intermediates.

Rsum: Combustion of 1,6-dicyclopropane-2,4-hexyne is initiated by the unimolecular

oxidation. In this context, oxygen attacks any one of three different positions on the fuel

molecule. Numerous radicals are created, causing the combustion to be unstable towards

explosion.

Resulting distributions at the end of the simulation at different temperatures (not outlines

here) show that H2O, H2, and CO concentrations grow with increasing temperature.

Obviously, more radical reactions appear at high temperature. The rate of the exothermic

combustion process is much higher and its temperature is much lower than the according

quantity in pyrolysis.

2.2 OUTPUT ANALYSIS EXTRACTING KINETIC PROPERTIES

D simulations on the multimolecular models of pyrolysis and combustion were

performed for several temperatures (1600-2500 K range, 100 K steps) to determine the

kinetic properties for pyrolysis and combustion. The according simulations were

accomplished for 100 ps at each temperature with a 0.25 fs time step for the pyrolysis model

and for 1 ns with a 0.25 fs time step for the combustion model.

FIGURE 5: KINETIC ANALYSIS OF PYROLYSIS AND COMBUSTION [3]

In Figure 5, the log of the initial rate of the loss of fuel molecules is plotted versus (1/T) for

pyrolysis and combustion. First-order kinetics exhibit the behavior of a single Arrhenius

function (see upper right corner in figure 5). That suggests the extraction of an effective

R

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activation energy and a pre-exponential factor A. An activation energy of

and a pre-exponential factor of can be gathered from the

pyrolysis results.

On the assumption of unimolecular decomposition, transition state theory gives

with , a negative activation of entropy which is

consistent with the TST for multimolecular reactions. That indicates the involvement of a

multimolecular transition state.

Regarding combustion of 1.6-dicyclopropane-2.4-hexyne, figure 5 gives

in combination with a pre-exponential factor of . More likely is a lower

for combustion because O2 can stabilize the initial steps of bond breaking and the initial

reaction steps tend to be more exothermic [3]. Comparing to the initial reaction step at

0 K of InitR1, InitR2 and InitR3 for the three different oxygen-attack positions leads to -

2.19 kcal/mol at 1500 K after correction of temperature. On the assumption of TST a of

-10.29 eu can be calculated. Oxygen attack causes the decrease of entropy at the transition

state.

3. CLOSING REMARKS

oday, molecular modeling and simulation techniques are routinely used to investigate

the structure, dynamics, reactivity, electronic charge distributions, dipoles and higher

multipole moments, surface properties and thermodynamics of inorganic, biological and

polymeric systems. Only the simplest calculations can be done by hand. Inevitably,

computers are required to carry out molecular modeling of any reasonably sized system.

The computer time and other quantities (e.g. memory or disk space) grow rapidly with the

size of the system being studied. As already stated, highly accurate methods, such as ab-

initio methods that are based entirely on the theory from the first principles of the

Schrdinger equation, are typically practical only for very small systems. Whereas other,

faster methods, mostly based on empirical and semi-empirical force fields, are less accurate

since they employ experimental results and relatively simple potential functions to

approximate some elements of the underlying theory. In addition, because these force fields

describe the system empirically rather than in a fundamental fashion, they are only

applicable to systems similar to the ones from the training set.

ReaxFF was developed to resolve this contradiction to a certain extent and seems to satisfy

that aspiration in the fields of hydrocarbon reactions, transition-metal-catalyzed nanotube

formation and high- energy materials. The chosen example pointed at its good accuracy in

comparison with QM methods. But ReaxFF provides a much faster method, especially when

implemented in an efficient way as by sPuReMD, see chapter 1. Thus, it opened up new

possibilities for computational chemistry and is worth it to be dealt with.

T