Benchmark ab initio characterization of the abstraction and substitution pathways of the OH + CH 4 /C 2 H 6 reactions

We report a comprehensive ab initio investigation of the OH + CH 4 /C 2 H 6 reactions using a high-level composite approach based on CCSD(T)-F12b/aug-cc-pVTZ geometries and CCSD(T)-F12b/aug-cc-pV n Z n = 5/Q energies augmented with additive corrections of post-CCSD(T) correlation, core correlation, scalar relativity, spin–orbit coupling, and zero-point energy. Besides the hydrogen-abstraction (HA) channel leading to H 2 O + CH 3 /C 2 H 5 ( D H 0 = (cid:2) 14.37/ (cid:2) 18.19 kcal mol (cid:2) 1 ), we reveal, for the first time, hydrogen-substitution (HS) and methyl-substitution (MS) pathways resulting in H + CH 3 OH/C 2 H 5 OH ( D H 0 = 13.19/7.12 kcal mol (cid:2) 1 ) and CH 3 + CH 3 OH ( D H 0 = (cid:2) 2.20 kcal mol (cid:2) 1 ) products, respectively. The adiabatic barrier heights for HA, MS, and HS in OH + CH 4 /C 2 H 6 are 4.78/2.18, 39.60, 43.53/41.73(52.48) kcal mol (cid:2) 1 , respectively, where substitution proceeds with Walden-inversion or (front-side-attack retention). In the entrance channels van der Waals wells with depths of 0.5–0.8 kcal mol (cid:2) 1 are found and in the exit channels the HOH (cid:3)(cid:3)(cid:3) C 2 H 5 , HOH (cid:3)(cid:3)(cid:3) CH 3 , H 3 C (cid:3)(cid:3)(cid:3) CH 3 OH, and H (cid:3)(cid:3)(cid:3) C 2 H 5 OH complexes are characterized with D e values of 2.4, 1.7, 0.7, and 0.3 kcal mol (cid:2) 1 , respectively. n Z computations with n = 5 and 4(Q) for OH + CH 4 and OH + C 2 H 6 , respectively. Post-CCSD(T) correlation ( (cid:2) 0.9 to (cid:2) 0.1), core correlation ( (cid:2) 0.1 to +0.4), scalar relativistic (+0.0 to +0.2), SO (+0.2), and ZPE ( (cid:2) 2 to (cid:2) 1) eﬀects are determined resulting in typical values for the title reactions as indicated in parentheses in kcal mol (cid:2) 1 . We conclude that the present theoretical predictions provide sub-chemically accurate relative energies with an estimated uncertainty of around 0.1 kcal mol (cid:2) 1 , which is about an order of magnitude better than that of the standard quantum chemistry studies. The outstanding accuracy of the present results can be confirmed by the comparison of the computed reaction enthalpies with the corresponding experimental data 61 showing only 0.07 kcal mol (cid:2) 1 mean absolute deviation.


I. Introduction
Moving beyond the reactions of atoms with alkanes, 1-16 the reactions of the OH radical with methane (CH 4 ) and ethane (C 2 H 6 ) have been thoroughly investigated by theory and experiment to uncover the fundamental rules of polyatomic chemical reactivity.  The main product channel of the OH + CH 4 /C 2 H 6 reactions results in H 2 O + CH 3 /C 2 H 5 via hydrogen-abstraction (HA). In the early years the kinetics of the OH + CH 4 /C 2 H 6 reactions were investigated using experimental techniques as well as transition-state theory. 17,18,28,30,31 The stationary points along the HA pathway were characterized by various ab initio and density functional methods reporting pre-and postreaction complexes separated by a transition state for each reaction. 19,22,23,27,28,33,35,38 In the case of the OH + CH 4 system, the CH 4 Á Á ÁOH and H 2 OÁ Á ÁCH 3 complexes were also studied by different experimental techniques using stimulated Raman, infrared and electronic excitation, 24,36,37 photoelectron-photofragment coincidence, 34 and infrared spectroscopy in helium nanodroplets. 26,32 Furthermore, detailed reactive scattering experiments were performed for the different isotope-variants of the OH + CH 4 -H 2 O + CH 3 reaction by Liu and co-workers. 29 For the OH + C 2 H 6 system, the nascent H 2 O vibrational distributions were measured by infrared chemiluminescence. 21 In order to simulate some of the above-mentioned experiments the development of a full-dimensional potential energy surface (PES) was necessary. Following the early work of Espinosa-García and co-workers, 22 Li and Guo 38 developed such a PES for the OH + CH 4 reaction and investigated its dynamics using quasi-classical trajectory and reduced-dimensional quantum methods. 