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Multireference Generalized Van Vleck Perturbation Theory (GVVPT2) Study of the NCO + HCNO Reaction: Insight into Intermediates† Yvonne E. Bongfen Mbote, Yuriy G. Khait, Cynthia Hardel, and Mark R. Hoffmann* Chemistry Department, UniVersity of North Dakota, Grand Forks, North Dakota 58202-9024 ReceiVed: March 6, 2010; ReVised Manuscript ReceiVed: May 23, 2010
Possible mechanisms for the NCO + HCNO reaction, previously studied using single reference methods, have been revisited using the second-order generalized Van Vleck perturbation theory (GVVPT2) variant of multireference perturbation theory. Large scale GVVPT2 calculations, with 25 active orbitals, demonstrate that the electronic structures of the ground states of all eight previously identified plausible doublet spin intermediates of this reaction are substantially multiconfigurational with maximum configuration amplitudes not larger than 0.87. Moreover, comparison of GVVPT2 results with underlying MCSCF calculations demonstrates a pronounced effect of dynamic correlation on the configurational structure. GVVPT2 calculations of vertical excitation energies of the intermediates showed that all the intermediates, except one, have significant excitation energies to both the same and other spatial symmetries as the ground states. The relative GVVPT2 energies of the intermediates were found to be consistent with earlier calculations, including the prediction of a negative temperature dependence of the rate constant, and support available experimental observations. 1. Introduction Recently, fulminic acid (HCNO) has attracted special attention since it was found to be an important intermediate in the NOreburning process that involves the reduction of the NOx pollutants from fossil fuel combustion emission.1 NOx is reduced to HCNO through the reaction of ketenyl (HCCO) and NO.2 The study of the reaction of fulminic acid and the NCO radical is of interest because NCO is an intermediate in several combustion environments, including that of the RAPRENOx process, which reduces NOx emissions.3-5 Four thermodynamically accessible product channels are possible for this reaction.6-9
NCO + HCNO f HCN + NO + CO
(a)
f CO2 + HCNN
(b)
f CO + HCO + N2
(c)
f N2O + HCCO
(d)
The recent experimental study of the kinetics of this reaction by Feng and Hershberger10 showed that HCN + NO + CO 0 (∆H298 ) -183.69 kJ/mol) is the major product channel with only a minor contribution from the thermodynamically more 0 ) -232.31 kJ/mol) channel. favorable HCNN + CO2 (∆H298 Theoretical studies on possible pathways of this reaction have been carried out at the QCISD(T)/6-311G(d,p)//UB3LYP/631G(d,p)11 and CBS-QB3//B3LYP/6-311++G(d,p)12 levels of theory. Zhang et al.12 found that the most feasible pathway for the formation of HCN + NO + CO was related to overcoming an energy barrier of only 14.9 kcal/mol and predicted that, since the transition state energy is lower than that of the reactants (by 9.82 kcal/mol), the reaction’s rate constant should exhibit a negative temperature dependence. Intermediates of the HCNO + NCO reaction are necessarily open shell but, more importantly, can be expected to have †
Part of the “Klaus Ruedenberg Festschrift”. * Author for correspondence. E-mail:
[email protected].
