We find high multireference character for abstraction of H from the OH group of ethenol (also called vinyl alcohol); therefore we adopt a multireference approach to calculate barrier heights for the various possible reaction channels of OH+C2H3OH. The relative barrier heights of ten possible saddle points for reaction of OH with ethenol are predicted by multireference Møller–Plesset perturbation theory with active spaces based on correlated participating orbitals (CPOs) and CPO plus a correlated π orbital (CPO+π). Six barrier heights for abstracting H from a CH bond range from 3.1 to 7.7 kcal/mol, two barrier heights for abstracting H from an OH bond are both 6.0 kcal/mol, and two barrier heights for OH addition to the double bond are −1.8 and −2.8 kcal/mol. Thus we expect abstraction at high-temperature and addition at low temperature. The factor that determines which H is most favorable to abstract is an internal hydrogen bond that constitutes part of a six-membered ring at one of the abstraction saddle points; the hydrogen bond contributes about 3 kcal/mol stabilization.

One of the challenges of modeling combustion and atmospheric chemistry is determining the reaction rates of intermediate species because their kinetics is often difficult to study directly. Quantum chemistry is playing an increasingly important role in this process. Enols have been implicated as intermediates in combustion,1–4 and they may play a role in atmospheric chemistry,5 but little is known about their reactions with hydroxyl radical, which is the most important oxidizing species in both environments. Here we compute the barrier heights for the possible reactions of ethenol with hydroxyl radical.

Preliminary calculations using several single-reference methods showed energy convergence problems for abstraction of H from the OH-group. Therefore, the calculations of the barrier heights and all geometry optimizations were carried out using multireference Møller–Plesset second order perturbation theory6,7 (MRMP2) based on complete active space self-consistent-field8–11 (CASSCF) (also known as the fully optimized reaction space12,13) reference wave functions. With few exceptions,14,15 the MRMP2 method has not been systematically applied for geometry optimization of reactive saddle points, but the application of this method to a single-point energy calculation at geometries optimized at a different level is more common.16–20 With both approaches, the resulting accuracy has been encouraging. The mean unsigned error in the exothermic-direction barrier heights calculated using the MRMP2/nom-CPO/aug-cc-pVTZ model chemistry for the reactions of the DBH24 database21 is 1.1 kcal/mol.14 The CASPT2 method22,23 (CAS stands for complete active space, and PT2 stands for second-order perturbation theory; CASPT2 is closely related to MRMP2) has also been used successfully for barrier height calculations, again usually with CASSCF geometries. (Representative applications may be consulted for details.24–32) Recently, calculations on the reactions of OH with propene were reported by Izsák et al.,33 who employed CASPT2 geometry optimizations. Harding et al.34,35 have obtained good results with CASPT2-optimized transition states.

The possible reaction channels considered in this paper may be divided into three groups: (i) Abstraction from a CH bond, (ii) abstraction from an OH bond, and (iii) addition of the OH radical across the CC bond to the α or β carbon of the ethenol. The active space in each case was constructed based on the correlating participating orbitals14 (CPOs) prescription. The active space used for (iii) is the nominal CPO (nom-CPO) defined previously,14 and the active spaces for two other reaction groups are the nom-CPO plus the pair of π and π orbitals of the double bond; this latter choice is denoted here as nom-CPO+π.

The nom-CPO active space is designed14 to capture the major portion of nondynamical correlation for a particular reaction channel. The nom-CPO active space involves the bonding and antibonding combinations of the breaking and forming bonds and the singly occupied molecular orbital (SOMO) of a radical (the orbital which is singly occupied in its ground electronic state). We use the convention14 that a pipe between two orbitals indicates an orbital of the reactant (left) and the corresponding orbital of the product (right). With this notation, the active spaces used in the present calculations contain the σCHσOH, σCHσOH, π, π, and SOMO(O)SOMO(C) orbitals for the CH abstraction reactions, the σOHethenolσOHwater, σOHethenolσOHwater, π, π, and SOMO(OOH)SOMO(OOCHCH2) orbitals for the OH abstraction reaction, and πCCσCO, πCCσCO, and SOMO(O)SOMO(C) pairs of orbitals for addition reactions. The active space for the abstraction reaction channels thus corresponds to five electrons in five orbitals, and the active space for the addition reactions corresponds to three electrons in three orbitals.

All calculations employed the aug-cc-pVTZ basis set.36 All calculations of the barrier heights were performed using the GAMESS suite of programs.37 Additionally, reaction energies have been calculated by single point energy evaluations using the G3SX (Ref. 38) method at geometries optimized using the M05–2X (Ref. 39) density functional. These calculations have been performed with the GAUSSIAN40 code.

