6832
J. Phys. Chem. A 2010, 114, 6832–6836
Reactions of Negative Ions with ClN3 at 300 K Nicole Eyet,†,‡,§ Keith Freel,‡,| Michael C. Heaven,| and A. A. Viggiano*,‡ Department of Chemistry, St. Anselm College, 100 Saint Anselm DriVe, Manchester, New Hampshire 03102, USA, Institute for Scientific Research, Boston College, USA, Space Vehicles Directorate, Air Force Research Laboratory, 29 Randolph Road, Hanscom Air Force Base, Massachusetts 01731-3010, USA, and Chemistry Department, Emory UniVersity, Atlanta, Georgia 30322, USA ReceiVed: April 1, 2010; ReVised Manuscript ReceiVed: May 20, 2010
The reactivity of ClN3 with 17 negative ions has been investigated at 300 K. The electron affinity (EA) of ClN3 was bracketed to be between that of NO2 and N3, giving EA(ClN3) ) 2.48 ( 0.20 eV, in agreement with an electronic structure calculation. Reaction rate constants and product ion branching ratios were measured. In nearly all cases the major product of the reaction was chloride ions. Charge transfer, N3- production, and O atom incorporation is also observed. DFT calculations of stable complexes and transition states are presented for two typical ions. Mechanistic details are discussed in terms of reaction coordinate diagrams. Introduction Halogen azides have been reported in the literature since 1900.1 The structures of these azides have been determined and the configuration found to be planar and trans-bent,2,3 with an N-N-N angle of approximately 172° and a X-N-N angle of 108°. Beyond the structure, however, the tendency of these compounds to spontaneously detonate has limited studies on their reactivity, and these have been mostly limited to the condensed phase.4,5 Recent interest in potential applications of ClN3 has fueled new experiments. The explosive nature of these compounds implies they store significant energy. These high energy density materials have applications as detonators and propellants and in energy storage. Additionally, theoretical work has predicted a cyclic N3 isomer could result from photodissociation.6-8 This N3 isomer can be used to synthesize higher order Nx compounds. Recently, several studies of the photodissociation of ClN3 have been carried out. These studies reported N3 products with two distinctive internal mode energy distributions; the higher energy product appeared to be consistent with predictions for cyclic N3.9,10 Photodissociation studies have also shown that ClN3 can dissociate to form NCl(a 1∆),11 a molecule that is isoelectronic with O2(a 1∆). Like O2(a 1∆), NCl(a 1∆) can be used to produce chemically driven iodine lasers.12,13 NCl(a 1∆) has the advantage of being the product of gas precursors, whereas O2(a 1∆) is produced from a combination of gas phase and solution chemistry. Development of an all gas iodine laser has been the subject of recent interest. Given the applications of ClN3, general knowledge of its gasphase reactivity is needed. No studies of the reactivity of ClN3 with ions have been reported. In this study, we have examined the reaction of ClN3 with 17 negative ions. The reactants chosen contain a variety of functional groups, allowing for general reaction trends to be observed. In addition, the reactivity of these * To whom correspondence should be addressed. † St. Anselm College. ‡ Air Force Research Laboratory. § Boston College. | Emory University.
ions with Cl2 was determined to eliminate contributions from possible unreacted Cl2 from ClN3 preparation. Experimental Section These experiments were carried out using the selected ion flow tube (SIFT) at the Air Force Research Laboratory. This instrument has been described in detail elsewhere14 so only a brief description will be provided here. Ions are produced in a moderate pressure source by introducing the appropriate precursor. Introducing O2 produces O2- and O-, N2O4 produces NO2and NO3-, and CH3CN produces CN-. SF6-, SF5-, and F- were produced by introducing SF6. Introduction of H2O produces OH-. NH2- is produced by allowing O- (from N2O) to react with NH3. Bromide ions are produced by introducing CBrF3; iodide ions were produced by introducing C2H5I. Methoxide is produced by introducing methanol and injecting CH3O-(CH3OH) with sufficient energy to fragment the cluster. Cland Cl2- are produced by introducing chlorine gas. The desired reactant ion is mass selected with a quadrupole mass filter and injected through a Venturi inlet into the reaction flow tube, where they are thermally equilibrated to room temperature though multiple collisions with helium buffer gas (∼0.4 Torr). Neutral reagents are added though a stainless steel inlet 59.0 cm upstream from the sampling orifice. The depletion of the reactant ion and the formation of product ions are monitored by a quadrupole mass filter coupled to a counting electron multiplier. Reactant rate constants are determined by monitoring the depletion of the reactant ion as a function of neutral reagent flow. Branching ratios are determined by plotting product fractions as a function of ClN3 concentration and extrapolating to zero. This removes contributions from any secondary chemistry. The production of chlorine azide is described by eq 1. H2O
NaN3(s) + Cl2(g) 98 ClN3(g) + NaCl(s)
(1)
Approximately 5 g of NaN3 is evenly distributed on an approximately 0.5 cm × 5 cm × 20 cm piece of glass wool. The glass wool is sprayed with ∼2 mL of distilled water, rolled
10.1021/jp102951z 2010 American Chemical Society Published on Web 06/04/2010
Reactions of Negative Ions with ClN3 at 300 K
J. Phys. Chem. A, Vol. 114, No. 25, 2010 6833
Figure 1. Semilogarithmic plot of fluoride ion reacting with chlorine azide. The line through the F- data is a least-squares fit.
