3244 New J. Chem., 2013, 37, 3244--3251 This journal is c The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2013

Cite this: NewJ.Chem.,2013,37, 3244

An extensive investigation of reactions involved in thenitrogen trifluoride dissociation†

Simone S. Ramalho,a Wiliam F. da Cunha,b Alessandra F. Albernaz,b

Pedro H. O. Neto,b Geraldo Magela e Silvab and Ricardo Gargano*b

In the course of our studies on nitrogen trifluoride dissociation, we consider in this paper two different

sets of reactive systems: the first one consists of the abstraction and the exchange channels of NF3 + F

and the other is composed of the unimolecular and the abstraction production of N2 + F. Accurate

electronic properties are determined and applied in the scope of the transition state theory (TST) to

obtain thermal rate constants for these systems. An extensive investigation in terms of minimum energy

paths and intrinsic reaction coordinates was previously carried out in order to ensure the good quality

of our TST results. We apply Wigner corrections to consider tunneling effects whenever their

importance is numerically verified. The obtained results for the abstraction channel thermal rate

constants are in good agreement with experimental data which indicates that this kind of study is of

potential use to help to clarify the decomposition mechanism of NF3.

I Introduction

In the last decades the environmental issue has continuouslygained importance due to the major industrial developmentobserved. New production lines are usually subjected to moresevere environmental statutes and governments throughoutthe world are led to follow several pro-environmental policies.An important example of the aforementioned policies is theper-fluorocarbons (PFC) emission reduction goal. It is a wellknown fact that the microelectronic industry is an importantconsumer of PFC, including tetrafluoromethane (CF4), as etchgases for chamber cleaning processes. As a candidate for acleaner substitute to CF4 we have focused attention on nitrogentrifluoride (NF3) which, besides avoiding contamination with carbonresiduals and providing a process of near zero PFC emission, alsopresents advantages in terms of energy consumption and longertool lifetime.1 Added to this is the fact that nitrogen trifluoridedecomposition is a source of fluorine atoms and NF2 radicals,essential structures for a number of experimental physiochemicalinvestigations.2–4 These evidences led to a substantial rise in overallNF3 consumption which, together with the fact that NF3 is animportant greenhouse gas, provides a necessity to investigate thedecomposition process of this compound.

Despite all recent efforts to understand this importantmechanism, the kinetics of NF3 decomposition remain con-troversial, particularly when it comes to the removal of thispotent greenhouse gas from the atmosphere.5,6 While theliterature is filled with experimentally dependent processeswith high quality and reliable data, the phenomenologicalunderstanding of a more general qualitative mechanism, albeitless accurate, is missing. As an instructive example, we canmention the successful use of plasma technology for removingpollutants from gas streams resulted from catalyst degradationrecently reported.7 In their work, Chen et al. propose a NF3

breakdown mechanism based on a cylindrical dielectric barrierdischarge reactor constructed for the bench-scale experimentsthat yield an excellent comparison between experimental andtheoretically predicted data. Another experimental study by Wanget al.8 investigates the effects of different experimental parameterson the NF3 decomposition process. We are interested in a moregeneral intermediate path of the NF3 gas phase dissociationmechanism, a class of work with little presence in the literature.

In this sense we have previously proposed a simple kineticmechanism composed of several elementary reactions takingpart as intermediary steps to reach the global reaction.9 Ourgoal was to gain a first understanding of the NF3 decompositionprocess as a whole, i.e., without concerning with the specificityof each particular experimental situation. These limitationswere accepted as a reasonable compromise between qualitativeunderstanding and simplicity of the proposed mechanism,although important effects and deviations of our results fromexperimental evidences can be partly attributed to this procedure.

a Goias Federal Institute of Education, Science and Technology, Brazilb Institute of Physics, University of Brasilia, Brasilia, 70.919-970, Brazil.