substantial multiconfigurational structures. Considering that previous studies relied on single-reference methods (i.e., coupled cluster with single and double excitations including perturbative triples [CCSD(T)],13 used within the CBS-QB3 model,14 or quadratic configuration including single and double excitations and perturbative triples [QCISD(T)]),13 a multireference study is warranted. In the present work, a theoretical study on the electronic structures, geometries, and relative energies of intermediates of the HCNO + NCO reaction has been performed using the second-order generalized Van Vleck perturbation theory (GVVPT2)15 variant of multireference perturbation theory with cc-pVDZ and cc-pVTZ basis sets.16 Moreover, vertical excitation energies for each of the plausible intermediates were calculated to survey the likelihood of significant nonadiabatic interactions. GVVPT2 provides a balanced treatment of dynamical and nondynamical correlation effects for both ground and excited electronic states, even for electronic structures with substantial multiconfigurational character. GVVPT2 is also rigorously spin-adapted, which removes a concern in the earlier studies. In previous work, GVVPT2 has been shown to give results comparable to those of CCSD(T), when such a method is applicable, but is itself applicable for the entire potential energy surface. This paper is divided into three additional sections. In section 2, computational details, including a detailed description of the reference space, are given. Section 3 contains the results of the study and their discussion. A final section summarizes the work. 2. Synopsis of the GVVPT2 Method and Computational Details Since the GVVPT2 method and its high performance implementation have been described in detail in previous publications (see refs 15 and 17, and references therein), here only its salient features will be reviewed. In GVVPT2, the configuration space, in which the states of interest are sought, is divided into two subspaces: a model subspace, specified by a given set of reference electron configurations involving internal (core and active) orbitals (i.e., typically an MCSCF space), and
10.1021/jp102051p 2010 American Chemical Society Published on Web 06/10/2010
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an external space, whose configurations are related to the model ones through single and double excitations (N.B. external, internal, and semi-internal excitations can be included). The method takes into account the first-order perturbative effects of external configurations on the MCSCF states and, in addition, unlike most multireference perturbation theories, describes variationally the interactions of the perturbed MCSCF states with unperturbed functions from the orthogonal complement to the set of MCSCF states in the model space. GVVPT2 supports both complete and incomplete model spaces, and its equations are invariant to the choice of configuration state functions (CSFs) within each subspace. The implemented macroconfiguration approach18 simplifies generation of physically well-defined model spaces. An important characteristic of the GVVPT2 method is that it is not subject to the intruder state problem and gives smooth potential energy surfaces, even when these surfaces are in close proximity. In studying the reactants and significant intermediates of the HCNO + NCO reaction, all of which have the Cs point group symmetry,12 the set of 25 valence molecular orbitals was subdivided into two groups: the orbital group G1 ) (7a′, 8a′, 9a′, 10a′, 11a′, 12a′, 13a′, 14a′, 15a′, 16a′, 17a′, 18a′, 1a′′, 2a′′, 3a′′, 4a′′), which is composed of the 16 high occupancy orbitals and G2 ) (19a′, 20a′, 21a′, 22a′, 23a′, 24a′, 25a′, 5a′′, 6a′′) with the remaining 9 low occupancy valence orbitals. The model space that was used included all configurations created by the three macroconfigurations: (G1)31(G2)0, (G1)30(G2)1, and (G1)29(G2)2. The macroconfiguration (G1)31(G2)0 generates all possible one open shell configurations (with correct space symmetry) over orbitals of the group G1, while (G1)30(G2)1 and (G1)29(G2)2 create all one- and two- electron excitation configurations to orbitals of the group G2 and take into account simultaneously all possible internal excitations within the orbital group G1. In the case of the 2A′ symmetry states, such model space creates 19 948 configurations and is spanned by 68 680 CSFs; and in the case of 2A′′ symmetry, the model space is spanned by 63 960 CSFs (17 292 configurations). Using the cc-pVDZ basis,16 the external space for the 2A′ symmetry states involves 10 838 623 868 CSFs (609 641 512 configurations), while, in the case of 2A′′ symmetry, it is spanned by 10 827 140 412 CSFs (604 126 460 configurations). Our current GUGA-based GVVPT2 program17 takes about 2.5 h for performing such largescale GVVPT2 calculations on a 2.0 GHz dual-core AMD opteron processor 2212. With the cc-pVTZ basis set,16 the dimensions of the model spaces remain the same but the dimensions of the external spaces increase significantly: 80 939 111 672 CSFs and 80 880 624 888 CSFs for the 2A′ and 2A′′ symmetry states, respectively. The corresponding single point GVVPT2 calculations took about 8 h on the above-mentioned processor. Geometry optimizations of the reactants and intermediates of the HCNO + NCO reaction were performed at both the MCSCF and B3LYP19,20 levels using the cc-pVDZ basis set [some structures were additionally optimized with the cc-pVTZ basis (see below)]. Vibrational frequencies were determined at the optimized B3LYP/cc-pVDZ geometries. Single point GVVPT2 energy calculations were performed at the optimized B3LYP and MCSCF geometries, while the vertical excitation energies were calculated only at the MCSCF geometries. Gaussian 0321 was used for the B3LYP calculations and the UNDMOL set of programs was used in performing the MCSCF and GVVPT2 calculations.