Ethenol can exist in two conformers: syn and anti. We used the M06 density functional41 with the aug-cc-pVTZ basis set to calculate that the anti conformer is 1.3 kcal/mol higher than syn, and the syn-to-anti barrier is 5.3 kcal/mol (and therefore the anti-to-syn barrier is 4.0 kcal/mol). Using MRMP2 as explained above, we found eight saddle points for abstraction reactions and two for addition reactions.42 The classical barrier heights with respect to reactants (OH+H2CCHOH) are given in Table I. For syn-ethenol these were obtained by comparing the saddle point energy to the energy of a syn-reactant. For anti-ethenol they were obtained by comparing the saddle point energy to the energy of an anti-reactant, and adding the anti-syn energy difference. The optimized geometries are given in tabular form in supplementary material43 and are displayed in Fig. 1. Geometries of reactants were fully optimized in the supermolecule approach, with the distance separating the reactants fixed at least at 25 Å. For each possible reaction, the reactants have been optimized separately to preserve the invariance of the orbital active space.

Table I.

Calculated barrier heights (using the MRMP2/nom-CPO+π/aug-cc-pVTZ model chemistry, except where indicated otherwise; Vsyn: Barrier for reaction of syn-ethenol relative to the OH+syn-ethenol asymptote; VantiΔEsyn-anti: Barrier for reaction of anti-ethenol relative to the OH+anti-ethenol asymptote; Vanti: Barrier for reaction of anti-ethenol relative to the OH+syn-ethenol asymptote. The values in the second last column are obtained by adding the M06/aug-cc-pVTZ syn-anti energy difference of 1.3 kcal/mol to the MRMP2/nom-CPO+π/aug-cc-pVTZ value of the barrier with respect to OH+anti-ethenol asymptote.) and reaction energies (using G3SX//M05–2X/aug-cc-pVTZ, in kcal/mol) for reactions of ethenol with OH radical.

ReactionLabelaVsynΔELabelaVantiΔEsyn-antiVantiΔE
(C)H abstraction s1 3.11 −4.5 s1a 5.39 6.7 −4.9 
(C)H abstraction s2 6.55 −6.0 s2a 6.40 7.7 −4.1 
(C)H abstraction s3 6.76 −10.1 s3a 4.42 5.7 −11.3 
(O)H abstraction s4 6.04 (5.50)b −34.2 s4a 4.68 6.0 −34.4 
CC alpha addition s5 −1.84 −31.9         
CC beta addition s6 −2.78 −33.2         
ReactionLabelaVsynΔELabelaVantiΔEsyn-antiVantiΔE
(C)H abstraction s1 3.11 −4.5 s1a 5.39 6.7 −4.9 
(C)H abstraction s2 6.55 −6.0 s2a 6.40 7.7 −4.1 
(C)H abstraction s3 6.76 −10.1 s3a 4.42 5.7 −11.3 
(O)H abstraction s4 6.04 (5.50)b −34.2 s4a 4.68 6.0 −34.4 
CC alpha addition s5 −1.84 −31.9         
CC beta addition s6 −2.78 −33.2         
a

Labels are for corresponding saddle point geometries shown in Fig. 1.

b

The value in parentheses is calculated using MRMP2/mod-CPO+π/aug-cc-pVTZ. The mod-CPO active space is constructed by adding to the nom-CPO active space the unshared pairs in p orbitals geminal to bonds that are broken or formed (Ref. 14).

FIG. 1.

Key geometrical parameters (distances in angstroms, angles in degrees) of the reactive saddle points (s1–s6, s1a–s4a) and the reactant complex (m1) for reactions of ethenol with the hydroxyl radical. All structures are optimized using the MRMP2/nom-CPO+π/aug-cc-pVTZ model chemistry.

FIG. 1.

Key geometrical parameters (distances in angstroms, angles in degrees) of the reactive saddle points (s1–s6, s1a–s4a) and the reactant complex (m1) for reactions of ethenol with the hydroxyl radical. All structures are optimized using the MRMP2/nom-CPO+π/aug-cc-pVTZ model chemistry.

Close modal

The invariance of the orbital active space implies that the active orbitals gradually transform from the reactant region to the product region of a potential energy and therefore cause no discontinuities on the global potential energy surface. This requirement, however, may result in an unbalanced treatment of products versus transition state structures for highly exothermic reactions (or reactants versus transition state structures for highly endothermic reactions), if the number of the orbitals in an active space is relatively small. This happens because the active space selected using the CPO prescription does not necessarily include the most correlated orbitals for a reactant (or product) structure if such a structure is considerably lower in energy than the transition state. For example, in the case of very exothermic addition reactions of ozone to π systems, the bond-making π-type orbital of the reactant transforms into a lower-lying σ-type (CO) orbital of the product, which is not the best candidate for an active space of the product structure if the latter were considered on its own. Therefore, the forward barrier heights for these reactions have been found to be more accurate than the reverse ones.44 Here, for that reason, since all of the reactions are exothermic and some are highly exothermic, we present only forward barrier heights.