up, placed in a glass vessel, and maintained at 0 °C using a recirculating chiller. A mixture of chlorine gas in helium (in this case either 1 or 10%) is flowed through the vessel, at a known flow rate, to produce ClN3. Residual water is removed from the flow of neutral reagents by passage through a trap, maintained at 7 °C, containing Drierite. To determine the total ClN3 concentration, the neutral flow passes though a PerkinElmer Lambda 10 UV-vis Spectrometer, where the spectrum taken over the range 190-300 nm was compared to the known ClN3 absorption spectrum. Absolute concentrations were determined in real time by measuring the absorbance at λmax ) 205.6 nm. The yield for this reaction ranged from 39 to 100%, with typical results of greater than 80%. In some cases, unreacted Cl2 was introduced into the reaction flow tube along with ClN3. To account for this complication, reaction rate constants and product ion branching ratios were also measured for all the ions interacting with Cl2. Any contributions from reactions with Cl2
were removed from the ClN3 data. This is discussed in more detail below. More detail on ClN3 production is given in our paper on electron attachment to ClN3, published separately.15 Efforts were made to minimize mass discrimination. Data were collected under lower resolution conditions. The semilogarithmic decays of Cl2 and ClN3 were observed to be linear in all cases. A typical decay plot is shown in Figure 1 for the reaction of Fwith ClN3. The F- ion decays linearly on the semilogarithmic plot and both Cl- and N3- increase. The N3- decreases at larger densities because it also reacts with ClN3. Decay of the primary ions was ∼20% for the slowest reactions and up to 80% for faster reactions. Due to the difficulties of this experiment, we assign large error bars of (35% to the reaction rate constants and (40% of the minor product to the product ion branching ratios. Electronic structure calculations were carried out using the Gaussian 03 program package.16 Reaction energetics and structures of complexes and transition states were calculated using B3LYP/6-311+G(d).17,18 The electron affinity of ClN3 was calculated using G3B3 theory as it has been shown to provide accurate thermochemical data.19 Stable structures were identified as having no imaginary frequencies. Transition states were identified as having exactly one imaginary frequency. Transition states were linked to ion dipole complexes by calculating internal reaction coordinates. Results and Discussion Reactions with Cl2. In some cases, unreacted Cl2 was introduced into the reaction flow tube along with ClN3, as evidenced by production of Cl2-. To account for this complication, reaction rate constants and product ion branching ratios were also measured for the same ions reacting with Cl2 as the sole neutral reagent. Reaction rate constants, reaction efficiencies, reaction enthalpies, and product ion branching ratios are given in Table 1. Reaction efficiencies are defined as the ratio of the measured rate constant to the collision rate constant; the collision rate constants were calculated using Langevin collision theory.20,21
TABLE 1: Reaction Rate Constant (10-10 cm3 molecule-1 s-1), Product Ion Branching Ratios, and Reaction Enthalpies (kJ mol-1) of Negative Ions with Cl2 reaction O2-
+ Cl2
eBEa (eV)
rate constant
eff
ionic products -
0.448
11.8
1.10
O- + Cl2
1.461112
17.3
1.24
NO2- + Cl2
2.273
7.87
0.83
SF6- + Cl2 SF5- + Cl2 F- + Cl2 OH- + Cl2
1.2 3.8 3.4012 1.8277
0.945
0.13 0.00 0.61 0.91
CN- + Cl2 NH2- + Cl2
3.862 0.771
0.126 1.34
0.01 0.10
N3- + Cl2 Br- + Cl2 I- + Cl2 CH3O- + Cl2
2.68 3.363538 3.059036 1.572
0.0346 0.268 0.496 0.945
0.00 0.03 0.07 0.09
a
7.87 12.7
Electron affinities are taken from the NIST Webbook.
