Development of the ReaxFF Reactive Force Field for Describing Transition Metal Catalyzed Reactions,with Application to the Initial Stages of the Catalytic Formation of Carbon Nanotubes
Kevin D.Nielson,Adri C.T.van Duin,Jonas Oxgaard,Wei-Qiao Deng,and
William A.Goddard III*
Materials and Process Simulation Center,Beckman Institute(139-74),California Institute of Technology,
Pasadena,California91125
Recei V ed:August19,2004;In Final Form:No V ember10,2004
With the aim of developing a computationally inexpensive method for modeling the high-temperature reaction
dynamics of transition metal catalyzed reactions we have developed a ReaxFF reactive force field in which
the parameters are fitted to a substantial quantum mechanics(QM)training set,containing full reaction pathways
for relevant reactions.In this paper we apply this approach to reactions involving carbon materials plus Co,
Ni,and Cu atoms.We find that ReaxFF reproduces the QM reaction data with good accuracy while also
reproducing the binding characteristics of Co,Ni,and Cu atoms to hydrocarbon fragments.To demonstrate
the applicability of ReaxFF we performed high-temperature(1500K)molecular dynamics simulations on a
nonbranched all-carbon feedstock in the presence and absence of Co,Ni,and Cu atoms.We find that the
presence of Co and Ni leads to substantial amounts of branched carbon atoms,leading eventually to the
formation of carbon-nanotube-like species.In contrast,we find that under the same simulation conditions Cu
leads to very little branching and leads to products with no nanotube character.In the absence of metals no
branching is observed at all.These results suggest that Ni and Co catalyze the production of nanotube-like
species whereas Cu does not.This is in excellent agreement with experimental observations,demonstrating
that ReaxFF can provide a useful and computational tractable tool for studying the dynamics of transition
metal catalytic chemistry.
1.Introduction
The behavior of short-lived species under extreme conditions is difficult to study via laboratory methods because of the limited information about the character of such species and the caustic conditions of the environment.Thus,it would be most useful to be able to use molecular dynamics(MD)simulations to study these species under realistic reaction conditions.In principle quantu
m mechanics(QM)could be used to predict the detailed behavior of such short-lived and high-energy chemical species,1-4 but these methods are impractical to apply in most cases for the range of temperatures and time scales required to fully elucidate the mechanism and rates.
As an alternative to QM,MD simulations,employing classical force field5-8(FF)methods,can be used.These methods are more practical in handling the relevant time scales and range of temperatures.Unfortunately,most classical force , MM3,9Dreiding,10Amber11)with their harmonic-like bond descriptions are incapable of describing chemical reactions, while reactive empirical potentials6,12-15have,until recently, only been available for a limited number of chemical systems and cannot be straightforwardly transferred to other systems. Over the last years we have been developing a branch of transferable reactive force fields(ReaxFF).Previously,we have reported ReaxFF descriptions for hydrocarbons,16nitramines,17 silicon/silicon oxides,18and aluminum/aluminum oxides.19For all these materials,force field parameters were determined by fitting them to a substantial database of QM data,covering ground-state systems as well as full reactive pathways.Here we report on the development of a ReaxFF description for all-carbon materials and for the interactions between carbon and Co,Ni,and Cu,three transition metals commonly employed in catalytic transformations.
In light of previous studies on fullerene formation3and the nature of the carbon nanotube(CNT)growth mechanism,4we have employed this ReaxFF description for metal-carbon interactions to identify the characteristics that make a metal a good CNT catalyst.It is known that both Co20,21and Ni22are effective catalysts of single-walled CNT formation,whereas Cu23,24is much less effective.To demonstrate the validity of the ReaxFF approach for the investigation of catalytic reactions and to gain a better understanding of the properties that define a good catalyst for CNT formation we have simulated the high-temperature dynamics of reactive Co,Ni,and Cu interactions with carbon fragments(monocyclic C20and acyclic C4frag-ments).We find,in good agreement with experimental observa-tions,that both Co and Ni lead to the formation of a large number of branched carbon atoms and eventually lead to the formation of species with a clear-cut nanotube character.Cu, on the other hand,instigates only very little branching,while in the absence of a metal catalyst the carbon fragments remain exclusively linear or monocyclic.