E-mail: gargano@unb.br

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3nj00553d

Received (in Porto Alegre, Brazil)23rd May 2013,Accepted 1st August 2013

DOI: 10.1039/c3nj00553d

www.rsc.org/njc

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This journal is c The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2013 New J. Chem., 2013, 37, 3244--3251 3245

Besides unimolecular type systems (NF = N + F, NF2 = NF + F, NF3 =NF2 + F, N2F = N2 + F, N2F3 = NF2 + NF), the reactions involved inour mechanism are either of abstraction (NF2 + F = NF + F2, NF3 +F = NF2 + F2, NF + N = N2 + F, NF3 + N = NF2 + NF) or of exchange(NF + F = NF + F, NF2 + F = NF2 + F, NF3 + F = NF3 + F). The successachieved by our methodology in treating the systems involvingNF2 + F9 and NF + F10 leads us to proceed in our route to describethe kinetics of the 14 reactions that compose the proposed gasphase mechanism of NF3 dissociation.

Our procedure is to first perform accurate electronic structurecalculations in order to obtain energies, geometries and frequenciesfor reactants, products and transition states. We also obtain theminimum energy path and intrinsic reaction coordinates, featuresthat allow us to better understand each reaction mechanism. Wemake use of these properties to apply the transition state theory(TST) method11 and thus to be able to calculate the thermal rateconstant (TRC) for each one of these reactions. We also included astandard Wigner correction of the theory12 in order to contemplatetunneling effects.

In this work, we treat two sets of different systems—onerelated to the reaction between NF3 + F and the other producingN2 + F—each one consisting of two different channels. Bystarting with the abstraction channel of the former set, NF3 +F = NF2 + F2, we obtained TRC in agreement with the experi-mental data present in literature. Endorsed by these results wethen applied the same methodology to tackle the other channel ofthe NF3 + F system, i.e., the exchange channel (NF3 + F = NF3 + F) aswell as the unimolecular and abstraction reactions of the N2 + Fsystem, N2F = N2 + F and NF + N = N2 + F, respectively.

The idea is to provide the literature with reliable theoreticaldata concerning the reaction rate of these three latter systems.Since no experimental data is available to this date, our resultsare of fundamental importance for those trying to elucidate thenitrogen trifluoride mechanism. This paper is organized asfollows: Section II describes the main features of the electronicstructure calculations performed and also briefly discuss theTST; our results are presented and discussed in Section III andits subsections, and finally summarized in Section IV. Furtherdetails on the electronic structure results can be found on theESI† of this work.

II Methodology

TST method is a mixed formalism that considers thermo-dynamic, kinetic theory and statistical mechanics treatments.It includes the best features of each one of these theories interms of precision without giving up the simplicity achieved byfocusing attention on activated complexes which are assumedto be in ‘‘quasi-equilibrium’’ with reactants and their rate oftransformation.13 Due to its accuracy and simplicity, TST stillis, nearly 80 years after its development, the standard methodfor obtaining reaction rate constants from the theoretical pointof view.14 Provided geometries, energies, frequencies of reactants,transition states (TS) and products, we can make use of this theoryto compute the thermal rate constant of the respective system inan elegant, accurate, reliable and simple fashion.15 In this work

we managed to obtain the aforementioned quantities for NF3,NF3F, NF2, F2, N2F, NF, N2 and N2F by performing accurateelectronic structure calculations with GAUSSIAN0916 packagewith different basis sets and levels of theory.

We determined the systems TS by applying full (all electronsincluded in the correlation calculation) second order Møller-Plesset(MP2) level of theory with the 6-31G(d) and cc-pVDZ basis sets. Asfor the other species—reactants and products—we also made useof extended basis sets at higher levels of theory. Two sets of energieswere obtained for these reactions. By starting from MP2/cc-pVDZoptimized geometries, the first set was determined using theaug-cc-pVDZ, cc-pVTZ and aug-cc-pVTZ Dunning basis sets atMP4(SDQ), MP4(SDTQ), QCISD, QCISD(T), CCSD and CCSD(T)levels. The second set was determined starting from MP2/6-31G(d) optimized geometries at the same six levels of theoryand the following Pople basis sets: 6-31++G(d,p), 6-311++G(d,p),6-311++G(df,pd) and 6-311++G(3df,3pd). To determine an accuratethermal rate constant, the frequencies are scaled by a factor to takeinto account the known deficiencies of the MP2 level. This factor iscalculated as follows:

