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An ab initio study of H abstraction in halogen-substituted methanes by the -OH radical
Journal of Molecular
Structure
Elsevier Science Publishers
(Theochem),
279 (1993) 299-309
299
B.V., Amsterdam
An ab initio study of H abstraction in halogen-substituted methanes by the *OH radical Andrea
Botton?,
Gabriella
Poggi”
and
Salvatore
S. Emmib
aDipartimento di Chimica “G. Ciamician” deN’Universitci di Bologna, bIstituto di Fotochimica
e Radiazioni d’Alta Energia
(FRAE)
Via Selmi 2, 40126 Bologna (Italy)
de1 CNR, via de’ Castagnoli I, 40126 Bologna (Italy)
(Received 8 June 1992)
Abstract The H-abstraction reaction by the OH radical from methane and various halomethanes (CH,Cl, CH,F, CH,Cl,, CH,ClF, CH,F,, CHCl,F and CHF,) was studied using ab initio unrestricted Hartree-Fock (UHF) and multiconfigurational self-consistent field (MCSCF) computational methods. It was found that the structure of the transition state determined at the UHF and MCSCF levels is very similar and that the topology of these reaction surfaces is satisfactorily described using a UHF wavefunction. It is pointed out that to obtain values of the activation energies in good agreement with experiment it is essential to take into account the correlation energy contribution on reactants and transition states. The MP2/6-31G*//3-21G* approach (6-31G* single-point second-order Moller-Plesset (MP2) computations on the 3-21G* optimized geometries) is proposed as the minimal computational level needed to obtain a description of these reactions in reasonable agreement with the experimental evidence.
Introduction Methane and halo-substituted methanes are very important species in atmospheric chemistry. CH, together with CO, seem to play a major role in determining the greenhouse effect, while fluoroand chloro-substituted methanes are together considered key factors responsible for the destruction of the stratospheric ozone layer. A reaction which accounts for most of the destruction of methane in the troposphere is the oxidation by hydroxyl radicals:
CH, + -OH --, CH, + H,O
(1)
The same type of reaction occurring with halomethanes is considered an important interceptor mechanism which can remove these gases from the Correspondence to: A. Bottoni, Dipartimento di Chimica “G. Ciamician” dell’Universit9 di Bologna, Via Selmi 2, 40126 Bologna, Italy.
troposphere and hence prevent their transport into the stratosphere. Furthermore, the reaction of hydroxyl radical with CH, is of special interest because it represents a prototype for the principal initiator step in hydrocarbon combustion. For these reasons hydroxyl radical reactions with methane and halo-substituted methanes have attracted considerable attention from experimentalists [l]. In particular, various experimental measurements of the rate coefficients over a wide range of temperatures have been performed both for reaction (1) and for reactions involving chloro- and fluoro-substituted methanes that contain at least one abstractable H atom [l(b)]. Reaction (1) has also been studied from a theoretical point of view and a few ab initio calculations with accurate basis sets have recently been performed [2]. Conventional transition state theory and tunnelling corrections based on the Wigner expression [2(e)] or the Eckart model [2(d)] have been used to predict rate constants and activation