Mbote et al. 3. Results and Discussion Preliminary GVVPT2 calculations showed that, in agreement with the previous CBS-QB3 results by Zhang et al.,12 interactions of NCO with HCNO lead to only eight intermediates that are thermodynamically stable relative to the reactants. All of these intermediates are related to attacks of NCO on the carbon atom of HCNO. There are three possible orientations for such attacks: from the end with the nitrogen atom of NCO (see Figure 1); from the oxygen atom on the end (see Figure 2); or from the carbon atom in the middle (see Figure 3). The attack with the nitrogen atom can lead to a chain-like intermediate IM1 (N.B. we refer to the intermediates using the nomenclature introduced in ref 12), or its cis isomer IM1A, or a five-membered ring IM2. The attack with the C atom on HCNO leads only to one chain-like intermediate IM4, while the attack with the O atom can lead to the ring structures IM7 and IM8. According to the calculations by Zhang et al.,12 the dissociation of IM1 into HCN + NO + CO is prevented by a high barrier (of about 48 kcal/mol), while its cis-isomer IM1A can dissociate into the same products only through formation of a higher lying (by about 18 kcal/mol) intermediate IM3, whose decay is prevented by a barrier of about 30 kcal/mol. IM4 can be transformed into intermediate IM5 (with a barrier of about 20 kcal/mol), but the possible decomposition of IM5 to HCN + NO + CO requires overcoming several high barriers. IM8 can decay only into HCCO + N2O (with a barrier of about 22 kcal/mol). The pathway from intermediate IM7 has been predicted to be the lowest-energy channel: the decomposition of IM7 into HCN + OCNO is expected to be prevented by a barrier of only 14.9 kcal/mol, while OCNO can decay into NO + CO almost without a barrier.12 Our GVVPT2 calculations of all these intermediates show that their ground state wave functions have substantial multiconfigurational nature (see Table 1). In each case, the amplitude of the leading configuration does not exceed 0.86-0.87 (i.e., its weight does not exceed 0.76), and hence the cumulative weight of excited (both model and external) configurations proves to be quite essential. Table 1 shows that amplitudes of a few excited model space configurations can be as large as 0.05-0.08. Moreover, our analysis shows that the amplitude of the leading configuration can be significantly larger at the MCSCF level than at the GVVPT2 level (e.g., 0.94 vs 0.87 for IM1A), while amplitudes of other model space CSFs remain almost the same. This demonstrates the large effect of dynamic correlation on the configurational structure of the intermediates’ wave functions and shows that the MCSCF level can be insufficient, at least in some cases, for a correct description of the intermediates. At the same time, the existence of one leading single determinant configuration with a relatively large amplitude presumably should ensure the applicability of the B3LYP and CCSD(T) methods for studying the intermediates under consideration, since these methods treat dynamic and nondynamic electron correlation on an equal footing but rely on the dominance of a single determinant. GVVPT2/cc-pVDZ calculations of vertical excitation energies of the intermediates at the MCSCF/cc-pVDZ geometries are given in Table 2. The lowest excitation energy to states of the same symmetry is 2.6 eV, and hence no quasidegeneracy problems should be expected in studying such species. The separation of ground and first excited states of the same symmetry strengthens the validity of previous single reference results. Excitation energies to states of different symmetry than the ground state are lower, but are all greater than 0.90 eV with one exception. The separation between the ground 2A′ state of
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Figure 1. Various pathways for the NCO + HCNO reaction occurring through attack of NCO through the N atom on the C atom of HCNO.
Figure 2. Intermediates in the NCO + HCNO reaction occurring through attack of NCO through the O atom on the C atom of HCNO.