Scale Factor ¼

PNi¼1

wiðexp:Þ=wiðtheor:Þ

N; (1)

where N is the number of frequencies, wi(exp.), and wi(theor.)are the experimental and theoretical vibrational frequencies. Itobtained scale factors of 0.977884 and 0.962846 for the cc-pVDZand 6-31G(d) basis sets, respectively.

In the scope of the TST formalism, the thermal rate constantof a general bimolecular reaction such as A + BC - X‡ - C + ABis given by:15,17–19

kTST ¼ kBT

h

QXz

QAQBCexp �V

Ga

RT

� �(2)

where QX‡, QA, and QBC are the partition functions of transitionstate (TS) and reactants A and BC, respectively. kB is theBoltzmann constant; h is Planck’s constant; T is the tempera-ture; R is the universal gas constant and V G

a is the potentialbarrier given by

V Ga = VMEP + eZPE. (3)

In this expression eZPE is the harmonic zero-point energy (ZPE)and VMEP is the Eckart classical potential energy20 point mea-sured from the overall zero energy of the reactants:

VMEP ¼ay

1þ yþ by

ð1þ yÞ2; (4)

where y = ea(s–s0), a = DH00 = V G‡

a (s = +inf) � V G‡a (s = �inf),

b = (2V G‡a � a) + 2(V G‡

a (V G‡a � a))1/2, s0 ¼ �

1

aln

aþ b

b� a

� �,

a2 ¼ � m ozð Þ2b2Vz Vz � að Þ, and m is the reduced mass. a and b depend

on the reactants (V G‡a (s = �inf)), products (V G‡

a (s = +inf)) andTS (V G‡

a ) energies, as well as the imaginary frequency on theTS (o‡),21,22 and y is related to the reaction coordinate.

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In order to take tunneling effects along the reaction coordinateinto account, we introduce the transmission coefficient kW(T),thus obtaining k = kW(T)kTST(T), where kW(T) stands for Wignercorrection. The Wigner correction (kW(T)) for tunneling assumes aparabolic potential for the nuclear motion near the TS. Thepotential used takes the form:17,23

kWðTÞ ¼ 1þ 1

24

�hoz

kBT

��������2

: (5)

The characteristics of the MEP and the TRC, with the Wignertunneling corrections, are determined using our own code,which is described in the literature.18,19,24 The TRC are then

expressed in the Arrhenius form as kðTÞ ¼ ATN exp � Ea

RT

� �,

where A is the pre-exponential factor, N is the temperaturepower factor, and Ea is the activation energy.

III Results and discussions

As we consider a TST approach in this work, we first need toanalyze the values of geometries, energies and frequencies ofreactants, products and transition state species. Table 1 ismeant to deal with the first of these tasks for reactants andproducts. We performed geometry calculations at MP2/cc-pVDZand MP2/6-31G(d) levels. The table lists a summary of calcu-lated inter-atomic distances and bond angles for each level

together with a standard value obtained in the literature (whenavailable) for comparison purposes. The good agreementachieved for both bond distances and bond angles for all thementioned calculations is readily seen and can be quantified bycalculating the maximum absolute error for each case whichwas found to be no larger than 0.04 Å and around 1.01,respectively. Also, the theoretical references available inTable 1 provide an efficient criterion when deciding whichvalues, or in other words, which basis set, is to be used in theTST formalism.