Cl Cl2ClClOCl2ClCl2Cl2N/R ClClClOCl2ClClCl2ClClClClCl2-
hypothesized neutral products ClO2 O2 ClO Cl O NO2Cl NO2 SF6 FCl HClO HCl OH ClCN NH2Cl NH2 ClN3 BrCl ICl CH2O + HCl CH3O
branching fraction
∆Hrxn
0.67 0.33 0.06 0.11 0.83 0.09 0.91 1
-80 -188 -234 -95 -91 7 -15 -132
0.18 0.03 0.79
-43 -163 -61 -54 -162
0.14 0.86 1 1 1 0.59 0.41
-152 -250 -14 -365 -296 -76
6834
J. Phys. Chem. A, Vol. 114, No. 25, 2010
Eyet et al.
TABLE 2: Reaction Rate Constant (10-10 cm3 molecule-1 s-1), Product Ion Branching Ratios, and Reaction Enthalpies (kJ mol-1) of Negative Ions with ClN3a reaction O2-
+ ClN3
O- + ClN3
EA (eV) 0.448
rate constant 11.4
1.461112
16.4
eff
ionic products -
0.09 0.01 0.11 0.65 0.11 0.09 0.15
ClN3ClN3-
2NO + N2 NO2Cl NO2
0.31 0.06 0.63
-46 +10 +9
35
ClFN3SF5FN3SF4N3ClN3ClClOClN3Cl-(ClN3) ClN3Cl-
37
0 +175 +72 +366 +119 -63* -62* -372 -69 -36*
N2 + CNN ClCN 2N2 + H2 N3 + NH2 3N2 BrN3 IN3 ICl CH3O + N3 N2 + NO + CH3 CH3OCl CH3N3 N3
1.0 0.34 0.66 0.66 0.34 0.64 0.36 0.67 0.12 0.12 0.09 0.41 0.59 1.0
0.96
N3ClO2ClN3Cl-
3.26 2.273
no reaction 10.4
0.00 0.90
37
NO3- + ClN3 Cl- + 35ClN3 SF6- + ClN3
3.937 3.6144 1.20
no reaction 3.1 2.42
0.00 0.25 0.28
SF5- + ClN3
3.8
0.390
0.04
F- + ClN3
3.4012
8.98
0.57
OH- + ClN3
1.8277
13.0
0.80
CN- + ClN3
3.862
9.30
0.66
NH2- + ClN3
0.771
1.72
0.10
N3- + ClN3 Br- + ClN3 I- + ClN3
2.68 3.363538 3.059036
0.0969 0.0824 0.574
0.01 0.01 0.06
CH3O- + ClN3
1.572
1.64
0.12
ClClClN3Cl-
0.26
N3ClOCl3-
2.61 37
-
The reaction rate for Cl was corrected for the natural abundance of calculations were used to estimate exothermicities.