0166-1280/93/$06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
300
A. Bottoni et a1.l.l. Mol. Strut.
energies and to explain the significant curvature at low temperature observed in experimental Arrhenius diagrams. These studies have shown that the choice of accurate basis sets and the inclusion of correlation energy corrections have a significant effect on transition state vibrational frequencies and are definitely needed to reproduce the experimental activation energies. Since ab initio studies have so far been limited to the oxydryl-methane H-abstraction reaction and no calculations are available which explore on an ab initio basis the effect of systematic structural changes such as halogen substitution near the reaction site, we decided to investigate the potential energy surface associated with the reactions of various fluoro- and chloro-substituted methanes with the OH radical. In the present paper we report the results of ab initio calculations at the unrestricted Hartree-Fock (UHF), UHF second order Moller-Plesset (UHF/MP2) and multiconfigurational self-consistent field (MCSCF) computational levels of the structures and energetics of reactants and transition states for the oxydryl abstraction reaction involving methane and the following halomethanes: CH,Cl, CH, F, CH,Cl,, CH,ClF, CH,F,, CHCl,F and CHF,. For two examples (CH, and CH,Cl) we describe the results obtained with various basis sets of double-zeta quality to establish the minimum computational level required to obtain an accurate description of the reaction surface. Computational
method
All the ab initio molecular computations reported in this paper were performed with the GAUSSIAN 8s [3] and GAUSSIAN 90 [4] series of programs. The restricted Hartree-Fock (RHF) theory was used for closed-shell systems (CH, and the various halomethanes) and the UHF theory for open-shell systems like the OH radical and the transition states. The geometries of the various critical points were fully optimized with the gradient method [5] at the 3-21G* [6] level (3-21G*// 3-21G* computations) and the nature of each
(Theochem) 279 (1993) 299-309
critical point was characterized by computing the harmonic vibrational frequencies. The contribution of dynamic correlation to activation energies was evaluated by an MP2 perturbation treatment [7] and the overall energetics of the reactions was obtained with single-point MP2 computations at the 6-31G* [8] level on the 3-21G* optimized geometries (MP2/6-31G*//3-21G* computations). As suggested by Sosa and Schlegel [9] we used spin-projected MP2 energies to cancel the spin contamination which affects the transition structures and which can be responsible for an overestimation of the reaction barriers. To check the reliability of our computational approach, for both CH, + *OH and CH,Cl + *OH reactions, we also optimized the geometries of reactants and transition states with the 6-31G* and 6-31G** [lo] basis sets (double-zeta plus polarization) and at these levels we carried out single point MP2 computations (in the case of CH4 we considered the 6-3lG** geometry reported in ref. (2(d)). Furthermore, to verify the validity of the UHF approach in describing the transition state region, we investigated the potential energy surfaces for these two reactions with the MCSCF method and the 3-21G* basis set. The MCSCF program that we used is that recently implemented in GAUSSIAN go. The MCSCF active space (three orbitals and three electrons) required to give a correct description of the C-H/O-H bond breaking and forming consisted of the r~ (doubly occupied) and the (T* (vacant) orbitals associated with the C-H bond involved in the abstraction reaction and the singly occupied orbital pa associated with the non-bonding electron of the OH radical (see Scheme 1). Results and discussion
Our first aim is to define a minimal computational level which is capable of providing a reliable description of the potential surface for the series of reactions that we have considered. For this purpose we begin with a detailed discussion of the attacks on CH, and CH,Cl by the OH radical; the related results are collected in Table 1 and Fig. 1, and
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309
‘RCH
pu %H
++
H
X
\
o_
_
_
_
_
_
_
H2
/
‘---z
bY Scheme 1. Table 2 and Fig. 2 respectively. In Tables 1 and 2 we give the absolute and relative energies computed at the UHF and UHF/MP2 levels with the 3-21G*, 6-3 lG* and 6-3 lG** basis sets. In Tables 1 and 2 we have also collected the zero-order vibrational energy corrections (ZPE) and the computed activation energy values Ea.These activation energies include net zero-point vibrational energies, thermal energy corrections at 300K and an RT value of 0.59 kcalmol-‘; they can be compared with the experimental Arrhenius activation energies. In all cases the ZPE and the thermal corrections are those determined for a given reference optimized geometry: for example, the activation energies determined at the 3-21G*//3-21G* level and at the MP2/3-21G*//3-21G* level include the same ZPE (- 1.79 kcalmol-’ ) and the same thermal corrections (- 0.94 kcal mol-‘) obtained for the 3-21 G* optimized geometry. For both reactions a transition state corresponding to the attack on the C-H bond has been located. The geometry of the transition state for the reaction involving CH, is shown in Fig. 1, where we have reported the optimum values of the geometrical parameters determined at the various computational levels. As has already been pointed out in refs. 2(d) and 2(e), the methyl fragment is staggered with respect to the O-H bond at all the computa-