39 In this study we focus on the high-level ab initio characterization of the PES of the OH + CH 4 /C 2 H 6 reactions providing benchmark structures and energies for the stationary points, thereby complementing our recent work on atom (F, Cl, Br, I) + CH 4 /C 2 H 6 systems. [13][14][15] Several aspects of the present study move beyond the previous work: (1) unlike most of the early work except ref. 38, we use the explicitly correlated CCSD(T)-F12 method 40 to obtain structures, frequencies, and energies; (2) basis sets as large as aug-cc-pV5Z (OH + CH 4 ) and aug-cc-pVQZ (OH + C 2 H 6 ) are employed; (3) post-CCSD(T) correlation effects are considered up to the CCSDT(Q) level of theory; (4) the correlation energy contribution of the core electrons is taken into account; (5) scalar relativistic corrections are determined; and (6) spin-orbit effects are computed. Furthermore, besides the above-mentioned quantitative advances, we investigate several new alternative reaction pathways for the OH + CH 4 / C 2 H 6 systems, namely hydrogen-substitution and methylsubstitution forming H + CH 3 OH/C 2 H 5 OH and CH 3 + CH 3 OH products, respectively. Knowing the energetics of the above channels is essential to develop global PESs for the title reactions and to advance our knowledge on complex reaction mechanisms of multi-channel reactions.
In Section II we describe the computational details of the composite approach used to determine the best technically feasible stationary-point properties. The results are presented and discussed in Section III. The paper ends with summary and conclusions in Section IV.

II. Computational details
Stationary-point search is performed on the basis of previous studies 14,38 and chemical intuition using the second-order Møller-Plesset perturbation theory 41 (MP2) with the aug-cc-pVDZ basis set. 42 The obtained minima and saddle points are further optimized with the explicitly-correlated coupled-cluster singles, doubles, and perturbative triples (CCSD(T)-F12b) method 40 using the aug-cc-pVDZ and aug-cc-pVTZ basis sets. 42 Harmonic vibrational frequencies are computed for each stationary point using the MP2/aug-cc-pVDZ, CCSD(T)-F12b/ aug-cc-pVDZ, and CCSD(T)-F12b/aug-cc-pVTZ (except for some of the OH + C 2 H 6 stationary points) levels of theory.
In order to achieve sub-chemical accuracy we perform the following singe-point energy computations at the best geometries obtained at the CCSD(T)-F12b/aug-cc-pVTZ level: (1) CCSD(T)-F12b computations are carried out using the aug-cc-pVQZ and, in the case of the OH + CH 4 system, the augcc-pV5Z basis sets.
(2) CCSD(T), 43 CCSDT, 44 and CCSDT(Q) 45 methods are used with the cc-pVDZ and, in the case of the OH + CH 4 system, the aug-cc-pVDZ basis sets.
(3) All-electron (AE) and frozen-core (FC) computations are performed at the CCSD(T)-F12b/cc-pCVTZ-F12 level of theory. 40,46 In the usual FC treatment only the valence electrons are correlated, whereas the AE computations correlate the 1s 2 electrons of the C and O atoms as well.
(5) Spin-orbit (SO) corrections are determined using the Breit-Pauli Hamiltonian in the interacting-states approach 48 using the Davidson-corrected 49 multi-reference configuration interaction 50 (MRCI+Q) method with the aug-cc-pVDZ and augcc-pVTZ basis sets. The MRCI computations utilize an active space of 15/21 electrons in 8/11 spatial orbitals keeping all the 4/6 core electrons frozen for OH + CH 4 /C 2 H 6 . Two doublydegenerate electronic states are determined, non-SO 1 and non-SO 2 , resulting in a 4 Â 4 SO matrix, whose eigenvalues correspond to the two-fold ground (SO 1 ) and excited (SO 2 ) spinorbit states.
The benchmark classical relative energies are calculated by the following composite energy expression: where n = 5 and 4(Q) for the OH + CH 4 and OH + C 2 H 6 systems, respectively, and D SO = SO 1 (MRCI+Q/aug-cc-pVTZ) À non-SO 1 (MRCI+Q/aug-cc-pVTZ).