With the exception of SF5-, which did not react at all, Cl- is a product of all of the ion-Cl2 reactions. As shown below, this channel also occurs in all the ClN3 reactions and is not useful in determining the Cl2 background. The presence of Cl2- in many of the reactions is more useful, since it cannot be produced from ClN3 in any reaction. The electron binding energy of Cl2 is 2.4 eV. As expected, ions having an electron binding energy greater than 2.4 eV produce exclusiVely Cl- (except the nonreactive SF5-). Fortunately for this study, all ions having an electron binding energy less than the electron affinity of chlorine do produce Cl2- as at least one of the products. This is the case in reactions with O2-, O-, NO2-, SF6-, OH-, NH2-, and CH3O-. Known reaction rate constants and product ion branching ratios can be used to subtract the unreacted Cl2 contribution in the ClN3 reactions. For systems where no Cl2is formed in the reaction with Cl2, a reaction that did form Cl2was run immediately before or after the ClN3 study so that the Cl2 contribution could be subtracted. All corrections were small (less than 10% of the largest product) and affected mainly the branching of the minor channels. Reactions of O- and OH- with Cl2 additionally form ClOas a product. In the reaction of O- with Cl2, it is likely that ClO- (and Cl-) form as a result of electron transfer within the
∆Hrxn -110 -534 -20 +92 -170* -12 -628 -191 -152 -80*
Cl
CO3- + ClN3 NO2- + ClN3
a
branching fraction
N3 + O 2 N2 + NO2 Cl + O2 N3 O2 N3 + O N2 + NO ClO
0.88
N3ClOClN3-
Cl2- + ClN3
hypothesized neutral products
ClN3 SF5Cl ClF + N3 SF4Cl FCl FN3 FCl N2 + HNO HN3 OH
35
0.80
1.0 1.0 0.83 0.17 0.75 0.15 0.10 1.0
-67 -120 -721 -74 -808 +3* -13* (+21) -59* -67 -255 -187 -67 -362
Cl in ClN3. Asterisks indicate where electronic structure
product ion-dipole complex [Cl · ClO]-. In the reaction of OH-, it is likely that proton transfer within the [ClO- · HCl] product ion dipole complex results in both the ClO- (and Cl-) products. The reactions of O2-, O-, NO2-, SF6-, and F- with Cl2 have been studied previously.22-25 The results measured here are in agreement with previous observations (both reaction rate constants and product ion branching ratios) within our experimental error. Reactions with ClN3. Table 2 summarizes reaction rate constants, reaction efficiencies, reaction enthalpies, and product ion branching ratios for reaction of the various ions with ClN3. In this case, collisional rate constants were calculated using parametrized trajectory collision rate theory.26 The dipole moment and polarizability of ClN3 used in the collision rate determinations were calculated using B3LYP theory with a 6-311+G(d) basis set. The dipole moment was determined to be 0.5363 D; the polarizability was determined to be 5.42 × 10-24 cm3. As discussed above, many of the Cl2 reactions (a contaminant gas in some experiments) produce Cl2-. Reactions with O-, O2-, NO2-, OH-, and CH3O- indeed showed trace amounts of Cl2produced as a result of the Cl2 contaminant. All other reactions showed no signs of contamination, even when run consecutively
Reactions of Negative Ions with ClN3 at 300 K
J. Phys. Chem. A, Vol. 114, No. 25, 2010 6835
with reactions that would produce Cl2-. This incomplete reaction of Cl2 is likely due to small variations in the preparation of the NaN3-coated glass wool. The data in Table 2 were corrected for the small Cl2 contaminant in the reactions listed above, and the error bars reflect this correction. Table 2 also shows that Cl2- reacts with ClN3 to produce Cl3-. In the reactions where unreacted Cl2 was present, this ion is not observed because no secondary chemistry results from the contaminant gas. One of the goals of the present study was to determine the electron affinity of ClN3. To bracket the electron affinity, we allowed ClN3 to react with ions having a variety of electron binding energies. The observation of electron transfer from a reactant ion to ClN3 suggests that the electron affinity of ClN3 is larger than the electron binding energy of the reactant ion. Lack of electron transfer from a reactant ion to ClN3 suggests that the electron binding energy of the reactant ion is greater than the electron affinity of ClN3. Unfortunately, we were unable produce ClN3- in our source in order to observe electron transfer in the other direction. Electron transfer to ClN3 occurs in reactions with O2-, O-, OH-, and NO2-, where the overall reaction proceeded with near unit efficiency. Electron transfer is not observed in reactions with N3-, I-, Br-, and F-, with only the F- reaction proceeding rapidly to form other products. The above leads us to conclude that the electron affinity of ClN3 lies between that of NO2 and N3, estimated to be EA ) 2.48 ( 0.20 eV. The electron affinity of ClN3 was calculated using G3B3 calculations to be 2.32 ( 0.1 eV. These values are in good agreement considering the uncertainty in the experimental and theoretical determinations. In cases where electron transfer is predicted to be considerably exothermic, is it likely that both nondissociative and dissociative charge transfer occur, as is the case for reactions of both O2- and O-, where only a minor charge transfer product is observed. Additionally, we cannot rule out the occurrence of some thermal dissociation of the ClN3-, -1 ClN3 + He f Cl + N3 + He - 55 kJ mol