301 tional levels that we have considered, the eclipsed conformation being a second-order saddle point (SOSP). The three atoms involved in the transfer .C)are nearly collinear, with the O-H’(0 ...H'.. C angle assuming the values 171.7” (3-21G*), 175.9” (6-31G*) and 176.1” (6-31G**). Furthermore, the other geometrical parameters do not change dramatically when we compare the results obtained with the 3-21G*, 6-31G* and 6-31G** basis sets. The most significant differences can be found in the lengths of the breaking C-H and forming O-H bonds: the optimum lengths of the C-H bonds are in fact 1.364 A, 1.314A and 1.299 A at the 3-21G*, 6-31G* and 6-31G** levels respectively; the corresponding values of the O-H bond are 1.172 A, 1.2OOAand 1.205 A. Thus the reactantlike character of the transition state increases with the increasing accuracy of the basis set. To examine the product or reactant-like character of the transition states it is useful to define the quantity 8 = 6R,,/dR,_,where SRoH = R,_,/&-,,, and R,_, In these expressions S&n = Ro-n I&W,. and R,, are the lengths of the breaking C-H and forming O-H bonds respectively, and RC_H,eq and are the corresponding equilibrium distances %-H&q in the reactant (halomethane) and product (H,O) molecules. A value of unity for 8 corresponds to a transition state in which one bond is broken to the same extent as the other one is formed; a value greater than unity is associated with a product-like character of the transition state; a value lower than unity corresponds to a more reactant-like transition state. In the previous case the value of 0 decreases on passing from the 3-21G* to the 631G* and 6-31G** basis sets (0 = 1.039,0.979 and 0.938 respectively). The analytical Hessian has been computed for this transition structure at all computational levels and it is always characterized by a negative eigenvalue. The normal coordinate corresponding to the imaginary frequency is a linear combination of the new forming O-H’ bond and the breaking C-H’ bond. The first real frequency is associated with a normal coordinate which describes an almost free
302
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309
TABLE 1 Absolute energy E, relative energy 6E, zero-point vibrational energy correction ZPE and activation energy E, computed for the reaction CH, + *OH + *CH, + Hz0 at various computational levels (E,,,pt = 3.92 kcal mol-‘)
;.u.,
6E (kcalmol-I)
ZPE (kcalmol-‘)
E, (kcal mol- ’)
3-21G*//3-21G* Reactants Transition state
- 114.947106 - 114.900461
0.00 29.27
35.28 33.54
27.71
MP2/3-21G*//3-21G* Reactants
- 115.131132
Transition
-115.111918
12.06
10.50
MCSCF/3-21G*//MCSCF/3_2lG* Reactants Transition state
- 114.945784 - 114.920854
0.00 15.64
14.08
MP2/6-31G*//3-21G* Reactants
- 115.854969
0.00
Transition
state
- 115.842640
7.74
6-31G*//6-31G* Reactants Transition state
- 115.577447 - 115.527663
0.00 31.24
MP2/6-31G*//6-31G* Reactants Transition state
- 115.854562 - 115.839825
0.00 9.25
6-31G**//6-31G** Reactants Transition state
- 115.590036 - 115.543524
0.00 29.19
MP2/6-31G**//6-31G** Reactants Transition state
- 115.897854 - 115.886133
0.00 7.35
state
0.00
_
_ 6.18 34.99 33.89
30.33
10.16 35.58 33.77
_
27.58
5.74
“See ref. l(b).
rotation of the CH3 fragment around the C-H’ direction. Let us now discuss the energetics of this reaction. An activation energy of 27.71 kcalmoll’ has been obtained at the 3-21G*//3-21G* level. Thus this computational level largely overestimates the value of the activation energy (experimental value of 3.92 kcalmol-‘). A more realistic estimate of the barrier is obtained when correlation energy is taken into account: at the MP2/3-21G*//3-21G* level in fact the energy barrier significantly decreases (12.06 kcal mol-’ ) and the resulting activation energy becomes 10.50 kcal molli . The importance
of correlation energy in providing a value of the activation barriers in good agreement with experiment is stressed by the results obtained with the 6-31G* basis set, which in addition includes polarization d functions on carbon atoms and can give a better description of the correlation contribution. With this basis set we obtain an activation energy of 6.18 kcalmol-’ (MP2/6-31G*//3-21G* level), a value which is quite close to that determined experimentally. Very similar results were obtained using the 6-31G* and the 6-31G** optimized geometries. In these cases the activation energies are likewise overestimated when we neglect the contribution of
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309 0
=
f59.80
0
(60.10)
[60.15] c59.902
102.15
171.70
(100.17)
(175.93)
l99.911
[176.10] z
-
1.1719 (1 .1998) [1.2052] <1.2081>
1.0778
<103.61>~~
-kO (1.3135)
"*I"='
\w
1.0779
101.89
[1.2986]
(104.81) \
<1.3799>
[103.11]
(1.0791) Il.07951 H"
<1.0775>
<105.42> 0
Fig. 1. Structure of the transition state for H abstraction by *OH from CH, computed at the UHF/3-21G*, (UHF/631G*), [UHF/6-31G**] and (MCSCF/3-21G*) levels (Q is the dihedral angle between the two planes H-C-O and H-O-C).