2.Methods
QM Calculations.All metal-hydrocarbon QM calculations were performed using the hybrid DFT functional B3LYP as implemented by the Jaguar5.0program package.25This DFT functional utilizes the Becke three-parameter functional26(B3) combined with the correlation functional of Lee,Yang,and
Par27
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J.Phys.Chem.A2005,109,493-499
10.1021/jp046244d CCC:$30.25©2005American Chemical Society
Published on Web12/31/2004
(LYP)and is known to produce good descriptions of reaction profiles for transition metal containing compounds.28,29The metals were described by the Wadt and Hay 30core-valence (relativistic)effective core potential (treating the valence electrons explicitly)using the LACVP basis set with the valence double- contraction of the basis functions,LACVP**.All electrons were used for all other elements using a modified variant of Pople et al.’s 316-31G**basis set,where the six d functions have been reduced to five.For the all-carbon training set the QM training set was composed from DFT/B3LYP/6-31G**calculations.
ReaxFF Method.ReaxFF 16is based on a bond order/bond distance relationship,a concept introduced by Tersoff 32and first employed to carbon chemistry by Brenner.6Instantaneous bond orders (BO ij ′),in
cluding contributions from sigma,pi,and double-pi bonds are calculated from the interatomic distances,using eq 1;this first approximation is then corrected with overcoordination and undercoordination terms to force systems toward the proper number of bonds.
Equation 2shows that ReaxFF partitions the overall system energy into contributions from various partial energy terms.These partial energies include bond energies,valence angle,lone pair,conjugation,and torsion angle terms to properly handle the nature of preferred configurations of atomic and resulting molecular orbitals and terms to handle van der Waals and Coulomb interactions.These latter nonbonded interactions are calculated between e V ery atom pair,irrespective of connectivity,and are shielded to avoid excessive repulsion at short distances.This treatment of nonbonded interactions allows ReaxFF to describe covalent,ionic,and intermediate materials,thus,greatly enhancing its transferability.
During the re-parametrization of the hydrocarbon ReaxFF description (ReaxFF CH )with the QC data for all-carbon clusters we found that the energy terms described above were sufficient to capture the relative energy and geometry of most of these clusters,the only exception being the C 2molecule.ReaxFF CH erroneously predicts that the two carbons form a very strong (triple)bond,while in fact the triple bond would get de-stabilized by terminal radical electrons,and for that reason the carb
on -carbon bond is not any stronger than a double bond.Because the stability of C 2is relevant for the application described here,we introduced a new partial energy contribution (E C 2).Equation 3shows the potential function used to de-stabilize the C 2molecule:
where ∆i is the level of under/overcoordination on atom i as
obtained from subtracting the valency of the atom (4for carbon)from the sum of the bond orders around that atom and k c2is
the force field parameter associated with this partial energy contribution.The factor 0.04is chosen to ensure that the correction term only affects the C 2molecule and has no or marginal impact on the energies of the other molecules in the training set.
The parameters involved in the force field terms were tuned to the QM data using a single-parameter search optimization technique as described by van Duin et al.33The full set of ReaxFF equations and force field parameters have been supplied in Supporting Information.
MD Simulations.The NVT-MD simulations on C 20+C 4mixtures were performed using a velocity Verlet approach with a time step of 0.1fs.This relatively short time step was chosen to ensure good MD beha
vior at the high temperatures (1500K)employed in our simulations.When low to moderate temperatures are used (0-1000K)ReaxFF MD will conserve energy in NVE simulations with time steps up to 0.5fs,and at more elevated temperatures smaller time steps need to be used to obtain good energy conservation.A Berendsen thermostat 34with a temperature-damping constant of 250fs was used to control the system temperature.3.Results and Discussion
3.1.QM Calculations and Force Field Development.All-Carbon Interactions.To validate the ReaxFF method for the all-carbon chemistry expected to occur during nanotube forma-tion,a number of relevant cases were added to the original hydrocarbon training set,after which the force field parameters were reevaluated to optimize the reproduction of both the hydrocarbon and the all-carbon data.In the original hydrocarbon training set we already included graphite,diamond,and bucky-ball crystals;to these crystal cases we added the relative stabilities of a number of nanotubes and compared the ReaxFF calculated stability of these systems with the results obtained from the nonreactive graphite force field of Guo et al.35Table 1shows the ReaxFF results for the all-carbon phases in the training set.