(2)
We have seen cluster ions with approximately this bond strength dissociate previously.27,28 Although the reaction does not proceed to completion, it may result in a small underestimation of ClN3- production and an overestimation of Clproduction. The most stable ions, CO3- and NO3-, do not react. Reactions of O2-, O-, NO2-, F-, CN-, I-, and CH3O- produced both Cland N3-. These reactions proceed with efficiencies of at least 50%, except for the reactions I- and CH3O-, which are only 12 and 6% efficient, respectively. In general, the relative exothermicities of the two channels were reflected in the branching ratios. In nearly all cases Cl- is the major product; in the reaction with CN-, N3- production is more exothermic and accounts for 60% of the ionic products. These two products account for at least 75% of the total product ions in these reactions; in the reaction of NO2-, charge transfer dominates. The reaction coordinate for the reaction of F- with ClN3 has been calculated and is shown in Figure 2. The production of Cl- is the result of a syn attack on the terminal N in ClN3 and proceeds with almost no barrier. An electrostatic Cl-(FN3) complex is found in the exit channel. Attack of the fluoride ion on the chlorine atom results in the formation of neutral ClF and N3-. A distinct barrier is found in that channel. Although these products resemble those that would be predicted from an SN2-like mechanism, the geometries of the transition states are
Figure 2. Reaction coordinate diagram for the reaction of F- with ClN3. Chlorine atoms are green, nitrogen atoms are dark blue, and fluorine atoms are light blue.
not those typical of the “backside attack” characteristic of such a mechanism. That is, the fluoride attack does not occur 180° away from the leaving group. Similar mechanisms for the production of both Cl- and N3- can be drawn for all of these reactions. Isotope exchange of Cl was studied by injecting 37Cl- and allowing it to react with ClN3. Exchange was found to occur in ∼25% of collisions, when accounting for the natural abundance of 35Cl. If the reaction made a long-lived complex in every collision, an efficiency of 50% would be expected. The lower efficiency implies that either the complex is not formed efficiently or there is a barrier to product formation. N3-, Br-, and I- inefficiently produced only Cl-. The maximum efficiency for these ions is only 6%. N3- is probably slow because the products must incorporate 6 nitrogens, which are labeled as 3N2 molecules in the table. Formation of four products is generally not very efficient. The Br- reaction is thermoneutral within uncertainty, and the low efficiency may indicate that it is in fact slightly endothermic. The I- reaction is both more exothermic and more efficient. Cl2- is found to make Cl3- at 25% of the collisional value. Reactions of SF6- and SF5- produced exotic and unexpected anions (FN3- and SF4N3-), with the rate constants being 28 and 4% efficient, respectively. Electronic structure calculations of the reaction energetics predict these pathways to be endothermic. However, this cannot be the case. Calculations of SF6- and SF5energetics have been shown to be difficult and inaccurate.29 In reactions with both anions, FN3- is formed, likely through a syn attack on the terminal nitrogen and elimination of SFx-1Cl. The production of SF4N3- and SF5-, which would both result in the production of neutral ClF, likely occurs through the same mechanism. The four oxygen-containing anions all produced minor products containing O, for example, ClO2- from O2-, ClO- from O-, and OH- and CH3O-. In order to gain more insight into the reaction mechanism, the energetics of the reaction have been investigated computationally for the reaction of O- with ClN3. An exhaustive search for a transition state for the formation of ClO- was performed, using both MP2 and B3LYP levels of theory, without success. This leads us to believe that the transfer of the chlorine atom to the oxygen occurs in a barrierless process, similar to that of an exothermic proton transfer. The calculated internal reaction coordinate for the further reaction is shown in Figure 3. Transfer of a chlorine atom to the oxygen
6836
J. Phys. Chem. A, Vol. 114, No. 25, 2010
Figure 3. Intrinsic reaction coordinate for production of Cl- in the reaction of O- with ClN3. Oxygen atoms are red, chlorine atoms are green, and nitrogen atoms are blue.