correlation energies: 30.33 kcalmol-’ at the 631G*//6-3 lG* level and 27.58 kcalmol-’ at the 63 1G**//6-3 1G** level. These values significantly decrease when the correlation corrections are included and become 10.16 kcal mol-’ and 5.74 kcal mol- ’respectively. The results obtained in the study of the reaction between *OH and CH,Cl are very similar to those just described for methane. The transition state located in this case (Fig. 2) is almost identical to that found for CH, even if the C-Cl bond is now eclipsing the O-H bond: in this case the conformation in which the two C-H bonds are staggered to the O-H bond is a SOSP only 1.2 kcal mol- ’higher in energy (3-21G* value) with respect to the transition state. The three atoms involved in the transfer are almost collinear and the 0-H’-C angle does not change dramatically at the various computational levels (< OH’C is 172.2”, 176.1” and 175.2” at the 3-21G*, 6-31G* and 6-31G** levels respectively). Also the variations of the other geometrical parameters are fairly small on passing from the 3-21G* to the 6-31G* and 6-31G** basis sets. Again, the most significant change can be found in the value of the breaking C-H’ bond which is 1.367A at the 3-21G* level and becomes 1.313A and 1.299A at the 6-31G* and 6-31G** levels respectively (the parameter 8 changes from 1.058 to 0.970 and 0.966, in agreement with increas-
303
ing reactant-like character of the transition state). Only one imaginary frequency has been found, indicating that the structure represented in Fig. 2 is a real transition state. The analysis of the values collected in Table 2 shows that, as for CH,, at all computational levels, when correlation energy is neglected, the activation energy is largely overestimated. Furthermore, as in the case of CH,, the best values (3.13 kcalmol-‘, 5.08 kcal mol- ’and 3.16 kcal mol-’ at the MP2/63 1G*//3-21G*, MP2/6-3 1G*//6-3 1G* and MP2/631G**//6-31G ** levels respectively) are obtained when 3d polarization functions on carbon and oxygen atoms are included in the basis set; the effect of p polarizations functions on hydrogen atoms (6-31G** level) seems to be less important. The optimum geometries of the two transition states obtained at the MCSCF level using the 321G* basis set are also reported in Figs. 1 and 2 (values in angle brackets). They are ,:uite similar to those obtained at the UHF level with the same basis set. This finding is in agreement with the fact that the MCSCF wavefunction is dominated by the SCF configuration: the configuration interaction coefficients of this configuration are 0.983 and 0.985 in the two cases. This means that the contribution of the structure-dependent correlation is very small and that the UHF method can provide a satisfactory description of the topology of this reaction surface. Even if the MCSCF corrections to the wavefunction are very small, the multireference wavefunction partially introduces a dynamic correlation energy contribution, which causes a decrease of the energy barriers (from 27.71 to 14.08 kcalmol-’ for CH, and from 28.21 to 23.68 kcal mol-’ for CH,Cl). Since a limited active space has been used (three electrons in three orbitals) this contribution is small and the barriers are still significantly higher than the experimental values. The results obtained for these two reactions clearly demonstrate that the inclusion of correlation energy is essential to obtain reasonable activation energies, as already pointed out in refs. 2(d)
304
A. Bottoni et al./J. Mol. Struct. (Theochem) 279 (1993) 299-309
TABLE 2 Absolute energy E, relative energy 6E, zero-point vibrational energy correction ZPE and activation energy E, computed for the reaction CH,Cl + *OH + *CH,Cl + H,O at various computational levels (I&,,, = 2.61 kcalmol-r)
3-21G*//3-21G* Reactants Transition state
t.u.,
6E (kcal mol-r )
ZPE (kcalmol-r)
2calmolV’)
- 571.765225 - 571.719176
0.00 29.90
30.65 28.59
28.21
MP2/3-21G*//3-21G* Reactants
- 572.076763
0.00
Transition
- 572.060957
9.92
MCSCF/3-21G*//MCSCF/3-2lG* Reactants Transition state
- 571.779966 - 571.739532
0.00 25.37
-
MP2/6-31G*//3-21G* Reactants
- 574.876551
0.00
_
Transition
-
state
state
- 574.868869
4.82
6-31G*//6-31G* Reactants Transition state
- 574.475428 - 574.426097
0.00 30.95
MP2/6-31G*//6-31G* Reactants
- 574.876434
0.00
Transition
- 574.865546
6.83
6-31G**//6-31G** Reactants Transition state
- 574.48623 1 - 574.440246
0.00 28.86
MP2/6-31G**//6-31G** Reactants Transition state
- 574.911326 - 574.903561
0.00 4.87
state
_ 11.94
31.16 29.06
23.68
3.13
29.20
5.08 31.16 29.09
_
27.15
3.16
“See ref. l(b).
