Article pubs.acs.org/JPCA
The Symmetric Exchange Reaction OH + H2O → H2O + OH: Convergent Quantum Mechanical Predictions Published as part of The Journal of Physical Chemistry virtual special issue “Mark S. Gordon Festschrift”. Aifang Gao,*,†,‡,§ Guoliang Li,*,∥ Bin Peng,∥ Yaoming Xie,§ and Henry F. Schaefer*,§ †
School of Water Resources and Environment, Hebei GEO University, Shijiazhuang 050031, China Hebei Key Laboratory of Sustained Utilization and Development of Water Resources, Shijiazhuang, Hebei Province 050031, China § Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States ∥ MOE Key Laboratory of Theoretical Chemistry of the Environment, Center for Computational Quantum Chemistry, South China Normal University, Guangzhou 510006, China ‡
S Supporting Information *
ABSTRACT: The symmetric hydrogen exchange reaction OH + H2O → H2O + OH has been studied using the “gold standard” CCSD(T) method with the correlation-consistent basis sets up to aug-cc-pV5Z. The CCSDT and CCSDT(Q) methods were used for the final energic predictions. Two entrance complexes and two transition states on the H3O2 potential surface were located. The vibrational frequencies and the zero-point vibrational energies of these stationary points for the reaction are reported. The entrance complex H2O···HO is predicted to lie 3.7 kcal mol−1 below the separated reactants, whereas the second complex HOH···OH lies only 2.1 kcal mol−1 below the separated reactants. The classical barrier height for the title reaction is predicted to be 8.4 kcal mol−1, and the transition state between the two complexes is only slightly higher than the second complex. We estimate a reliability of ±0.2 kcal mol−1 for these predictions. The capabilities of different density functional theory methods is also tested for this reaction. evaluations. Most recently, Anglada and co-workers15 predicted the energy barrier to be 8.75 and 8.56 kcal mol−1, respectively, with the CCSD(T)/aug-cc-pVQZ//BHLYP/6-311+G(2df,2p) and CCSD(T)/aug-cc-pVTZ//QCISD/6-311+G(2df,2p) methods including zero-point vibrational energy (ZPVE) corrections. All these studies show that the overall transition state connects two identical complexes, in which there is a hydrogen bond between the H2O molecule and the OH radical. However, as stated by Anglada and co-workers,15 “there is a controversy in the literature regarding the hydrogen bonded complex”, and an “unresolved question concerns whether the pre-reactive complex is the HOH···OH species, as suggested by Hand et al., or the global minimum H2O···HO, as pointed out by Masgrau et al. and by Uchimaru et al.” The low-lying isomers for the isolated (H2O)OH complex (Scheme 1) with hydrogen bonding were predicted theoretically in 1991 and 1993,16,17 and the global minimum is the H2O···OH complex (structure III, Scheme 1). Subsequently, there are a series of papers that study these structures both experimentally18−24 and theoretically.12,14,21,24−26 Neumark et
1. INTRODUCTION Hydrogen atom abstraction (transfer) reactions are important in various fields of chemistry, such as atmosphere, environmental, combustion, and biochemistry.1−8 Of these reactions, the symmetric exchange OH + H2O → H2O + OH reaction has been studied extensively,9−15 because it is simple and archetypal for more complicated reactions. In 1992, Nanayakkara, BalintKurti, and Williams9 adopted various ab initio methods to estimate the barrier height for this reaction. Their best result for the classical potential energy barrier was 12.9 kcal mol−1 with the PUMP2/6-311++G(3d,2p)//UMP2/6-311G(d,p) method. In 1997, Dubey and coauthors10 reported an adiabatic energy barrier of 19.2 kcal mol−1 for the reaction with the UMP2/631G(d,p)//6-31G(d,p) method. Hand and coauthors12 in 1998 predicted the classical barrier for the symmetric hydrogen exchange reaction to be 10.1 kcal mol−1 with the QCISD(T)/6311+G(3df,2p)//UMP2/6-31G(d) method and 9.9 kcal mol−1 with the G2 composite approach. Masgrau and co-workers (1999)13 reported the values of 8.6 and 9.0 kcal mol−1 using the CCSD(T)/6-311G(3d,2p)//UMP2/6-311G(3d,2p) and the CCSD(T)/6-311G(3d,2p)//B3LYP/6-311G(3d,2p) methods, respectively. In 2003, Uchimaru and coauthors14 estimated for the classical barrier height for this hydrogen abstraction to be 7.8 kcal mol−1, which was obtained from CBS-APNO energy © XXXX American Chemical Society
Received: October 6, 2016 Revised: November 23, 2016 Published: November 29, 2016 A
DOI: 10.1021/acs.jpca.6b10008 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Scheme 1. Reported Low-Lying Hydrogen Bonded Complexes of H2O and OH
Figure 1. Stationary points on the OH + H2O potential energy surface. Internuclear separations are given in angstroms. Because this is a symmetric reaction (inset of Figure 1), only one side is shown in detail. Note that the potential energy surface in the region of TS1 and CP2 is very flat.