The data in Table 1indicate that ReaxFF gives a good nonreactive description of these stable all-carbon phases.To obtain a valid description of potential intermediates in nanotube formation,however,
we also have to test the ReaxFF energies for smaller all-carbon fragments.To perform this test,we performed QM simulations on a number of these fragments and tested the ReaxFF description against these relative stabilities.Figure 1shows the comparison between the ReaxFF and the DFT results.
The results in Figure 1demonstrate that ReaxFF gives a good description of the relative energies for the all-carbon fragments.In accordance with the DFT data,ReaxFF predicts that for fragments smaller than C 10the linear form is the most stable configuration,while polycyclic structures become energetically favorable for structures with 20carbon atoms or more.ReaxFF reproduces the strain in three-membered ring species,which are likely to be important intermediates in all-carbon reactions.
BO ij ′)BO ij σ+BO ij π+BO ij ππ
)
exp [p bo1(r ij r 0σ
)p bo 2]+exp [p bo3(r ij r 0π)p bo4]+exp [p bo5(r ij
r 0
ππ)p bo6
]
(1)
E system )E bond +E lp +E over +E under +E val +E pen +
E coa +E C 2+E tors +E conj +E H -bond +E vdWaals +E Coulomb
(2)
E C 2)k c2(BO ij -∆i -0.04∆i 4-3)
2
if BO ij -∆i -0.04∆i 4>3(3)
E C 2)0if BO ij -∆i -0.04∆i 4e 3
TABLE 1:Relative Energies for All-Carbon Phases
compound E ref (kcal/mol)
E ReaxF
F (kcal/mol)
graphite
0.000.00diamond 0.80.52graphene
1.3  1.5610_10nanotube
2.8  2.8317_0nanotube    2.84  2.8312_8nanotube    2.78  2.8116_2nanotube    2.82  2.82C 60buckyball
11.5
11.3
494J.Phys.Chem.A,Vol.109,No.3,2005
Nielson et al.
Table 1and Figure 1establish the ReaxFF credentials as a nonreactive force field for all-carbon materials;Figures 2-4demonstrate how ReaxFF performs when tested against DFT data describing reactive events.
The results in Figure 2demonstrate that ReaxFF can describe angle bending in all-carbon compounds,even beyond the reactive limit,while the results in Figures 3and 4show that ReaxFF can describe the formation and dissociation of chemical bonds in complicated configurations.As mentioned,all the reactive and nonreactive data in the hydrocarbon training set (including dissociation of single,double,and triple bonds,radical rearrangement reactions,reactions including conjugated systems,
and Diels -Alder,methyl-,and hydrogen-shift reactions)were used in addition to these all-carbon data to train the ReaxFF parameters.The results for these hydrocarbon cases are com-parable or better than those reported earlier.16As such,we believe that ReaxFF should provide a reliable,computationally inexpensive method for simulating reactive events in all-carbon materials.
Metal -Carbon Interactions.Important structures (depicted in Figure 5)were identified,constructed,and optimized to give ground-state structures.Dissociation profiles of these structures were then constructe
d,constraining a bond length or angle of choice over a range both below and above the equilibrium value.Furthermore,by calculating the energies on reactants and reaction products separately key bond dissociation energies were determined (Table 2).
reactive metalStructures were selected so that a rigorous,quantum chemical description would exist for geometrically significant or common atomic arrangements while still limiting the number of calcula-tions to be performed.We believed it to be important to characterize a metal’s ability to singly bind one,two,or three carbons because this occurs very frequently and indicates the ability to achieve high coordination states,a strongly dif-ferentiating characteristic among catalysts.Also important to this characteristic is the freedom for bond angle bending about the metal,indicating the ease with which new carbon atoms can be coordinated.The behavior of doubly bound carbon is important because of the role it plays in ring formation,of key interest in many catalysis problems.
The behavior of metals around rings and proto-rings is also an important descriptor.To this end,the behavior of metals in five-and six-membered metallocycles (four-and five-C chains)is important because it determines the rate at which a catalyst can enter or leave these formations,indicating the relative rate of small ring expansion.Upon formation of stable six-membered rings,the most likely role of a metal is as part of a benzyne complex.Also important is the dissociation of a metal from an aromat
ic six-membered ring,as in benzene,with a dissociation path parallel to the axis of the πsystem.