and 2(e). Furthermore, they suggest that the MP2/ 6-3 lG*//3-21 G* level is an adequate computational approach for studying the reactions of the OH radical with halomethanes. Consequently we have decided to study all the remaining reactions using single-point MP2 computations at the 3-21G* optimized geometries. Figures 3-8 show the optimized geometries of the transition structures (all characterized by one imaginary frequency) for the various reactions. Table 3 lists the corresponding total and relative energies for reactants and transition states and the computed activation energies. In all cases the transition structures that we have located are very similar to those determined for
CH4 and CHCl. These structures are all characterized by a nearly collinear arrangement of the C, H’ and 0 atoms with the lengths of the breaking C-H’ bond and of the newly forming O-H’ bond almost constant in the various cases and close to the values determined for CH, and CH,Cl (about 1.37 A for C-H’ and 1.16-l. 17 A for O-H’). This result is reflected by the almost constant value of the parameter 8 (in the range 1.05-l .09). Only for CHF, is the C-H’ distance larger (1.407 A), the O-H’ distance becoming shorter (1.121 A). This corresponds to a value of 1.140 for the parameter 8 and to a more pr’onounced product-like character of the transition state.
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309
@
= f118.38
305
(118.98) [118.78] <118.22>
1.0738 (1.0756) [1.0763] d.0733,
Fig. 2. Structure of the transition state for H abstraction by -OH from CH,Cl computed at the UHF/3-21G*, (UHF/631G*), [UHF/6-31G**] and (MCSCF/3-21G*) levels (@ is the dihedral angle between the two planes H-C-O and H-O-C).
of Figs. 3-8 shows that the halogenInspection carbon bond is eclipsed to the O-H bond in the OH * - - CH,F and OH. . * CHF, transition states (Figs. 3 and 8 respectively). For CHCl,F the situation is different: two transition states, TS, and TS, (see Fig. 7), have been located. The energies of the two transition states are almost identical, TS, being only 0.3 kcalmoll’ lower than TS,. While the TS, structure has a plane of symmetry (C, symmetry) with the C-F bond eclipsing the O-H bond, no symmetry element characterizes the TS, structure, in which the C-F and C-Cl’ bonds are approximately staggered with respect to the O-H bond. Furthermore, a more pronounced geometrical distor-
Fig. 4. Structure of the transition state for H abstraction by *OH from CH,Cl, computed at the UHF/3-21G* level (a is the dihedral angle between the two planes Cl-C-O and H-O-C).
tion with respect to a collinear arrangement of the 0, H’ and C atoms can be observed in TS, , in which the 0-H’-C angle becomes 164.7”. A similar distortion is found in the OH. . . CHF, transition state, in which this angle has a value of 167.2”. When only two halogen atoms are bonded to carbon, as in CH,Cl, (Fig. 4) and CH,F, (Fig. 6), the transition state is characterized by a staggered arrangement of the two halogen-carbon bonds with respect to the O-H bond, the transition state structure again possessing a C, symmetry. This symmetry disappears in the case of the OH * . . CH,ClF transition state (Fig. 5). In this case the O-H and C-F bonds become almost eclipsed, the dihedral angle H-O-C-F (Q) 0
=-9.18
O’= -126.49 a’=
109.31
104.85 t,H_j
Fig. 3. Structure of the transition state for H abstraction by *OH from CH,F computed at the UHF/3-21G* level (@ is the dihedral angle between the two planes H-C-O and H-O-C).
Fig. 5. Structure of the transition state for H abstraction by -OH from CH,ClF computed at the UHF/3-21G*, level (a, W and W’ are the dihedral angles between the two planes F-C-O and H-O-C, Cl-C-O and H-O-C, and H-C-O and H-O-C respectively).