al.18 and Continetti et al.19 reported the photoelectron spectra of H3O2− in the transition state region of the OH + H2O → H2O + OH reaction. Quickenden et al.20,21 and Lester, Francisco, and McCoy22 observed the IR spectrum of H2O·HO complex in Ar matrixes to support the assignment of structure III. The IR results from Engdahl, Karlström, and Nelander23 also supported the complex III with the OH radical as proton donor. Endo and co-workers24 reported the first laboratory identification of H2O·HO in the gas phase via microwave spectroscopy, and supported the previously predicted17 theoretical geometry. Wang et al.25 and Zhou et al.26 used CCSD(T) and density functional theory (DFT) methods to study the isomers of the (H2O)OH complex, and they confirmed the global minimum predicted by the previous theoretical studies.17 All these studies show that the global minimum (III) is the structure for which the hydrogen bond is formed between the O atom in water and the H atom of the OH radical. The other minimum (structure I) is the one that displays hydrogen bonding between the water H atom and the O atom of the OH radical. Structure I was predicted to lie above III by ∼2 kcal mol−1 (2A″ ground electronic state) or ∼3 kcal mol−1 (2A′ excited electronic state).
The geometry of the transition state for the HO + H2O reaction is quite different from that of the global minimum (complex III, H2O···HO),17 but it is similar to the local minimum (complex I, HOH···OH). Thus, further research may be needed to determine the potential surface for the OH + H2O → H2O + OH reaction in detail. There could be three pathways: (a) the transition state goes down to the very shallow local minimum (I), as the only relevant complex, and then directly dissociates to the separated OH and H2O without visiting the global minimum (III); (b) the transition state goes directly down to the global minimum (III), ignoring the higherenergy local minimum (I); (c) the transition state goes to the local minimum (I) first, then via another (very small barrier) transition state to the global minimum (III), and finally dissociates to the separated OH plus H2O. In the present paper, we will re-examine the potential surface for the OH + H2O → H2O + OH reaction in more detail and attempt to answer the questions raised by Anglada and coauthors.15
2. THEORETICAL METHODS In this research, the “gold standard” CCSD(T) method27−29 with aug-cc-pVnZ (n = D, T, Q, 5) basis sets was adopted. The CCSD(T) abbreviation denotes the coupled cluster single and B
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kcal mol−1 by Anglada and coauthors in 2011.15 The hydrogen bonding distance is predicted to be 1.911 Å at the CCSD(T)/ aug-cc-pV5Z level of theory (Figure S2). This distance and other geometry parameters are also close to the previous theoretical results,9−14,16,17,19 including those in the earliest research.17 Structure TS1 (Figure S3) is a transition state connecting the two minimum CP1 and CP2. The geometry and energy of TS1 is very close to those of CP2, a planar structure with Cs symmetry at its 2A″ ground electronic state. Compared with the very shallow complex CP2, structure TS1 has a somewhat longer HOH···OH hydrogen bond (from 2.071 to 2.119 Å) and a smaller ∠H···OH bond angle (from 97.9° to 87.8°). Accordingly, the energy of TS1 is only marginally higher than that of CP2, by less than 0.05 kcal mol−1. The unusual flatness of this region of the PES is the reason that no such transition state was reported in previous theoretical studies. In light of the flat potential surface around TS1, there is only a small imaginary vibrational frequency (73i cm−1), much smaller in magnitude than that (1958i cm−1) for TS2, the conventional transition state. The corresponding