The accuracy obtained for the geometrical parameters allowus to rely on the levels of theory and basis sets used for thepresent calculations and proceed in the task of obtaining thequantities required by TST with the frequency calculation forreactants and products, summarized in Table 2. Comparing todata present in the literature, our calculations presented smallabsolute error values, which is an indication of their accuracy.As we would expect, it is noted that a tendency of the higherlevel of theory results in calculated frequency values nearer tothe experimental ones. This fact also indicates the consistencyof our calculations. An interesting feature present in the lastcolumn of Table 2 is the zero point energy (ZPE) correction.The idea is to express all the calculated energies referring tothe same energy level, and the correction should be made as

Table 1 Geometrical parameters for reactants and products of the unimolecular,abstraction and exchange reactions calculated at MP2/cc-pVDZ and MP2/6-31G(d)levels

Species Bases

Interatomic distances (Å) Bond angles (1)

RNF RFF RNN AFNF ANNF

F2 cc-pVDZ — 1.424 — — —6-31G(d) — 1.421 — — —Exp. — 1.41225,26 — — —

— 1.43527 — — —Theor. — 1.42128 — — —

N2 cc-pVDZ — — 1.129 — —6-31G(d) — — 1.130 — —Exp. — — 1.09427, 1.09826 — —Theor. — — 1.13128 — —

NF cc-pVDZ 1.317 — — — —6-31G(d) 1.330 — — — —Exp. 1.31726,29 — — — —Theor. 1.33028 — — — —

N2F cc-pVDZ 1.579 — 1.318 — 65.36-31G(d) 1.578 — 1.321 — 65.2

NF2 cc-pVDZ 1.349 — — 103.7 —6-31G(d) 1.359 — — 103.3 —Exp. 1.37025,30 — — 104.225,30 —Theor. 1.35928 — — 103.328 —

NF3 cc-pVDZ 1.377 — — 102.0 —6-31G(d) 1.385 — — 101.7 —Exp. 1.37125 — — 102.925 —Theor. 1.38531 — — 101.731 —

1.38028 — — 101.728 —

Table 2 Harmonic vibrational frequencies (cm�1) and zero-point energy(kcal mol�1) for reactants and products of the unimolecular, abstraction andexchange reactions at MP2/cc-pVDZ and MP2/6-31G(d) levels

Species Bases n1 n2 n3 n4 eZPE

F2 cc-pVDZ 933.4 — — — 1.3056-31G(d) 1007.8 — — — 1.387Exp. 892.027,32 — — — —

916.626 — — — —Theor. 957.028 — — — —

N2 cc-pVDZ 2176.2 — — — 3.0426-31G(d) 2178.7 — — — 2.999Exp. 2359.627,32 — — — —

2358.626 — — — —Theor. 2118.728 — — — —

NF cc-pVDZ 1175.3 — — — 1.6436-31G(d) 1192.0 — — — 1.641Exp. 1115.025 — — — —

1141.426,29 — — — —Theor. 1138.529 — — — —

1104.628

N2F cc-pVDZ 814.7 939.3 1382.0 — —6-31G(d) 862.0 932.5 1386.8 — —

NF2 cc-pVDZ 586.0 982.8 1126.6 — 3.7686-31G(d) 574.0 1026.1 1147.0 — 3.781Exp. 573.025 931.025 1074.025 — —

573.430 930.730 1069.530 — —Theor. 569.728 908.128 1078.628 — —

NF3 cc-pVDZ 496.8 656.1 915.8 1043.8 6.3266-31G(d) 489.3 653.7 959.9 1062.0 6.351Exp. 492.025 642.025 906.025 1032.025 —

497.033 648.033 898.033 1027.033 —Theor. 489.331 653.731 959.331 1061.631 —

484.628 644.228 860.628 1032.828 —

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eZPEcorr = eZPEprod � eZPEreact, whenever the minimum of thepotential energy curve is not the minimum energy of thevibrational ground state. We make use of this definitionthroughout the present study.