Structures were constructed so as to provide as simple an electronic arrangement as possible.For Co and Cu cases,singlet states were frequently constructed through the addition of a methyl group as compared to the Ni cases.This allowed for more accurate energy determination and decreased computa-tional expense.Also,hydrocarbon frameworks were used instead of all-carbon frameworks so as to clearly define the lowest energy spin state of the
system.
Figure 1.DFT and ReaxFF C relative stabilities for small all-carbon
fragments.
Figure 2.DFT and ReaxFF energy profiles for the cyclization reaction in C 9.This reaction profile was obtained by constraining all C -C -C
angles.
Figure 3.DFT and ReaxFF energy profiles for the coalescence reaction between two C 20
dodecahedrons.
Figure 4.DFT and ReaxFF energy profiles for the dissociation of one bond between two coalesced C 20dodecahedrons.
ReaxFF Reactive Force Field J.Phys.Chem.A,Vol.109,No.3,2005495
For cases making a spin state transition during dissociation, dissociation curves for both spin states were calculated.The lowest of the two is assumed to be the natural dissociation path. These data represent the important options for interactions between the carbon and the metal atoms and were used to calibrate the force field.For each case,good agreement between the QM data and the ReaxFF energies is observed(Figure5, Table2).
In addition to the parametrization of ReaxFF,a number of important observations can be made from these data.Both Co and Ni readily form multiple bonds(g3)necessary for creating new C-C bonds,and bond angles are flexible((25°at a cost of∼5kcal/mol)allowing coordination of additional carbons. Cu coordinates a single carbon very tightly(∼54kcal/mol)but accepts secondary and tertiary carbons very reluctantly(only 28and26kcal/mol,respectively),indicating a tendency to remain inactive under conditions where Co and Ni would likely be active,thus,indicating that Cu may fail to catalyze small ring formation.
Co,Cu,and Ni all dissociate readily from benzene rings (binding energy∼3kcal/mol),allowing them to catalyze the formation of highly stable rings and subsequently depart for
further catalysis.Both Co and Ni bind well to five-membered rings(∼65kcal/mol and∼125kcal/mol,respe
ctively),making it unlikely that the ring will close on its own before having another carbon introduced to form a six-membered ring.
In benzyne complexes,both Co and Ni bind well to benzyne (∼40kcal/mol and∼60kcal/mol,respectively)allowing them to play a role in extending graphitic sheets.Cu binds weakly in this situation(∼30kcal/mol),suggesting that it cannot function to extend graphitic sheets.For Co and Ni cases,small changes in the bond angle are energetically inexpensive,allowing new carbons to bind to the benzyne,displacing the metal and extending the graphitic sheet.
3.2.Application of ReaxFF to the Initial Stages of Metal Catalyzed Nanotube Formation.To test the validity of the ReaxFF method for studying metal catalyzed nanotube growth, we performed NVT-MD simulations at a temperature of1500 K on a20×20×20Åperiodic box containing5C20 monocyclic rings and10C4acyclic chains.This initial config-uration was chosen in accordance with earlier mechanistic studies that indicate that nanotube growth initiates from mono-cyclic carbon rings.36,37To test the impact of metal catalysts on this system and to differentiate between the relative capability of Cu,Ni,and Co to catalyze nanotube growth these simulations were performed without metal atoms and with15Cu,Ni,or Co atoms added(Figure6).To avoid formation of metal clusters, which might lower the catalytic ability of the metals,we lowered the metal-metal bond dissociation parameters to0.0kcal/mol.T
hese conditions were chosen to maximize the possible effect of metal catalysis,thus,to increase the odds of differentiating between the various transition metals,and were not aiming to directly reflect realistic nanotube growth conditions.More realistic growth conditions,involving a more diverse carbon feedstock and a lower metal concentration,thus,requiring larger systems and longer simulations due to reduced metal-carbon reaction rates,will be the subject of future studies.