The benchmark adiabatic relative energies are obtained as including the terms defined in eqn (1)

III. Results and discussion
The topology of the PESs with the benchmark classical and adiabatic energies of the OH + CH 4 and OH + C 2 H 6 reactions are shown in Fig. 1 and 2, respectively, and the corresponding stationary-point geometries showing the most important structural parameters at different levels of theory are given in Fig. 3 Fig. 3 and 4. Thus, the exothermic HA processes feature early barriers in accord with the Hammond postulate 55 and the more exothermic OH + C 2 H 6 reaction has lower and more reactant-like barrier as the above-discussed data show. In the product wells of both systems there are post-reaction minima (HA PostMINs), where H 2 O binds to the CH 3 /C 2 H 5 units with a single hydrogen-bond. The D e (D 0 ) values of the HA PostMIN complexes are 1.73(0.65)/ 2.36(1.35) kcal mol À1 , in accord with the ratio of the intermolecular CÁ Á ÁH distances of 2.383/2.312 Å. The greater stability of the latter can be explained by the fact that the C 2 H 5 unit has larger dipole moment than the CH 3 fragment.
For the OH + CH 4 reaction we have found an endothermic, DE(DH 0 ) = 14.33 (13.19) kcal mol À1 , hydrogen-substitution (HS) pathway resulting in H + CH 3 OH products via a Walden-inversion TS (HS W TS) with a classical(adiabatic) barrier height of 44.30 (43.53) kcal mol À1 as shown in Fig. 1. The HS W TS has C s symmetry with nearly collinear O-C-H arrangement, where the O-C and C-H distances are 1.717 and 1.415 Å, respectively, stretched by 0.297 and 0.327 Å relative the corresponding bonds in CH 3 OH and CH 4 (Fig. 3); thus, HS has a central or slightly-late barrier. The HS pathway of the OH + CH 4 reaction is revealed for the first time in the present study, but for atom + methane reactions HS is not unprecedented. 4,[56][57][58][59][60] For the H and O( 3 P) + CH 4 reactions HS was investigated both experimentally 4,56 and theoretically. 4,57 For Cl + CH 4 we found a Walden-inversion barrier height of 42.08(38.84) kcal mol À1 , 58 which is similar to that of OH + CH 4 . Besides Walden inversion, for the O( 3 P) and Cl + CH 4 reactions front-side attack TSs with C 2v and C 4v symmetry, respectively, were reported. 4,60 In the case of OH + CH 4 we do not find front-side attack TS; however, reaction dynamics simulations may reveal retention trajectories as we found that the retention pathways of the Cl + CH 4 -H + CH 3 Cl reaction avoid the high-energy C 4v TS. 60 In the case of the OH + C 2 H 6 reaction HS pathways leading to H + C 2 H 5 OH also exist as shown in Fig. 2. The endothermicity of the HS channel, DE(DH 0 ) = 9.10(7.12) kcal mol À1 , is less than that of the OH + CH 4 reaction, DE(DH 0 ) = 14.33 (13.19) kcal mol À1 , whereas the Walden-inversion classical(adiabatic) barrier heights of the two systems are similar, i.e., 43.32(41.73) kcal mol À1 for OH + C 2 H 6 and 44.30(43.53) kcal mol À1 for OH + CH 4 . Furthermore, these HS barrier heights are also very similar to that of the Cl + C 2 H 6 system, 41.60(37.66) kcal mol À1 . 14 For the OH + C 2 H 6 reaction we have found a front-side (FS) attack retention pathway via a higher barrier with classical(adiabatic) height of 54.13(52.48) kcal mol À1 . 14 At the HS W TS the forming O-C and breaking C-H bonds are nearly collinear (168.31) and the H 2 C-C unit is almost planar, whereas at the HS FS TS the O-C-H angle is 58.21 along the reaction coordinate and the H 2 C-CH 3 unit is ethane-like retaining its reactant configuration. Similar HS FS TS was found for the X + C 2 H 6 [X = F, Cl, Br, I] reactions, comparing the barrier heights again the X = Cl case has similar, though slightly larger, value of 59.14(54.97) kcal mol À1 . For the OH + C 2 H 6 reaction we have found weakly-bound HÁ Á ÁC 2 H 5 OH complexes in the exit channels of the HS inversion and retention pathways with small D e values of 0.26 and 0.32 kcal mol À1 , respectively. However, these shallow HS product-channel wells may not support a bound vibrational state, because the ZPE-corrected energies of the HS W PostMIN and HS FS PostMIN complexes are slightly above the vibrationally ground-state product asymptote by 0.05 and 0.04 kcal mol À1 (Fig. 2).