normal mode for TS1 involves mainly the bending of the ∠H···OH angle (a′ mode), which is going toward CP2 in the “forward” direction (left to right in Figure 1). However, the other direction of the normal mode does not appear lead to CP1, and we have to examine the IRC (intrinsic reaction coordinate) to characterize that part of the reaction path. The appropriate IRC discussion is found later, in section 3.3. The very shallowly bound complex CP2 (Figure S4) has a higher energy than CP1, by 2.23 kcal mol−1 (=5.74−3.51), and it has a geometry moving toward TS2, with the hydrogen bond between the O atom of the OH radical and the H atom of water. The very shallowly bound structure CP2 is planar with Cs symmetry at its 2A″ electronic ground state equilibrium. This structure has been reported in a few previous studies, notably the 1991 and 1993 papers using the CISD method.16,17 Hand and co-workers12 discussed only the hydrogen-bonded complex CP2 on the reaction pathway, namely, the planar HOH···OH with the water molecule as a proton donor, like CP2 in the present paper. We see in this research that although the intermediate complex CP2 may dissociate directly into the products (reactants) H2O + OH, it is easy to overcome a tiny barrier and collapse to a lower-lying complex CP1 via a transition state TS1. Our quintuple-ζ (5Z) CCSD(T) method found the “standard” transition state TS2, which is similar to that suggested in Anglada’s paper in 2011.15 Compared with the classical relative energy of 9.48 kcal mol−1 by Anglada and coauthors with the CCSD(T)/aug-cc-pVQZ//BHLYP/6311+G(2df,2p) method, we predict the classical energy barrier to be 9.45 kcal mol−1 at the CCDS(T)/aug-cc-pV5Z level. Our higher-level energetics will be reported later in the text. The transition state TS2 has C2 symmetry, with the central H atom connecting two OH fragments with equal O···H distances of 1.162 Å (Figure S5). These O···H distances are close to the 1.150 Å (BHLYP) or 1.160 Å (QCISD) predictions reported by Anglada and coauthors.15 We predict a large imaginary vibrational frequency (1958i cm−1) for TS2, and the corresponding normal mode is the antisymmetric O···H stretching (b mode), which leads to the hydrogen-bonded complex CP2 with all real vibrational frequencies. 3.2. Performance of DFT Methods. Density functional theory (DFT) is a popular and effective tool, and DFT
double excitations method with a perturbative treatment of triple excitations, whereas the aug-cc-pVnZ (n = D, T, Q, 5) basis sets represent the augmented correlation-consistent basis sets developed by Dunning and coauthors.30−33 In the present study, the theoretical results converge very well with respect to the size of the basis sets. Thus, unless specifically noted, the results discussed in the text are predicted with the CCSD(T) method using the aug-cc-pV5Z basis set. All stationary points on the potential surface for the OH + H2O reaction were fully optimized (the convergence criterion used for the geometry optimizations is 10−5 hartree/bohr) and characterized by vibrational frequency analyses with the CCSD(T) method. For the final energetic predictions, the higher-level CCSDT and CCSDT(Q) methods were used. We did not consider the multireference character further; the T1 diagnostic is T1 = 0.037. The MPW1K DFT method proposed by Truhlar and coworkers34 is also used, because it has been reported that among many DFT methods MPW1K predicts the best agreement barrier with the CCSD(T)/cc-pV5Z result for the isoelectronic F + H2O reaction.35 The training set used to parametrize the MPW1K method included the related F + H2 and H + H2 reactions. Intrinsic reaction coordinate (IRC)36,37 analyses were performed with the MPW1K method to ensure that the transition state connects the desired entrance and exit complexes. The MPW1K computations were carried out using the Gaussian 09 program suite,38 whereas the CCSD(T) computations were achieved with the CFOUR program.39