Table 3 presents the TS optimized geometries, harmonicvibrational frequencies, and zero-point energy for the abstraction ofNF3 + F and N2 + F systems (TSa and TSd, respectively) and also forthe exchange channel of NF3 + F (TSb) and the unimolecularreaction N2F = N2 + F (TSc). The notation is clarified in Fig. 1,which represents the transition structures for all the studiedsystems. The imaginary frequency ni is also reported. FromTable 3, one can see that our results are in good agreement withthe experimental and theoretical data available in the literature.

We present the reactant and product formation enthalpywith ZPE correction for the species considered in this work inTable 4. We also add theoretical and experimental references

for comparison with our results. One can readily note a widerange of results for the formation enthalpies reported in theliterature for the different reactions. This is due to the differentlevels of theory and basis sets employed in each case. We cansee that the results systematically present good agreement withboth experimental and theoretical data. The complete set ofab initio properties, total electronic energies, forward barrier,reverse barrier, and calculated and experimental DH0 values at298 K are available in the ESI.† All these properties werecalculated using several basis sets (cc-pVDZ, aug-cc-pVDZ,cc-pVTZ, aug-cc-pVTZ, 6-31G(d), 6-31++G(d,p), 6-311++G(d,p),6-311++G(df,pd) and 6-311++G(3df,3pd)) and at MP2, MP4(SDQ),MP4(SDTQ), QCISD, QCISD(T), CCSD, CCSD(T) levels of theory forreactant, product and TS for abstraction (NF3 + F = NF2 + F2 andNF + N = N2 + F), exchange (NF3 + F = NF3 + F) and unimolecular(N2F = N2 + F) reactions. The final TRCs for all reactions werecalculated using the MP4/cc-pVTZ level. This level was chosenby comparing the ab initio and experimental DfH

0 values forunimolecular, abstraction and exchange reactions and concludingthat it yielded the smallest difference between these data.

With all the static properties needed in a TST treatmentavailable, the remainder of this section is divided into twosubsections, to accomplish the TRC calculation for each one ofthe desired systems. In order to gather a qualitative feeling ofhow each reaction takes place it is worth first studying thebehavior of the intrinsic reaction coordinate of each system.After that, we present the minimum energy path (MEP) resultsfor the reactive systems and finally discuss the obtained TRCsfor both reactions. We chose to explicitly present and discusshere our main results of TRC plots together with the discussionof the main features of IRC and MEP plots, that we left in theESI† in favor of succinctness.

Table 3 Transition state geometrical parameters (inter-atomic distances in Å and bond angles in degrees), harmonic vibrational frequencies (cm�1), and zero-pointenergy (kcal mol�1) calculated at MP2/cc-pVDZ and MP2/6-31G(d) levels for NF3 + F = NF2 + F2 (TSa), NF3 + F = NF3 + F (TSb), N2F = N2 + F (TSc) and NF + N = N2 + F (TSd)reactions. The imaginary frequency (ni) was also reported

NF3 + F = NF2 + F2 (TSa) NF3 + F=NF3 + F (TSb) N2F = N2 + F (TSc) NF + N = N2 + F (TSd)

cc-pVDZ 6-31G(d) cc-pVDZ 6-31G(d) cc-pVDZ 6-31G(d) cc-pVDZ 6-31G(d)

RNF 1.347 1.355 1.338 1.350 1.985 2.006 1.329 1.340RNF0 2.607 2.353 1.507 1.499 — — — —RNF00 — — 1.507 1.499 — — — —RF00F0 0 0 1.586 1.661 — — — — — —RN0F0 — — — — 1.440 1.437 — —RNN0 — — — — 1.270 1.266 1.971 1.983AFNF0 103.76 103.37 105.67 105.31 — — — —AF0NF00 107.08 101.17 100.13 99.75 — — — —ANF0F00 173.70 173.70 — — — — — —AF00NF0 — — 146.14 147.58 — — — —AN0NF — — — — 93.98 95.60 — —ANF0N0 — — — — — — 100.95 100.14n1 25.42 39.91 300.40 302.32 268.85 260.54 1166.18 1174.32n2 28.55 45.06 402.23 400.94 1116.03 1140.73 1478.56 1493.54n3 55.97 80.48 453.69 452.34 — — — —n4 77.76 116.18 580.54 590.03 — — — —n5 122.98 170.68 651.05 644.47 — — — —n6 587.89 578.12 738.13 733.50 — — — —n7 987.05 1031.38 1037.16 1071.56 — — — —n8 1129.01 1148.61 1055.63 1100.62 — — — —ni 570.73i 399.00i 1441.55i 1309.92i 471.45i 462.76i 509.36i 539.34ieZPE 4.214 4.419 7.296 7.345 1.936 1.929 3.698 3.672