As Figure7and Table3demonstrate,we did not observe any meaningful steps toward nanotube formation in the absence of metal atoms;the C4acyclic chains polymerized and some of the C20rings opened but no branching(as defined by carbon atoms with three or more strongly bound neighbors)was observed.Although nanotube formation would eventually be exothermic,the energy barriers for the initial branching steps seem too high to be observable on the time scales of our simulations without addition of a catalyst.In the presence of transition metal catalysts,however,we do see a significant amount of branching occurring in our simulations,leading, especially in the Ni case,to the formation of small polycyclic structures(Figure7c)that provide nucleation points for the formation of nanotube-like structures after prolonged simulations (Figure8).Furthermore,our data suggest that Ni and Co are far more capable of initiating carbon branching than Cu,which is in good agreement with experimental observations.These results demonstrate that ReaxFF provides a computationally inexpensive method to establish the catalytic potential of
TABLE2:Bond Dissociation Energies(in kcal/mol)Used in Parameterizing the Force Field
reactant products E diss(QM)E diss(ReaxFF) CuCH3Cu+CH354.250.3
Cu(CH3)2CH3Cu+CH326.430.2
Cu(CH3)3(CH3)2Cu+CH328.216.5
CH3Cu d CH2CH3Cu+CH244.836.1
Cu s benzene Cu+benzene  2.50  2.5 CoCH3Co+CH353.342.6
Co(CH3)2CH3Co+CH337.438.4
CH3Co d CH2CH3Co+CH260.859.5
Co s benzene Co+benzene  3.1  4.2
Ni(CH3)2NiCH3+CH339.542.4
Ni(CH3)4Ni(CH3)3+CH330.227.6
Ni d CH2Ni+CH276.064.1
Ni s benzene Ni+benzene  2.5
2.9
Figure6.Initial configuration,involving5C20monocyclic rings,10
C4acyclic chains,and15Cu atoms,employed in the NVT-MD
simulations.
TABLE3:Number of Branched and Unbranched Carbon
Atoms Observed in the90-ps Configuration of the NVT-MD
Simulations a
system description
number of
unbranched carbons
number of
branched carbons
no metal1400
Cu1373
Co10436
Ni8555
a A branched carbon is defined as a carbon involved in three or more
bonds,each with a bond order greater than0.3,to other carbon atoms;
an unbranched carbon has one or two bonds.
ReaxFF Reactive Force Field J.Phys.Chem.A,Vol.109,No.3,2005497
transition metals by allowing fully dynamical reactive simula-tions on complicated chemical systems.4.Conclusions
Using the ReaxFF strategy of combining a generic form of a force field suitable for describing reactive processes with data from a substantial QM training set,including full pathways for relevant reactions,we managed to develop a reactive force field for hydrocarbons,all-carbon materials,and Cu -,Co -,and Ni -carbon interactions.We applied ReaxFF to the study the activity of Cu,Co,and Ni metal atoms for initiating nanotube growth.
We find that,during high-temperature (1500K)NVT-MD simulations in the presence of Co and Ni,substantial amounts of branched carbon atoms are formed from a linear and monocyclic all-carbon feedstock.This leads to the formation of small polycyclic structures that serve as nucleation points for further nanostructure formation.In contrast to Ni and Co,we find that Cu barely instigates branching,while in the absence of a metal catalyst no branching is observed at all.These findings are in good agreement with experimental observations,indicating that reactive force fields,if properly parametrized against a relevant QM-derived training set,can provide a useful tool for studying transition metal catalytic processes.Acknowledgment.K.D.N.thanks NSF-CSEM for a MURF-summer fellowship.This research was supported partially by NSF-NIRT and MARCO-FENA.The computation facilities of the MSC have been supported by grants from ARO-DURIP,ONR-DURIP,NSF (MRI,CHE),and IBM-SUR.In addition the MSC is supported by grants from DoE ASCI,ARO-MURI,ARO-
DARPA,ONR-MURI,NIH,ONR,General Motors,ChevronTexaco,Seiko-Epson,Beckman Institute,and Asahi Kasei.We thank the reviewers for their useful comments on this manuscript.
Supporting Information Available:A document containing the full ReaxFF potential functions and an ASCI-text file with the force field parameters described in this manuscript (readable by the ReaxFF program).This material is available free of charge via the Internet at
Figure 7.Configurations obtained after 90ps of NVT-MD simulation without metal (a)and with 15Co (b),Ni (c),and Cu
(d).
Figure 8.Configuration obtained from the NVT-MD simulation with 15Ni atoms after 750ps.
498J.Phys.Chem.A,Vol.109,No.3,2005Nielson et al.

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