When OH approaches ethenol there is a complex at an energy 4.4 kcal/mol lower than the separated syn-ethenol and OH, as calculated by MRMP2. After that there are barriers to α and β addition but they are below the reactant asymptote. The barriers to H abstraction are positive though, and the lowest of them equals 3.1 kcal/mol. Therefore we expect the dominant reactions to be α and β addition at low temperatures and H abstraction at high temperatures.

The key geometrical parameters of the optimized saddle point structures are shown in Fig. 1. The geometries in Fig. 1 explain why s1 has a considerably lower energy than the other abstraction saddle points; in particular, s1 shows an internal hydrogen bond as part of a six-membered ring (present at the transition state and the complex, but not for reactants and not for the other seven of the eight transition states), and Table I shows that this stabilizes the s1 saddle point by about 3 kcal/mol. Other examples of stabilizing abstraction transition states by five- and six-membered ring hydrogen bonds are available for comparison.45 Although the hydrogen bonding lowers the energy of one of the transition states, it also probably raises its zero point energy and lowers its entropy because the vibrational frequencies will be higher at the tighter transition state; both of those effects will partly or fully compensate the favorable energetic effect of the hydrogen bonding. One must consider zero point vibrational energy and vibrational-rotational thermal energy and entropy as well as electronic energy in estimating the free energy of activation for passing though a transition state or generalized transition state, and a reliable calculation of these effects will require treating vibrational anharmonicity as well.46 

Correlations47,48 between geometric and energetic features, e.g., the correlations implied by the Hammond postulate,49 can be found for the reaction channels (of the same group) that do not involve formation of the hydrogen bond. For example, when considering the s2, s3, s2a, and s3a transition state structures in terms of the OH and the CH distances and the corresponding barrier heights, one can see that the lowest barrier in the case of s3a corresponds to the earliest transition structure and the highest barrier in case of s3 corresponds to the latest transition structure.

Additional calculations on the reaction channel (ii) have been performed by employing the MRMP2/mod-CPO+π/aug-cc-pVTZ model chemistry. The difference between the nom-CPO and mod-CPO active spaces is that the latter also includes the unshared electron pairs in p orbitals geminal to bonds that are broken or formed,14 in the present case, the unshared electron pairs in p orbitals of the oxygen atoms. The difference of about 0.5 kcal/mol between the barrier heights calculated by applying the MRMP2/nom-CPO+π/aug-cc-pVTZ and MRMP2/mod-CPO+π/aug-cc-pVTZ model chemistries is within the uncertainty14 of the methods. One may anticipate that the effect of the larger active space would even be smaller in the cases of the reaction channels (i) and (iii) because only one oxygen atom involved in the bond breaking-bond making process in these cases.

It is interesting to ask whether a multireference approach was essential for this reaction. To examine this question, we computed the M diagnostic14 for each saddle point. The M diagnostic is defined in terms of the eigenvalues of the single-particle density matrix of the CASSCF wave function, and we found that M>0.04 often signals significant errors in calculated barrier heights if single-reference methods are applied.14 Table II shows that M=0.0500.055 for the reactants and reactive saddle points in the present article. In all cases the M diagnostic is dominated by the static correlation of the π bond, and this does not change appreciably from case to case; hence M is not larger for s4 and s4a than for the other structures. On the basis of the convergence problems with the single-reference wave functions and the large M values we concluded that multireference methods are essential for comparing the various saddle point energies in a balanced way. The MRMP2 method has performed well in previous tests for barrier heights,14,15,17,19,44 and this gives added confidence in the reliability of the present results.

Table II.

Multireference diagnostics for reactions of ethenol with OH radical (M is defined in Ref. 14).

ReactionLabelaMLabelaM
Saddle pointReactantsSaddle pointReactants
(C)H abstraction s1 0.050 0.050 s1a 0.055 0.053 
(C)H abstraction s2 0.052 0.050 s2a 0.054 0.052 
(C)H abstraction s3 0.052 0.051 s3a 0.053 0.053 
(O)H abstraction s4 0.052 0.052 s4a 0.055 0.054 
CC alpha addition s5 0.052 0.052       
CC beta addition s6 0.055 0.052       
ReactionLabelaMLabelaM
Saddle pointReactantsSaddle pointReactants
(C)H abstraction s1 0.050 0.050 s1a 0.055 0.053 
(C)H abstraction s2 0.052 0.050 s2a 0.054 0.052 
(C)H abstraction s3 0.052 0.051 s3a 0.053 0.053 
(O)H abstraction s4 0.052 0.052 s4a 0.055 0.054 
CC alpha addition s5 0.052 0.052       
CC beta addition s6 0.055 0.052       
a

Labels are for corresponding saddle point geometries shown in Fig. 1.

This work was supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences under Grant No. DE-F602-86ER13579. This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-06CH11357 and resources of Minnesota Supercomputing Institute of the University of Minnesota.

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