Fig. 1 Schematic representation of transition structures for (a) abstraction (TSa),(b) exchange (TSb), (c) unimolecular (TSc), and (d) abstraction (TSd) reactions.

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A. NF3 + F system

The channels considered in the NF3 + F system are those ofabstraction and exchange. As already mentioned, the IRCs of allreactive systems are placed in the ESI,† and the abstractionchannel of this set is represented in Fig. 1. We can note thebreaking of a F atom from the NF3 molecule expressed by thecontinuous deviation of the upper line from the others. Thesubsequent formation of the F2 molecule is manifested in theconvergence of the remaining two lines. The exchange channelpresented in Fig. S2 of the ESI† on the other hand is representedby a characteristic symmetrical IRC plot, consistent with theinterchange of two indistinguishable fluorine atoms: one fromthe molecule and the other from the atomic species.

We then analyze the minimum energy path for both reactions,figures that are also presented in the ESI.† Fig. 3 consists of theMEP representation for the abstraction channel. We present twoplots in the figure: VMEP associated with the standard representa-tion of the minimum energy path, andVa

G, which consists of VMEP

added to eZPE in each region. We obtained an exoergecity of21.8863 kcal mol�1 and the experimentally expected absence ofcomplexes, reactants and products. The minimum energy pathof the exchange channel presented in Fig. S4 of the ESI† shows aresult in strikingly good accordance with the expected lack ofenergy gain or loss from reactants to products. The reasoningshould be obvious from the indistinctness of the fluorine speciesmanifested in Fig. 2. Another important feature is the relativelylower barrier this channel presents when compared to the formerreaction. Conventional and Wigner-corrected TRCs are plottedagainst reciprocal temperature for the abstraction channel inFig. 2 of this work.

We can see that in the high temperature regime (3000–4000 K),the two curves are almost coincident. This is due to the lowimportance tunneling has in this regime, since thermal excitationprevails in promoting the reaction.

In the low temperature regime, tunneling effects were found tobe of intermediate importance. In this case, the coincidencebetween Wigner-corrected and conventional TRC is quite interesting

and can be attributed to the influence of the harmonic potential.Also, the intermediate importance of tunneling effects is consistentwith the intermediate value of 52.761 for the skew angle obtained.These features are more readily observed when describing theobtained TRC in Arrhenius form as:

kTST = 2.8692 � 1012T1.7636e�56982/RT

kTSTW = 1.6373 � 1012T1.828e�56699/RT,

where R = 1.9859 kcal�1 mol�1 is the universal gas constant. Itis important to note that in this work, we expressed all theactivation energy quantities (Ea) in the Arrhenius fitting in unitsof cal mol�1 so as to better present our results. The valuesobtained for the coefficients provide a useful way to compareour results with others from the literature. The main resultobtained for this system is expressed in the inset of Fig. 2. Fromthis figure and Table 5, one can see that our conventional and

Table 4 Reactant and product formation enthalpy (kcal mol�1) with ZPE correction for all species involved in the unimolecular, abstraction and exchange reactions