3. RESULTS AND DISCUSSION 3.1. Structures and Energies of Stationary Points. In previous studies of the OH + H2O → H2O + OH reaction, one hydrogen bonded complex and one transition state were reported on its potential energy surface (PES).14 However, it is unresolved whether the prereactive complex is the HOH···OH species or the global minimum H2O···HO.15 In the present study, we first try to answer this question with the CCSD(T), CCSDT, and CCSDT(Q) methods. Different from the previous studies, two hydrogen bonded complexes (CP1 and CP2) are found on the PES (Figure 1), and an early transition state TS1 is found to connect these two complexes, in addition to the conventional transition state TS2. Stationary points on the CCSD(T) PES for the OH + H2O → H2O + OH reaction are reported in Figure 1. Because this is a symmetric reaction (upper left inset to Figure 1), only one side is shown in structural detail. Consider first the reactants/products (H2O and OH). The predicted geometric parameters for H2O and OH with the CCSD(T)/aug-cc-pVnZ (n = D, T, Q, 5) method are in excellent agreement with experiment.40,41 With the largest basis set (5Z), the O−H distance in the OH radical is 0.970 Å, whereas the experimental equilibrium separation is 0.9697 Å. Our prediction for the O−H distance in H2O is 0.958 Å and the ∠H−O−H angle is 104.4° (Figure S1, Supporting Information), whereas the experimental results are 0.9578 Å and 104.48°, respectively. The lowest-lying hydrogen-bonded complex CP1 (H2O··· HO) has a hydrogen bond between the H atom of the OH radical and the O atom of water (structure III in Scheme 1). The CCSD(T) CP1 complex is of Cs symmetry at its 2A′ ground electronic state, lying 5.74 kcal mol−1 below the reactants (H2O + OH). This result is consistent with the previous predictions, such as 5.67 kcal mol−1 in 199317 and 5.83 C
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Table 1. Relative Energies (kcal/mol) for the Stationary Points on the Potential Energy Surface from Nine DFT Methods with the aug-cc-pVTZ Basis Sets for the OH + H2O Reactiona methods
OH + H2O
CP1
TS1
CP2b
TS2
barrier of TS2 vs CP1
HF %
BHLYP MPW1K M06-2X ωB97X ωB97X-D mPW1PW91 B3LYP VSXC BLYP BP86 HF MP2 CCSD(T)/aug-cc-pV5Z
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
−5.9 −5.6 −6.1 −6.5 −5.8 −5.5 −5.5 −5.3 −5.1 −5.2 −4.7 −5.9 −5.7
−3.4 −3.0
−3.4 −3.2 −6.0 −6.4 −3.4 −3.1 −3.2 −5.9 −5.2 −5.3 −2.5 −3.6 −3.5
12.4 9.6 7.2 6.2 5.3 3.6 2.1 0.6 −5.2 −6.8 32.4 11.1 9.5
18.3 15.2 13.2 12.7 11.1 9.1 7.6 5.8 −0.1 −1.6 37.1 17.0 15.2
50 42.8 54 LCc LCc 25 20 0 0 0 100 100 100
−3.3 −2.9
−2.4 −3.5 −3.5
ref 42, 34 44 45 46 47, 49 50 43, 51,
43
48
51 52
a The methods are reported in the order of the predicted energy barrier for TS2. The HF, MP2, and CCSD(T) results are also listed for comparison. Every entry in this table represents a fully optimized stationary-point geometry. bCP2 was predicted to have an imaginary vibrational frequency by the M06-2X, ωB97X, BLYP, and BP86 methods. cThe percentage of Hartree−Fock component varies with the long-range corrections.
method, which has predicted PES features closest to that from CCSD(T) and is much less expensive. On the PES for the symmetric OH + H2O → H2O + OH reaction, the highest-lying transition state TS2 (HO···H···OH, with C2 symmetry) has an imaginary vibrational frequency with a significant value (2087i cm−1 by MPW1K), which corresponds to an antisymmetric O···H stretching normal mode. It is clear that this mode leads to the hydrogen bonded complex HOH···OH, i.e., CP2 (Scheme 2).