Unlike for OH + CH 4 , for the OH + C 2 H 6 reaction a third product channel is possible resulting in CH 3 OH + CH 3 via methyl substitution (MS). As Fig. 2 shows, MS is slightly exothermic DE(DH 0 ) = À0.94(À2.20) kcal mol À1 and goes over a classical (adiabatic) Walden-inversion barrier of 39.89(39.60) kcal mol À1 height. Thus, similarly to the halogen + C 2 H 6 reactions, 14    values in the product and reactant (Fig. 4). For the halogen + C 2 H 6 systems we reported a higher-energy front-side attack MS pathway as well, 14 however, for OH + C 2 H 6 MS FS TS is not found, though its existence cannot be ruled out. Nevertheless, we have found a H 3 CÁ Á ÁCH 3 OH complex in the product channel of MS with D e (D 0 ) values of 0.69(0.38) kcal mol À1 . The stability trend, D e = {2.4, 0.7, 0.3} kcal mol À1 , of the {HA, MS, HS} PostMIN complexes, {HOHÁ Á ÁC 2 H 5 , H 3 CÁ Á ÁCH 3 OH, HÁ Á ÁC 2 H 5 OH}, reflects the facts that HA PostMIN is stabilized by dipole-dipole interaction and CH 3 is more polarizable than the H atom.
The above-discussed stationary-point properties correspond to our new benchmark values obtained by the composite ab initio approach described in Section II. Now let us discuss the accuracy of the computed results. The most important structural parameters of the stationary points obtained by the MP2/aug-cc-pVDZ, CCSD(T)-F12b/aug-cc-pVDZ, and CCSD(T)-F12b/aug-cc-pVTZ levels of theory are shown in Fig. 3 and 4. As seen, the MP2 and CCSD(T)-F12b results may differ by about 0.01 Å, whereas the CCSD(T)-F12b distances with the aug-cc-pVDZ and aug-cc-pVTZ basis sets usually agree within 0.001 Å, except for large intermolecular distances where an order of magnitude larger uncertainties are found due to the flatness of the potential along the dissociation coordinate.
The convergence of the relative energies are shown in Tables 1  and 2 for the OH + CH 4 and OH + C 2 H 6 systems, respectively, and the corresponding auxiliary corrections are detailed in Tables 3 and 4. The MP2 and CCSD(T)-F12b relative energies differ by 1-6 kcal mol À1 , for example, MP2 overestimates the HA barrier heights by 2.4-2.8 kcal mol À1 and underestimates the endoergicity of the HS channels by 5.8-6.0 kcal mol À1 as seen in Tables 1 and 2. Thus, it is clear that the use of the CCSD(T)-F12b method is needed to achieve chemical accuracy (uncertainty less than 1 kcal mol À1 ). For the OH + CH 4 system we have CCSD(T)-F12b energies up to the large aug-cc-pV5Z basis and on the basis of Table 1 we find that the average absolute deviations of the aug-cc-pVDZ, aug-cc-pVTZ, and augcc-pVQZ relative energies from the aug-cc-pV5Z data decrease as 0.25, 0.06, 0.04 kcal mol À1 , respectively, showing the excellent basis convergence of the explicitly-correlated CCSD(T)-F12b method. Thus, we expect that even the CCSD(T)-F12b/ aug-cc-pVQZ result is basis converged within 0.1 kcal mol À1 . This finding for OH + CH 4 is useful for the larger OH + C 2 H 6 system, where we do not perform the CCSD(T)-F12b/aug-cc-pV5Z computations. For OH + C 2 H 6 , the aug-cc-pVDZ and augcc-pVTZ CCSD(T)-F12b relative energies are converged with average absolute deviations of 0.27 and 0.04 kcal mol À1 , respectively, with respect to the CCSD(T)-F12b/aug-cc-pVQZ results.