Species This work Experimental references Theoretical references

F2 0.403 025,34,35 0.3a, 0.3b, 0.688i, 1.288 j

0.980c, 0.056d, 0.686e

�2.027c, 0.927d, �2.142e

N2 1.786 025,34,35 1.3b, 2.004i, 1.994 j

�2.027c, 0.927d, �2.142e

NF 53.757 55.688 � 0.72,34 55.6 � 0.536 54.9a, 54 f, 53.9g, 56.18h

59.501 � 7.8925 46.698c, 54.635d, 51.903e

N2F 146.344 — —

NF2 7.234 10.7 � 1.9125, 8.8 � 1.2034 6.6a, 8 f, 8.5g, 8.67h

8 � 1,32 8.3 � 0.536 �3.411c, 5.845d, 5.852e

NF3 �31.600 �30.20 � 0.2725,34 �33.8b, �26.5g, �30.2 f

�41.310c, �35.271d, �32.321e

a At G2 level.37 b At G2 level.38 c At B3LYP/6-311++(3df,3pd) level.28 d At G2 level.28 e At G3 level.28 f For G3 level.39 g At BAC-MP4(SDTQ) level.40

h At CCSD(T) level.41 i Estimated from DfH0(298) at G3 level.42,43 j Estimated from DfH

0(298) at G3 level.42,43

Fig. 2 Conventional (kTST), and Wigner (kTSTkTSTW ) plots of thermal rate constant

in the temperature range of 200–4000 K for the abstraction channel NF3 + F =NF2 + F2.

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Wigner-corrected TRCs are in excellent agreement with theexperimental data of Diesen.44

An analysis of this result allows one to conclude that theused methodology is suitable to treat this kind of system. This factalso finds support in the good agreement between theoretical datarecently published by our group and experimental evidences.9,10

We thus have demonstrated the suitability of the TST formalism fortreating this kind of reactive system. Therefore, we can proceed inthe same fashion for the remaining reactions—in which experi-mental evidences are absent—with the goal of providing reliabledata for future comparison.

For the TRC of the exchange channel, we observe in Fig. 3 aneven more coincident behavior between conventional andtunneling-corrected thermal rate constants. We can note anegligible deviation of the curves, even in the low temperatureregime. This fact, again, is in complete agreement with thecalculated skew angle of 74.481 and can be confirmed by theTRC Arrhenius coefficients as follows:

kTST = 1.2187 � 108T1.4352e�23893/RT

kTSTW = 4.0064 � 107T1.5577e�23011/RT.

A last feature worthy of note in the TRC of this system lies inthe fact that the exchange reaction is around twelve times fasterthan the abstraction in the low temperature regime, andfive times faster for higher temperatures, as can be directlycompared between Fig. 2 and 3. This is attributed to theenergetic difference between each system’s barrier. Since tempera-ture is known to promote the reactions, it is only natural that thedifference in reaction rate is lower for higher temperature. Thishappens because in this regime, thermal excitation tends to favorthe transition of an appreciable number of complexes through thebarrier.

B. N2 + F system

This subsection is meant to deal with the abstraction and theunimolecular channels of the N2 + F system considered. Wefirst consider each channel IRC (whose plots are placed in theESI†) in order to achieve a better understanding of the dynamicmechanism. Comparing Fig. S5 and S6—referring to theESI†—we observe the same final value for RNN0, which isconsistent with the fact that both channels yield the sameproducts. By analyzing the initial values in each case, we obtainbonding values for the molecules consistent with experimentalevidences.

A thermochemical investigation of N2F = N2 + F results in anexoergicity of�131.29 kcal mol�1, whereas that of NF + N = N2 +F results in �148.97 kcal mol�1, as shown in Fig. S7 and S8 ofthe ESI.† In the high level of exoergecity of the present systemlies an important difference between this and the one presentedin the previous subsection. In that case we observed endoergicreactions. Also, the barriers presented in the MEP of the N2 + Fsystems were considerably smaller than those of Subsection IIIA.