methods are now routinely applied to the study of a range of chemical reactions. Nowadays there are more and more functionals proposed, and they are constructed with different strategies. Because various functionals can predict very different results,35 it is important to compare and evaluate the performance of a range of functionals. In the present study, we choose nine of the more commonly used functionals,34,42−52 and their results with aug-cc-pVTZ basis sets for the OH + H2O → H2O + OH reaction are shown in Table 1. The reliable CCSD(T)/aug-cc-pV5Z results are also shown for comparison. From the results reported in Table 1, we see the following: (1) The energy barrier (TS2 vs CP1) is predicted to be very different by the diverse DFT methods (from −1.6 to +18.3 kcal mol−1). Thus, we should be very cautious in choosing density functionals to study the PESs of some classes of chemical reactions. (2) The functionals fall in same energetic order as reported in our previous study35 of the F + H2O reaction barrier. The percentage of Hartree−Fock exchange terms plays an important role. The functionals with larger H−F exchange fractions generally predict higher (i.e., more reasonable) energy barriers. (3) Interestingly, as shown in the F + H2O study,35 the MPW1K functional predicts the energy barrier closest to that from the CCSD(T)/aug-cc-pV5Z method. This is in part due to the fact that the related reaction F + H2 was used in the training set for MPW1K. However, the MPW1K method also predicts the other stationary points on the potential energy surface close to the CCSD(T) results. This is also consistent with the earlier work by Truhlar and coauthors.34,53 (4) Certain functionals, such as M06-2X, ωB97X, BLYP, and BP86, predict somewhat different PES features. These methods yield only one transition state and one hydrogen bonded complex; i.e., structure CP2 is no longer a stationary point but collapses to CP1 without a barrier. However, given the extreme flatness of the OH + H2O PES near TS1 and CP2, this should not be taken as a criticism of these three functionals. 3.3. Reaction Path. To ensure the transition states are correctly linked to the minima shown in our PES (Figure 1), we performed IRC evaluations with the MPW1K/aug-cc-pVDZ
Scheme 2. Normal Modes Corresponding to the Imaginary Vibrational Frequencies of TS2 and TS1 (Red Arrows)a
a
Both transition states lead (from different directions) to the hydrogen bonded complex CP2.
The first transition state TS1 has a very small imaginary vibrational frequency (73i cm−1), indicating a remarkably flat potential curve in the nearby area. Indeed, energetically TS1 lies only marginally in energy above the complex CP2. The geometry of TS1 is very close to that of CP2. The normal mode (a′) corresponding to this imaginary vibrational frequency is an in-plane vibration mixing the bending of the ∠HOH···O−H angle with the H···O stretching. There is no doubt that one direction of this mode leads to CP2 (Scheme 2). However, the geometry of TS1 (HOH···OH) is very different from that of CP1 (H2O···HO). Furthermore, the inplane normal mode (a′) corresponding to the imaginary vibrational frequency of TS1 in the other direction does not appear to connect the nonplanar CP1. How does TS1 connect D
DOI: 10.1021/acs.jpca.6b10008 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Scheme 3. Normal Mode of TS1 in the Direction of the Reactants (Red Arrows)a
a
Following this mode, there is a valley-ridge inflection (VRI) point on the pathway, and then it goes to the lowest-lying hydrogen bonded complex CP1.
Table 2. Relative Energies, with and without Zero-Point Vibration Energy (ZPVE) Corrections (in kcal/mol), Harmonic Vibrational Frequencies (ω in cm−1) and Zero-Point Vibrational Energies (ZPVE, in kcal/mol) for the Stationary Points of the OH + H2O → H2O + OH Reaction from the CCSD(T) Method with Four Diffuse Correlation-Consistent Dunning Basis Sets vibrational frequencies ω ΔE
ZPVE
ΔZPVE
ΔEZPVE
H2O + OH CP1 TS1 CP2 TS2
0.00 −5.88 −3.78 −3.79 9.91
18.61 20.70 19.96 20.10 18.14
0.00 2.10 1.36 1.50 −0.46
0.00 −3.78 −2.42 −2.29 9.45
H2O + OH CP1 TS1 CP2 TS2