Figure 3. Various pathways for the NCO + HCNO reaction occurring through attack of NCO through the C atom on the C atom of HCNO.
IM4 and its lowest 2A′′ state is only 0.28 eV, and nonadiabatic interactions, especially in the surrounding C1 symmetry parts of the PESs, would be a concern. However, the remoteness of IM4 from the main reaction pathway implies that PES features in its vicinity will have minimal effects on observed kinetics.
A comparison of geometries of all the intermediates, optimized at the B3LYP and MCSCF levels with the cc-pVDZ basis set, showed (see Supporting Information) that, while B3LYP and MCSCF equilibrium structures of IM1, IM2, and IM5 are comparatively close (e.g., the differences in the bond lengths and angles are less than 0.03 Å and 3°, respectively), the differences in the B3LYP and MCSCF geometrical parameters of IM3, IM8, and especially, IM4 (whose wave function has the most complex multiconfigurational structure) prove to be more significant: e.g., in the case of IM4, the differences in the N3-O4 bond length and in the C2-N3-O4 angle are 0.081 Å and 21.3°. In the case of the intermediate IM7, which is of the most interest, the B3LYP and MCSCF geometrical parameters optimized with the cc-pVDZ basis can be seen from Table 3 to be quite close except for the difference of 0.037 Å in the N3-O4 bond length. The B3LYP/cc-pVDZ geometries obtained in the present work are quite close to the B3LYP/6-311++G(d,p) geometries from ref 12 (e.g., differences in bond lengths are less than 0.01 Å). The differences between the B3LYP and MCSCF geometrical parameters are presumably due to lack of dynamical correlation effects within the MCSCF, which are implicitly accounted for in B3LYP through the exchangecorrelation functional. Relative GVVPT2 energies of the reactants and intermediates calculated with the cc-pVDZ and cc-pVTZ basis sets at the B3LYP/cc-pVDZ geometries are given in Table 4 and are compared with the CBS-QB3 values calculated by Zhang et al.12 As can be seen from the table, both the GVVPT2/cc-pVDZ and GVVPT2/cc-pVTZ energies are in agreement with the CBSQB3 energies (N.B. a maximum difference of 4.72 kcal/mol is observed for IM4), with one exception: IM7 differs by 8.03 kcal/mol. Since GVVPT2 relative energies calculated with a cc-pVTZ basis set are in substantially better agreement with CBS-QB3 (i.e., the difference for IM7 is only 2.10 kcal/mol), it appears that the cc-pVDZ basis set is not flexible enough to describe adequately the dynamic correlation in this intermediate.
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TABLE 1: Leading Electron Configurations for the Intermediates at the GVVPT2 Level symmetry term
intermediates
amplitudes
configurations
+0.87 -0.08 +0.05 -0.05 +0.87 +0.08 -0.08 +0.87 +0.05 -0.05 +0.86 -0.07 -0.05 -0.05 +0.86 -0.08 -0.08 -0.07 -0.06 +0.05 +0.87 -0.06 -0.06 +0.05 -0.05 +0.86 -0.07 +0.86 -0.08
... (17a′)2(18a′)1(3a′′)2(4a′′)2 double (4a′′)2 f (5a′′)2 excitation single (17a′)2(18a′)1 f (17a′)1(18a′)2 excitation single (16a′)2(18a′)1 f (16a′)1(18a′)2 excitation ... (17a′)2(18a′)1(3a′′)2(4a′′)2 single (16a′)2(18a′)1 f (16a′)1(18a′)2 excitation double (4a′′)2 f (5a′′)2 excitation ... (17a′)2(18a′)2(3a′′)2(4a′′)1 single (3a′′)2(5a′′)0 f (3a′′)1(5a′′)1 excitation double (3a′′)2 f (5a′′)2 excitation ... (17a′)2(18a′)1(3a′′)2(4a′′)2 single (3a′′)2(4a′′)1 f (3a′′)1(4a′′)2 excitation single (2a′′)2(4a′′)1 f (2a′′)1(4a′′)2 excitation double (3a′′)2 f (5a′′)2 excitation ... (17a′)2(18a′)1(3a′′)2(4a′′)2 double (4a′′)2 f (5a′′)2 excitation double (17a′)2 f (19a′)2 excitation single (17a′)2(18a′)1 f (17a′)1(18a′)2 excitation double (3a′′)2 f (6a′′)2 excitation single (15a′)2(18a′)1 f (15a′)1(18a′)2 excitation ... (17a′)2(18a′)1(3a′′)2(4a′′)2 double (4a′′)2 f (6a′′)2 excitation double (3a′′)2(4a′′)1 f (3a′′)1(4a′′)0(5a′′)2 excitation double (3a′′)2(4a′′)1 f (3a′′)1(4a′′)0(6a′′)2 excitation double (3a′′)2 f (5a′′)2 excitation ... (17a′)2(18a′)2 (3a′′)2(4a′′)1 double (3a′′)2(4a′′)1 f (3a′′)1(4a′′)0(5a′′)2 excitation ... (17a′)2(18a′)2 (3a′′)2(4a′′)1 double (3a′′)2(4a′′)1 f (3a′′)1(4a′′)0(5a′′)2 excitation
TABLE 2: Vertical GVVPT2/cc-pVDZ Excitation Energies (eV) of the Lowest Excited (2A′ and 2A′′ Symmetry) States of the Intermediates at Their Optimized MCSCF/cc-pVDZ Geometries
TABLE 3: Equilibrium Geometries (in Angstrom and Degrees) of IM7 Optimized at the B3LYP and MCSCF Levels with the cc-pVDZ Basis Set
IM1
2
A′
IM1A
2
A′
IM2
2
A′′
IM3
2
A′′
IM4
2
A′
IM5
2
A′
IM7
2
A′′
IM8
2
A′′
intermediate IM1 IM1A IM2 IM3 IM4 IM5 IM7 IM8
ground state 2
A′ A′ 2 A′′ 2 A′′ 2 A′ 2 A′ 2 A′′ 2 A′′ 2
lowest state of the same symmetry
lowest state of different symmetry
4.94 5.12 3.45 4.66 4.55 3.57 3.61 2.60
0.90 0.93 2.12 2.62 0.28 1.38 1.52 2.12
To corroborate this, the geometries of the reactants and IM7 were reoptimized at the B3LYP level with the cc-pVTZ basis, and single point GVVPT2 calculations at these new geometries with the cc-pVTZ basis set were performed. Though differences in B3LYP geometric parameters optimized with the cc-pVDZ and cc-pVTZ basis sets are small (N.B. the maximum difference is 0.011 Å for the H1-C2 bond length), the obtained relative GVVPT2/cc-pVTZ energy of this intermediate (-24.88 kcal/ mol) agree even better with that of CBS-QB3 (-24.72 kcal/ mol) (see Table 5). To ascertain that the better agreement using B3LYP/cc-pVTZ geometries for IM7 was not coincidental, the geometries of all studied isomers were reoptimized using the larger basis and GVVPT2 energies calculated for a representative subset. Of the four additional isomers studied in greater detail, all agreed with GVVPT2/cc-pVTZ//B3LYP/cc-pVDZ results to within 1.0 kcal/ mol. In particular, GVVPT2/cc-pVTZ//B3LYP/cc-pVTZ relative energies are: IM2, -61.00 kcal/mol; IM3, -29.84; IM4, -17.03; and IM5, -26.97. Of greatest interest, calculations at the better geometry confirmed the GVVPT2 prediction that,
RH1-C2 RC2-N3 RN3-O4 RC2-C6 RC6-O7 RC6-N5 RN5-O4 AH1-C2-N3 AC2-N3-O4 AH1-C2-C6 AC6-C2-N3 AO7-C6-C2 AC2-C6-N5 AC6-N5-O4 AC2-C6-N5 AC6-N5-O4
B3LYP/cc-pVDZ
MCSCF/cc-pVDZ
unsigned difference
1.089 1.277 1.490 1.487 1.224 1.401 1.304 121.7 103.4 126.4 111.9 130.0 104.8 107.2 104.8 107.2
1.092 1.275 1.453 1.501 1.203 1.418 1.317 121.9 105.3 127.2 111.0 130.5 104.1 106.8 104.7 107.4
0.003 0.002 0.037 0.014 0.021 0.017 0.013 0.2 1.9 0.8 0.9 0.5 0.7 0.4 0.1 0.2
contrary to CBS-QB3 results, IM5 is slightly more stable than IM7 (i.e., by 0.94 kcal/mol at the smaller basis geometry and by 2.09 kcal/mol at the larger basis geometry). To elucidate perhaps the most intriguing feature of the HCNO + NCO reaction, i.e., the predicted negative temperature dependence, the geometry of the transition state TS7, which prevents the decomposition of IM7 into HCN + OCNO, was optimized at the B3LYP/cc-pVTZ level, and its relative GVVPT2 energy using the cc-pVTZ basis set was calculated (see Table 5). The relative energy of the TS7 transition state (-12.52 kcal/mol) agrees reasonably well with that from the CBS-QB3 model (-9.82 kcal/mol) and shows that, at the GVVPT2 level of theory, the height of the barrier that involves the decomposition of IM7 into HCN + OCNO is expected to