306
A. Bottoni et al.lJ. Mol. Struct. (Theochem) 279 (1993) 299-309 (a)
TS2
0 = 38.18
4, 0 =
-78.6
QP’ =
157.12
Cl”
Fig. 6. Structure of the transition state for H abstraction by *OH from CH,F, computed at the UHF/3-21G* level (Q is the dihedral angle between the two planes F-C-O and H-O-C).
being
9.2”. A further
investigation
of the potential
CH,F, simiCH,Cl, the conformation with the two C-H bonds staggered to the O-H bond corresponds to an SOSP, whereas for CH,Cl, , CH,ClF and CH, F, an SOSP has been found when the C-H bond is eclipsed to the O-H bond. This SOSP is only slightly higher in energy than the transition state, the energy difference at the 3-21 G* level being 0.98 kcalmol-’ for CH,Cl, and 2.19 kcalmol-’ for CH,ClF. These small energy differences are in agreement with the very low value of the first real frequency, which characterizes all these transition structures, and which suggests an almost free rotation around the C-H’ direction (24cm-’ for CH,Cl, and 82cm-’ for CH,ClF). The activation energies computed at the various computational levels show the same behaviour already pointed out for CH, and CH,Cl and again emphasize the importance of the correlation contribution: they are in fact overestimated when this contribution is neglected, but become much more realistic at the MP2/6-31G*//3-21G* level. However, even if the MP2 activation energies are in reasonable agreement with experiment (except for CHCl, F, for which the computed activation energy is abnormally low and indicates a barrierless process), their trend is not always satisfactory when compared with the experimental values. For surface
larly
has shown
to what
that
occurs
in the case of
in
Fig. 7. Structure of the two transition states TS, (a) and TS, (b) for H abstraction by -OH from CHCl,F computed at the UHF/3-21G* level (for TS,, @ is the dihedral angle between the two planes Cl-C-O and H-O-C; for TS,, a’, @’and W’ are the dihedral angles between the two planes F-C-O and H-O-C, Cl’-C-O and H-O-C, and Cl”-C-O and H-O-C respectively).
Q
=*117.57
1.3336
Fig. 8. Structure of the transition state for H abstraction by *OH from CHF, computed at the UHF/3-21G* level (@ is the dihedral angle between the two planes F-C-0 and H-O-C).
A. Bottoni et al/J.
Mol. Strut.
(Theochem)
307
279 (1993) 299-309
TABLE 3 Absolute energy E, and relative energy 6E, zero-point vibrational energy correction ZPE, and activation energy E, computed for the reaction between various substituted halomethanes and the OH radical at various computational levels 6E
(kcalmol-I)
k.U.,
(A) CH,F + -OH + *CH*CH,F
+ H,O
-213.252121 -213.208213
MP2/6-31G*//3-21G* Reactants Transition state
- 214.857984 -214.851071
3-21G*//3-21G* Reactants Transition state
(E,,,,,
0.0 27.54
MP2/6-31G*//3-21G* Reactants
- 1033.898030
0.0
Transition
- 1033.894253
2.37
- 670.072042 - 670.026783
0.0 28.40
MP2/6-31G*//3-21G* Reactants Transiton state
- 673.887331 - 673.883152
0.0 2.62
3-21G*//3-21G* Reactants Transition state
0.00 29.45
MP2/6-31G*//3-21G* Reactants
-313.886075
0.0
Transition
- 313.879371
4.20
(E) CHCl,F
+ *OH + - CCI,F + H,O
3-21G*//3-21G* Reactants
26.72
_ 0.71
26.22 23.93
26.67
0.89
27.55 24.92
27.44
_ 2.19
(Ea,expt= 2.10kcalmol-‘)
T%
- 1126.882655 1126.837747 - 1126.837162
0.00 28.23 28.52
MP2/6-31G*//3-21G* Reactants
- 1132.913267
0.00
=I
25.05 22.70
(E,,_p, = 3.52 kcalmol-‘)
- 311.579332 -311.532359
state
2.71
(Ea,enpt= 2.28 kcal mol-‘)
3-21G*//3-21G* Reactants Transition state
(D) CH,F, + *OH + - CHF, + H,O
25.91
= 2.08 kcalmol-‘)
0.0 28.38
(C) CH,ClF + *OH + * CHClF + H,O
31.67 29.78
0.0 4.34
- 1028.576486 - 1028.531248 .-
state
E, (kcal mol-I)
(E._,,, = 3.75 kcalmol-‘)
3-21G*//3-21G* Reactants Transition state
(B) CH,C12 + - OH + - CHCl, + H,O
ZPE (kcal mol-‘)
-
19.78 17.43 17.26 -
26.59
26.81
308
A. Bottoni et al.lJ. Mol. Struct.
(Theochem)
279 (1993) 299-309
TABLE 3 (continued)
TSI
E
SE
(a.u.)