Table 5 Calculated thermal rate constants compared to the experimental datafor NF3 + F = NF2 + F2 reaction

T (K) Conventional Wigner Exp.44

1200 7.50376 7.51000 10.056971250 7.95041 7.95572 10.161941300 8.36387 9.36838 10.258841350 9.74780 9.75160 10.348561400 9.10532 9.10850 10.431871450 9.43912 9.44177 10.509431500 9.75156 9.75372 10.581831550 10.04466 10.04641 10.649551600 10.32021 10.32160 10.713041650 10.57979 10.58087 10.772681700 10.82478 10.82560 10.828821750 11.05642 11.05700 10.881741800 11.27579 11.27618 10.931731850 11.48389 11.48411 10.979011900 11.68157 11.68166 11.0238091950 11.86964 11.86960 11.066302000 12.04879 12.04869 11.10668

Fig. 3 Conventional (kTST), and Wigner (kTSTkTSTW ) plots of thermal rate constant in

the temperature range of 200–4000 K for the exchange channel NF3 + F = NF3 + F.

Fig. 4 Conventional (kTST) and Wigner (kTSTkTSTW ) plots of thermal rate constant in

the temperature range of 200–4000 K for the unimolecular channel N2F = N2 + F.

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3250 New J. Chem., 2013, 37, 3244--3251 This journal is c The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2013

Fig. 4 of this paper presents the thermal rate constant for theunimolecular channel N2F = N2 + F. A Wigner-corrected rate isplotted together with the conventional TRC.

A striking coincidence between the plots is perceived for alltemperatures investigated. This again is in complete agreementwith the high value of the skew angle obtained (83.11), whichdemonstrates the small role tunneling effects play in promotingthis reaction. The Arrhenius fitting for conventional and Wigner-corrected TRC were obtained as:

kTST = 1.230 � 1016T 0.0551e�1213/RT

kTSTW = 7.638 � 1015T 0.1099e�11895/RT.

The thermal rate constant of the abstraction channel NF +N = N2 + F is presented in Fig. 5. In the high temperature regimewe obtain a great agreement between the Wigner-corrected andthe conventional rates. We can note a rate coefficient at 300 Kvery close to the gas kinetic collision value, which is consistentwith the low value of the potential energy maximum obtained.

Similarly, the Arrhenius fitting for this set of systems turnedout as:

kTST = 2.5698 � 1013T 0.49652e�879.88/RT

kTSTW = 1.6811 � 1013T 0.54536e�671.94/RT.

These coefficient values provide easy means of comparisonwith those of future alternative works as well as being of use forresearch in the rich field of nitrogen trifluoride decomposition.

IV Conclusions

The present work is part of a series of papers with the shared goalof elucidating the complex mechanism of nitrogen trifluoridedecomposition by considering a simple kinetic intermediatemechanism recently proposed. We performed thermal rate con-stant calculations of four different reactions involved in the NF3

decomposition mechanism in the scope of transition state theory.In order to accomplish this, a complete and accurate ab initio studywas performed for all involved reactants, products and transitionstructures obtaining geometries, energies and frequencies. For thefour investigated channels, we observed the expected qualitativebehavior suggested by the systems IRC and MEP. Furthermore, asexperimental data for the thermal rate constant is available for theabstraction channel of NF3 + F, we were able to compare ourresults and thus to assess our methodology for use in this kind ofsystem. Since our results are in excellent agreement with theexperimental data, we conclude that the model used for thiscalculation is suitable for reactions of this type. Considering thatthe mechanism involved in the NF3 decomposition is composed ofsome of the reactions investigated in our work as well as of othersimilar systems, we conclude that besides providing the literaturewith data for the investigated reactions, we also have described anaccurate and elegant method for treating the different reactionsinvolved in the mechanism. Due to their accuracy, our results areof fundamental importance whenever NF3 decomposition is to beconsidered. The results obtained herein are of potential use forcomparison in future theoretical and experimental works on NF3

chemistry.

Acknowledgements

The authors gratefully acknowledge the financial support fromthe Brazilian Research Councils CNPq, CAPES, FINATECand FAPDF.

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