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TABLE 4: GVVPT2 Relative Energies (kcal/mol) of the Reactants and Intermediates, Calculated at the B3LYP/ cc-pVDZ Geometries Using the cc-pVDZ and cc-pVTZ Basis Sets species
GVVPT2/ cc-pVDZ
GVVPT2/ cc-pVTZ
CBS-QB3a
HCNO + NCO IM1 IM1A IM2 IM3 IM4 IM5 IM7 IM8
0 -48.39 -45.32 -59.00 -27.93 -15.32 -23.67 -32.75 -3.27
0 -49.91 -47.21 -61.80 -30.68 -18.08 -27.76 -26.82 -5.33
0 -48.08 -45.14 -58.72 -27.70 -13.36 -24.25 -24.72 -2.35
a
Reference 12.
TABLE 5: Total (hartree) and Relative GVVPT2 Energies (kcal/mol) of the Reactants, Intermediate IM7, and Transition State TS7 at the Optimized B3LYP/cc-pVTZ Geometries
species
total GVVPT2 energy
relative GVVPT2 energy
relative CBS-QB3 energya
HCNO + NCO IM7 TS7
-336.028 677 -336.068 325 -336.048 628
0 -24.88 -12.52
0 -24.72 -9.82
a
Reference 12.
be about 12.4 kcal/mol (14.9 kcal/mol at the CBS-QB3 level). Thus, our large-scale multireference GVVPT2 calculations confirm the conclusion by Zhang et al.12 that the rate constant of the HCNO + NCO reaction should exhibit negative temperature dependence. 4. Conclusions GVVPT2 calculations have been performed to investigate the electronic structures and relative energies of the eight plausible doublet-spin intermediates for the NCO + HCNO reaction previously identified by Zhang et al.12 GVVPT2 calculations reveal that these intermediates are multiconfigurational in nature, but each has one leading single determinant configuration. Consequently, the earlier B3LYP and CBS-QB3 based studies produced results that are perhaps more accurate than one might have expected. The lowest-energy channel, which leads to formation of the major products HCN + NO + CO, comes from one of two plausible five-membered ring intermediates (IM7). IM7 is predicted to lie 24.88 kcal/mol below the entrance channel and the transition state between it and the major products is 12.52 below the entrance channel. This multireference GVVPT2 study supports the previous single-reference theoretical prediction of a negative temperature dependence for the rate constant but predicts a barrier from the key intermediate that is 2.54 kcal/mol lower than previously predicted using the CBS-QB3 method (i.e., 12.36 vs 14.90 kcal/mol). The lowest lying excited states of the same and different symmetries of each of the eight plausible intermediates have been calculated for the first time. It was observed that excitation energies to states of the same symmetries as the ground states were all in excess of 2.6 eV. Consequently, quasidegeneracy effects in ground state calculations would be negligible, which provides further insight into the unexpectedly accurate previous single reference calculations. Excitation energies to states of different symmetries than the ground state had excitation