anion results in the formation of the ClO- anion; back transfer of the electron may occur to form N3- and ClO. Upon formation of ClO-, the products can separate or can go on to further react. Computations predict that ClO- will further react with neutral N3. In this case the oxygen attacks a terminal nitrogen, resulting in the formation of Cl- and NNNO, which is unstable and decomposes to form N2 and NO. Conclusion The electron affinity of ClN3 has been bracketed between that of N3 and NO2. This gives an electron affinity of 2.48 ( 0.20 eV, in good agreement with the predication of the G3 calculation. The reactivity of ClN3 with negative ions was also investigated. Chloride and azide ions (Cl- and N3-) were the dominant products of the reactions, which resulted from a substitution-type mechanism and correlate with relative exothermicities. Reaction with oxygen containing anions results in oxygen containing product ions. Acknowledgment. We are grateful for the support of the Air Force Office of Scientific Research for this work. K.F. acknowledges support from the National Research Council Fellowship Program. N.E. is under contract (FA8718-04-C-0055) to the Institute for Scientific Research of Boston College. We thank Raymond Bemish for helpful discussions concerning electronic structure calculations. Supporting Information Available: Geometries of stable complexes and transition states are provided. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Hantzsch, A.; Schumann, M. Ber. Dtsch. Chem. Ges. 1900, 33, 522.
Eyet et al. (2) Cook, R. L.; Gerry, M. C. L. J. Chem. Phys. 1970, 53, 2525. (3) Shen, S.; Durig, J. R. J. Mol. Struct. 2003, 661-662, 49. (4) Dehnicke, K. Angew. Chem. 1967, 6, 240. (5) Frierson, W. J.; Kronrad, J.; Browne, A. W. J. Am. Chem. Soc. 1943, 65, 1696. (6) Zhang, P.; Morokuma, K.; Wodtke, A. M. J. Chem. Phys. 2005, 122, 014106. (7) Babikov, D.; Zhang, P.; Morokuma, K. J. Chem. Phys. 2004, 121, 6743. (8) Kerkines, I. S. K.; Wang, Z.; Zhang, P.; Morokuma, K. J. Chem. Phys. 2008, 129, 171101. (9) Hansen, N.; Wodtke, A. M. J. Phys. Chem. A 2003, 107, 10608. (10) Hansen, N.; Wodtke, A. M.; Goncher, S. J.; Robinson, J. C.; Sveum, N. E.; Neumark, D. M. J. Chem. Phys. 2005, 123, 104305. (11) Hansen, N.; Wodtke, A. M.; Komissarov, A. V.; Heaven, M. C. Chem. Phys. Lett. 2003, 368, 568. (12) Ray, A. J.; Coombe, R. D. J. Phys. Chem. 1995, 99, 7849. (13) Rice, W. W.; Jensen, R. J. J. Phys. Chem. 1972, 76, 805. (14) Viggiano, A. A.; Morris, R. A.; Dale, F.; Paulson, J. F.; Giles, K.; Smith, D.; Su, T. J. Chem. Phys. 1990, 93, 1149. (15) Freel, K.; Friedman, J. F.; Miller, T. M.; Heaven, M. C.; Viggiano, A. A. J. Chem. Phys. 2010, 132, 134308. (16) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, ReVision D.01; Gaussian, Inc.: Pittsburgh, PA, 2004. (17) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (18) Lee, C.; Yang, W. T.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (19) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1998, 109, 7764. (20) Langevin, P. Ann. Chim. Phys. 1905, 5, 245. (21) Gioumousis, G.; Stevenson, D. P. J. Chem. Phys. 1958, 29, 294. (22) Streit, G. E. J. Chem. Phys. 1982, 77, 826. (23) Babcock, L. M.; Streit, G. E. J. Chem. Phys. 1982, 76, 2407. (24) Streit, G. E. J. Phys. Chem. 1982, 86, 2321. (25) Dunkin, D. B.; Fehsenfeld, F. C.; Ferguson, E. E. Chem. Phys. Lett. 1972, 15, 257. (26) Su, T.; Chesnavich, W. J. J. Chem. Phys. 1982, 76, 5183. (27) Arnold, S. T.; Morris, R. A.; Viggiano, A. A.; Johnson, M. A. J. Phys. Chem. 1996, 100, 2900. (28) Viggiano, A. A.; Arnold, S. T.; Morris, R. A. Int. ReV. Phys. Chem. 1998, 17, 147. (29) Miller, T. M.; Viggiano, A. A.; Troe, J. J. Phys.: Conf. Ser. 2008, 115, 012019.
JP102951Z