0.00 −5.89 −3.63 −3.68 9.12
18.72 20.79 19.98 20.13 18.27
0.00 2.07 1.26 1.41 −0.45
0.00 −3.82 −2.37 −2.27 8.67
H2O + OH CP1 TS1 CP2 TS2
0.00 −5.81 −3.57 −3.58 9.32
18.81 20.84 20.07 20.17 18.33
0.00 2.03 1.26 1.36 −0.48
0.00 −3.78 −2.31 −2.22 8.84
H2O + OH CP1 TS1 CP2 TS2
0.00 −5.74 −3.51 −3.51 9.45
18.82 20.83 20.08 20.19 18.36
0.00 2.01 1.26 1.37 −0.46
0.00 −3.73 −2.25 −2.14 8.99
CCSD(T)/aug-cc-pVDZ 3905 3787 1638 3903 3788 3588 3896 3765 3665 3890 3756 3669 3748 3743 1533 CCSD(T)/aug-cc-pVTZ 3920 3811 1646 3917 3810 3619 3907 3785 3698 3901 3776 3707 3774 3769 1573 CCSD(T)/aug-cc-pVQZ 3940 3831 1650 3939 3831 3635 3925 3799 3720 3922 3793 3726 3793 3789 1581 CCSD(T)/aug-cc-pV5Z 3943 3833 1649 3943 3835 3640 3929 3802 3724 3926 3796 3729 3797 3792 1588
(H2O); 1639 1639 1647 1367
617 431 403 910
3684 422 269 318 576
(OH) 189 156 165 443
168 144 133 370
165 91i 80 2074i
(H2O); 1646 1646 1657 1365
622 417 375 921
3718 423 258 304 579
(OH) 188 159 161 438
166 106 107 362
152 102i 95 1959i
(H2O); 1650 1651 1659 1362
618 412 381 922
3739 413 262 290 578
(OH) 189 161 163 437
164 107 109 363
141 75i 71 1965i
(H2O); 1650 1652 1659 1362
614 409 380 924
3742 409 261 289 579
(OH) 188 161 164 438
161 105 106 363
134 73i 72 1958i
3.4. Vibrational Frequencies and ZPVE Corrections. Table 2 reports the harmonic vibrational frequencies and zeropoint vibrational energies (ZPVEs) for all the stationary points of the OH + H2O reaction, predicted with the CCSD(T) method. The two transition states (TS1, TS2) have imaginary vibrational frequencies of 73i and 1958i cm−1 (aug-cc-pV5Z), respectively. Table 2 shows that the ZPVE corrections for separated OH plus H2O with different basis sets lie within a range of (18.61 − 18.82) = −0.21 kcal mol−1. At the CCSD(T)/aug-cc-pV5Z level, the ZPVE corrections (compared to OH + H2O) decrease the energy of TS2 by 0.46 kcal mol−1 and increase those of CP1, TS1, and CP2 by 2.01, 1.26, and 1.37 kcal mol−1, respectively. As reported in Table 2, with the ZPVE corrections, the predicted relative energies of the CP1, TS1, CP2, and TS2 become −3.73, −2.25, −2.14, and 8.99 kcal mol−1, respectively, at the CCSD(T)/aug-cc-pV5Z level of theory. 3.5. Further Refinement of the Energies. Table 3 shows that our predicted CCSD(T) energies appear well converged with respect to the size of basis set, especially from aug-ccpVTZ to aug-cc-pV5Z. It is critical to examine whether these
to CP1 on the potential surface? To answer this question, we examined a series of points along the reaction path from TS1 with the MPW1K method. We found that for TS1 the Hessian eigenvalue related to the out-of-plane mode is positive. However, along the path leading to the reactants, one Hessian eigenvalue related to the out-ofplane mode becomes negative. Thus, there exists a point on the reaction path that the Hessian has zero eigenvalue, where the corresponding eigenvector is orthogonal to the gradient. In other words, across this point, the out-of-plane vibrational frequency changes from real to imaginary. This point may be called a valley-ridge inflection (VRI) point or a valley-ridge transition point (VRTp).15 The geometry of this point is between TS1 and CP1 (Scheme 3). At the VRT one hydrogen bond is breaking, and another hydrogen bond is forming. This point VRT lies below TS1 by only 0.3 kcal mol−1 (MPW1K). After passing the VRI point, the reaction path goes down along the crest of ridge to a C2v structure (structure II in Scheme 1), which has an imaginary vibrational frequency (131i cm−1 by MPW1K) related to an out-of-plane (b1) mode. Following the imaginary frequency, the lowest-lying complex CP1 is eventually reached. E
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with experiment and some previous theoretical results.15,21−24,26 The other complex CP2 is planar in its 2A″ electronic ground state, and the hydrogen bond is formed between the oxygen of OH radical and the hydrogen of water. The HOH···OH distance is 2.071 Å, and CP2 lies 3.51 kcal mol−1 below the reactants. The transition state (TS1) between CP1 and CP2 has a geometry very similar to CP2, and its energy is only slightly (