energies that were greater than 0.90 eV, except for a small gap (of 0.28 eV) for an intermediate that is far from expected significant reaction paths. MCSCF calculations were found to significantly overemphasize the importance of the leading configuration, relative to the results from GVVPT2 calculations. The studied intermediates have electronic structures such that the nondynamic electron correlation could not easily be separated from the dynamic correlation. As a consequence, geometries optimized using MCSCF could not be expected to be more accurate than geometries optimized using a robust DFT method, such as B3LYP. A comparison of cc-pVDZ results with cc-pVTZ results did not demonstrate a strong basis set effect, except for one intermediate, which happened to be the most critical one for the physical process. This study suggests that the use of basis sets smaller than cc-pVTZ for reactions of the type here considered (e.g., relevant to NOx chemistry) be used with caution and validated for particular inquiries. This study further demonstrates the ability of the GVVPT2 variant of multireference perturbation theory to provide quantitative results for difficult and nonintuitive reactions, which compare well to the well-regarded CBS-QB3 method. Computational efficiencies realized for the GVVPT2 program (i.e., capable of using 25 active orbitals, a model space of more than 60 000 CSFs and an external space of more than 80 billion CSFs) speak positively to future prospects for the method. Acknowledgment. We gratefully acknowledge the DOE Office of Science under Award Number DE-FG02-06ER46292 and NSF Grant Number EPS-0814442 for financial support of the research presented here. Supporting Information Available: Geometric parameters for all eight intermediates studied are provided in nine separate tables. The tables list parameters from the B3LYP and MCSCF geometry optimizations using the cc-pVDZ basis set. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Miller, J. A.; Klippenstein, S. J.; Glarborg, P. Combust. Flame 2003, 135, 357. (2) Vereecken, L.; Sumathy, R.; Carl, S. A.; Peeters, J. Chem. Phys. Lett. 2001, 344, 400. (3) Siebers, D. L.; Caton, J. A. Combust. Flame 1990, 79, 31. (4) Perry, R. A.; Siebers, D. L. Nature 1986, 324, 657. (5) Miller, J. A.; Bowman, C. T. Int. J. Chem. Kinet. 1991, 23, 289. (6) Chase, M. W. J. Phys. Chem. Ref. Data 1998, 27, i. (7) Schuurman, M. S.; Muir, S. R.; Allen, W. D.; Schaefer, H. F., III. J. Chem. Phys. 2004, 120, 11586. (8) Clifford, E. P.; Wenthold, P. G.; Lineberger, W. C.; Petersson, G. A.; Broadus, K. M.; Kass, S. R.; Kato, S.; DePuy, C. H.; Bierbaum, V. M.; Ellison, G. B. J. Phys. Chem. A 1998, 102, 7100. (9) Osborn, D. L.; Mordaunt, D. H.; Choi, H.; Bise, R. T.; Neumark, D. M.; Rohlfing, C. M. J. Chem. Phys. 1997, 106, 10087. (10) Feng, W.; Hershberger, J. F. J. Phys. Chem. A 2007, 111, 3831. (11) Li, B.-T.; Zhang, J.; Wu, H. S.; Sun, G. D. J. Phys. Chem. A 2007, 111, 7211. (12) Zhang, W.; Du, B.; Feng, C. Chem. Phys. Lett. 2007, 442, 1. (13) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (14) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 1999, 110, 2822. (15) Khait, Y. G.; Song, J.; Hoffmann, M. R. J. Chem. Phys. 2002, 117, 4133. (16) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (17) Jiang, W.; Khait, Y. G.; Hoffmann, M. R. J. Phys. Chem. A 2009, 113, 4374. (18) Khait, Y. G.; Song, J.; Hoffmann, M. R. Int. J. Quantum Chem. 2004, 99, 210. (19) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
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(20) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; 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.;
Mbote et al. 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; Gaussian, Inc.: Pithsburgh, PA, 2004.
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