The large-basis CCSD(T)-F12b computations provide a very good estimate of the complete-basis-set limit of the CCSD(T) relative energies. If one aims to approach the ''exact'' energies additional small corrections, such as post-CCSD(T) and core electron correlation as well as scalar and SO relativistic effects should be considered. Furthermore, to get experimentally observable quantities the ZPE corrections have to be taken into account. These so-called auxiliary corrections are given in Tables 3 and 4   and d[CCSDT(Q)] corrections with the cc-pVDZ and aug-cc-pVDZ basis sets. As Table 3 shows even the small cc-pVDZ basis provides good estimates for these post-CCSD(T) correlation effects suggesting that it is sufficient to perform only the CCSDT(Q)/cc-pVDZ computations for the larger OH + C 2 H 6 system. In the case of the products and HA PostMIN of the OH + CH 4  For both reactions the core correlation corrections are in the range from À0.11 to +0.39 kcal mol À1 , whereas the scalar  Tables 3 and 4. SO interaction almost fully quenches at all the stationary points, while lowers the reactant asymptote, thereby increasing all the relative energies by 0.19 kcal mol À1 . As seen in Tables 3  and 4 we have performed SO computations with the aug-cc- a MP2/aug-cc-pVDZ relative energies obtained at MP2/aug-cc-pVDZ geometries. b CCSD(T)-F12b/aug-cc-pVDZ relative energies obtained at CCSD(T)-F12b/aug-cc-pVDZ geometries. c CCSD(T)-F12b/aug-cc-pVTZ relative energies obtained at CCSD(T)-F12b/aug-cc-pVTZ geometries.     To get deeper insight, we have computed SO and non-SO potential energy curves along the intermolecular coordinates of the CH 4 Á Á ÁOH and C 2 H 6 Á Á ÁOH systems while the OH approaches the CH 4 and C 2 H 6 molecules from different directions as shown in Fig. 5 and 6. The ground electronic state of the OH radical is the 2 Â 2-fold degenerate 2 P, which splits to a 2-fold SO ground ( 2 P 3/2 ) and a 2-fold SO excited state ( 2 P 1/2 ). As OH approaches CH 4 the two doublet non-SO state remains quasi-degenerate and the SO ground and excited states are below and above the non-SO states by e/2 as shown in Fig. 5.
There is a van der Waals well in the entrance channel whose depth is 0.5 and 0.7 kcal mol À1 with HCH 3 Á Á ÁOH and H 3 CHÁ Á ÁOH C 3v orientations, respectively. The well depths and positions are not affected by the SO interaction, because the wells are at CÁ Á ÁO distances of 3-4 Å, whereas the SO correction is almost constant until the CÁ Á ÁO distance decreases to about 2 Å, where the difference between the SO and non-SO ground state energies rapidly drops to zero (see insets in Fig. 5). This fast quenching of SO interaction occurs at high relative energies above 100 kcal mol À1 , where the quasi-degeneracy of the non-SO states starts lifting. Interestingly, in the case of the halogen (X) + CH 4 reactions, the HCH 3 Á Á ÁX minimum is the deeper with depth of 0.6(0.9) kcal mol À1 and the H 3 CHÁ Á ÁX well is the shallower, 0.3(0.3) kcal mol À1 , with(without) SO correction. 13,58 In the case of the H 3 CCH 3 Á Á ÁOH (C 3v ) and H 3 CH 2 CHÁ Á ÁOH (C s ) arrangements in the entrance well of OH + C 2 H 6 reaction, the conclusions are qualitatively the same as for OH + CH 4 , i.e., the former minimum is 0.6 kcal mol À1 deep, whereas the latter is deeper, 0.7 kcal mol À1 , and these are not affected by the SO interactions. If OH approaches C 2 H 6 perpendicularly to the C-C bond, the well is the deepest, 0.8 kcal mol À1 , and slightly affected by the SO interaction as the quenching and the departure of the two non-SO states occur in the 2.5-3.5 Å range of the CCÁ Á ÁO distance as seen in Fig. 6. For the X + C 2 H 6 systems, the H 3 CCH 3 Á Á ÁX (C 3v ) minimum was found to be the deepest, slightly below the perpendicular well, and the H 3 CH 2 CHÁ Á ÁX (C s ) arrangement gave the shallowest minimum. 14 These entrance-channel wells may play an important role in the dynamics of the title reactions at low collision energies, especially for OH + C 2 H 6 , which has a low barrier for HA. The ZPE effects on the relative energies are always negative and in the most cases the absolute corrections are in the range of 1-2 kcal mol À1 as shown in Tables 1 and 2. The mean absolute deviation of the MP2 ZPE corrections from the CCSD(T)-F12b results is about 0.2 kcal mol À1 , whereas the CCSD(T)-F12b/augcc-pVTZ data are converged within 0.1 kcal mol À1 as Tables 3  and 4 show. These ZPE effects are clearly not negligible if we aim to compute chemically accurate, measurable adiabatic relative energies.