(kcal mol-‘)
- 1132.910742 - 1132.910303
TS, (F) CHF, + *OH + - CF, + H,O 3-21G*//3-21G* Reactants Transition state
(E,,e,,
1.58 1.86
E, (kcal mol-‘)
_
- 0.06 0.13
22.69 19.57
32.23
= 5.79 kcalmol-‘)
- 409.921956 - 409.866814
0.00 34.60
MP2/6-31G*//3-21G* Reactants
-412.928833
0.00
Transition
-412.917293
7.24
state
ZPE (kcalmol-‘)
_ 4.87
BSee ref. 1(b).
example, the value for CH,F, (2.19 kcalmol-‘) is with CH,Cl too small when compared (3.13 kcal mol-‘) and the value for CH, (6.18 kcal mol-‘) is in general too large. Furthermore, for CH,Cl, and CH,ClF, even if the computed activation energies parallel the experimental trend, their absolute values are too low. All these results indicate that, even if the MP2/631G*//3-21G* computational approach can provide a satisfactory description of the transition state geometries and reasonable values for the activation energies, a more accurate computation of the energetics of these reactions probably requires a further geometry optimization with a correlated wavefunction and a more extended basis set, a higher level of Moller-Plesset theory, and, possibly, tunnelling corrections. Conclusions In this paper we have reported ab initio UHF and MCSCF computations for the reaction of *OH with methane and various halomethanes. Two reactions (-OH + CH, and *OH + CH,Cl) have been investigated in detail using a UHF and an MCSCF wavefunction, and various basis sets of different accuracy. These computations have shown the following. (i) The UHF scheme can provide a satisfactory description of these reaction
surfaces. The MCSCF wavefunction is in fact dominated by the SCF configuration, and the MCSCF optimized geometries do not differ significantly from the UHF optimized geometries with the same basis set. (ii) The UHF optimized geometries of the transition states do not change dramatically using basis sets of different accuracy (3-21G*, 6-31G*, 6-31G**). (iii) To obtain reasonable values of the activation energies it is essential to take into account the dynamic correlation energy contributions on reactants and transition states. We have also shown that this contribution can be satisfactorily included by performing single-point MP2 computations at the 3-2 1G* optimized geometries with the 6-31G* basis set, and we have indicated the MP2/6-3 1G*//3-21 G* approach as the minimal computational level required to obtain a reasonable description of these reactions. Thus we have used this approach to investigate all the remaining reactions. In all cases we have found that in the absence of the correlation contribution the activation energies are overestimated with respect to the experimental values and only when this contribution is included do these values come into reasonable agreement with the experiment. Acknowledgements S.S.E. acknowledges support from Minister0 dell
A. Bottoni et al./J. Mol. Strut.
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(Theochem) 279 (1993) 299-309
Universita’ e della Ricerca Scientifica e Tecnologica, 40% programs.
3
References (a) G. Paraskevopoulos, D.L. Singleton and R.S. Irwin, J. Phys. Chem., 85 (1981) 561-564. (b) K.-M. Jeong and F. Kaufman, J. Phys. Chem., 86 (1982) 1808-1815, 1816-1821. (c) N. Cohen, Int. J. Chem. Kinet., 14 (1982) 13391362. (d) N. Cohen and SW. Benson, J. Phys. Chem., 91 (1987) 162-170. (e) S.S. Emmi, G. Beggiato, G. Casalbore-Miceli and P.G. Fuochi, J. Radioanal. Nucl. Chem. Lett., 93 (1985) 189. (a) M. Sana, G. Leroy and J.L. Villaveces, Theor. Chim. Acta, 65 (1984) 109-125. (b) G. Leroy, M. Sana and A. Tinant, Can. J. Chem., 63 (1985) 1447-1456. (c) A.E. Dorigo and K.N. Houk, J. Org. Chem., 53 (1988) 1650-1664. (d) T.N. Truong and D.G. Truhlar, J. Chem. Phys., 93 (1990) 1761-1769. (e) C. Gonzalez, J.J.W. McDouall and H.B. Schlegel, J. Phys. Chem., 94 (1990) 7467-7471.