For the reaction enthalpies comparison between the present computed adiabatic relative energies and the ''experimental'' data deduced from 0 K enthalpies of formation taken from the Active Thermochemical Tables (ATcT) 61 is possible. Note that ATcT collects the best measured and computed thermochemical data, thereby providing the best available predictions for enthalpies of formation and their uncertainties of several chemical species. We call these ATcT data as ''experimental'' even if they rely on both theory and experiment. As Table 5 shows the agreement between the present ab initio 0 K reaction enthalpies and experiment is excellent; the mean absolute deviation between theory and experiment is only 0.07 kcal mol À1 and, in most cases, the theoretical predictions are within the error bars of the experiment. This comparison demonstrates that one needs to consider the auxiliary corrections (post-CCSD(T), core, scalar relativistic, SO) to achieve this outstanding accuracy, because the cumulative effect of these corrections averaged for the five reaction channels is 0.21 kcal mol À1 , which is  significantly larger than the above-mentioned mean deviation between theory and experiment. Furthermore, the excellent agreement for these measurable quantities confirms the accuracy of the present theoretical predictions for the experimentally hardly accessible properties, such as barrier heights.

IV. Summary and conclusions
The reactions of the OH radical with methane and ethane have become benchmark systems to understand the dynamics and mechanisms of polyatomic reactions. Despite many previous experimental and theoretical studies 16 3 OH products is also possible, which is exothermic, DH 0 = À2.20 kcal mol À1 , but has a large adiabatic barrier of 39.60 kcal mol À1 . For the product channel several complexes have been revealed and    ). 61 Uncertainties are derived from the uncertainties of each 0 K enthalpy of formation given in ATcT using the Gaussian errorpropagation law.
characterized, showing a stability order of HOHÁ Á ÁC 2 H 5 , HOHÁ Á ÁCH 3 , H 3 CÁ Á ÁCH 3 OH, and HÁ Á ÁC 2 H 5 OH with D e values of 2.4, 1.7, 0.7, and 0.3 kcal mol À1 , respectively. For the first time, we have performed SO computations for the entrance channel, thereby revealing van der Waals wells with depths of 0.5-0.8 kcal mol À1 depending on the relative orientation of the reactants. Unlike for the halogen + CH 4 /C 2 H 6 systems, 13,14 the well is the deepest for perpendicular C-CÁ Á ÁOH approach (0.8 kcal mol À1 ), followed by the H 3 CH/H 3 CH 2 CHÁ Á ÁOH (0.7 kcal mol À1 ) and HCH 3 /H 3 CCH 3 Á Á ÁOH (0.5-0.6 kcal mol À1 ) arrangements. These pre-and post-reaction wells may play significant roles in the dynamics of the hydrogen-abstraction processes, especially at low collision energies, by steering the reactants in the entrance channels and affecting product rotation in the exit channels, respectively. The stationary-point properties have been computed using an accurate composite ab initio approach which goes beyond the widely-used standard quantum chemistry. The completebasis-set limit of CCSD(T) is approached well within 0.1 kcal mol À1 with explicitly-correlated CCSD(T)-F12b/aug-cc-pVnZ computations with n = 5 and 4(Q) for OH + CH 4 and OH + C 2 H 6 , respectively. Post-CCSD(T) correlation (À0.9 to À0.1), core correlation (À0.1 to +0.4), scalar relativistic (+0.0 to +0.2), SO (+0.2), and ZPE (À2 to À1) effects are determined resulting in typical values for the title reactions as indicated in parentheses in kcal mol À1 . We conclude that the present theoretical predictions provide sub-chemically accurate relative energies with an estimated uncertainty of around 0.1 kcal mol À1 , which is about an order of magnitude better than that of the standard quantum chemistry studies. The outstanding accuracy of the present results can be confirmed by the comparison of the computed reaction enthalpies with the corresponding experimental data 61 showing only 0.07 kcal mol À1 mean absolute deviation.
The new insights into the mechanisms and alternative reaction pathways of the title reactions are essential to develop global PESs for the OH + CH 4 /C 2 H 6 systems, allowing dynamical investigations over a large collision energy range. Furthermore, the relative energies of the stationary points may guide future experimental investigations showing the thermodynamical and kinetical controls of the different processes. Finally, the present composite approach may be utilized in several similar ab initio investigations if high accuracy is desired.

Conflicts of interest
There are no conflicts of interest to declare.