4
5 6 7 8 9 10
(f) A.C. Lasaga and G.V. Gibbs, Geophys. Res. Lett., 18 (1991) 1217-1220. M.J. Frisch, M.H. Gordon, H.B. Schlegel, K. Raghavachari, J.S. Binkley, C. Gonzalez, D.J. Defrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R. Martin, L.R. Kahn, J.J.P. Stewart, E.M. Fluder, S. Topiol and J.A. Pople, GAUSSIAN 88, Gaussian Inc., Pittsburgh, PA, 1988. M.J. Frisch, M.H. Gordon, G.W. Trucks, J.B. Foresman, H.B. Schlegel, K. Raghavachari, M.A. Robb, J.S. Binkley, C. Gonzalez, D.J. Defrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R. Martin, L.R. Kahn, J.J.P. Stewart, S. Topiol and J.A. Pople, GAUSSIAN go,Gaussian Inc., Pittsburgh, PA, 1990. H.B. Schlegel, J. Comput. Chem., 3 (1982) 214. J.S. Binkley, J.A. Pople and W.J. Hehre, J. Am. Chem. Sot., 102 (1980) 939. J.S. Binkley and J.A. Pople, Int. J. Quantum Chem., 9 (1975) 229. P.C. Hariharan and J.A. Pople, Theor. Chim. Acta, 28 (1973) 213. C. Sosa and H.B. Schlegel, Int. J. Quantum Chem., 29 (1986) 1001; 30 (1987) 155. P.C. Hariharan and J.A. Pople, Chem. Phys. Lett., 66 (1972) 217.
Structure
Elsevier Science Publishers
(Theochem),
279 (1993) 299-309
299
B.V., Amsterdam
An ab initio study of H abstraction in halogen-substituted methanes by the *OH radical Andrea
Botton?,
Gabriella
Poggi”
and
Salvatore
S. Emmib
aDipartimento di Chimica “G. Ciamician” deN’Universitci di Bologna, bIstituto di Fotochimica
e Radiazioni d’Alta Energia
(FRAE)
Via Selmi 2, 40126 Bologna (Italy)
de1 CNR, via de’ Castagnoli I, 40126 Bologna (Italy)
(Received 8 June 1992)
Abstract The H-abstraction reaction by the OH radical from methane and various halomethanes (CH,Cl, CH,F, CH,Cl,, CH,ClF, CH,F,, CHCl,F and CHF,) was studied using ab initio unrestricted Hartree-Fock (UHF) and multiconfigurational self-consistent field (MCSCF) computational methods. It was found that the structure of the transition state determined at the UHF and MCSCF levels is very similar and that the topology of these reaction surfaces is satisfactorily described using a UHF wavefunction. It is pointed out that to obtain values of the activation energies in good agreement with experiment it is essential to take into account the correlation energy contribution on reactants and transition states. The MP2/6-31G*//3-21G* approach (6-31G* single-point second-order Moller-Plesset (MP2) computations on the 3-21G* optimized geometries) is proposed as the minimal computational level needed to obtain a description of these reactions in reasonable agreement with the experimental evidence.
Introduction Methane and halo-substituted methanes are very important species in atmospheric chemistry. CH, together with CO, seem to play a major role in determining the greenhouse effect, while fluoroand chloro-substituted methanes are together considered key factors responsible for the destruction of the stratospheric ozone layer. A reaction which accounts for most of the destruction of methane in the troposphere is the oxidation by hydroxyl radicals:
CH, + -OH --, CH, + H,O
(1)
The same type of reaction occurring with halomethanes is considered an important interceptor mechanism which can remove these gases from the Correspondence to: A. Bottoni, Dipartimento di Chimica “G. Ciamician” dell’Universit9 di Bologna, Via Selmi 2, 40126 Bologna, Italy.
troposphere and hence prevent their transport into the stratosphere. Furthermore, the reaction of hydroxyl radical with CH, is of special interest because it represents a prototype for the principal initiator step in hydrocarbon combustion. For these reasons hydroxyl radical reactions with methane and halo-substituted methanes have attracted considerable attention from experimentalists [l]. In particular, various experimental measurements of the rate coefficients over a wide range of temperatures have been performed both for reaction (1) and for reactions involving chloro- and fluoro-substituted methanes that contain at least one abstractable H atom [l(b)]. Reaction (1) has also been studied from a theoretical point of view and a few ab initio calculations with accurate basis sets have recently been performed [2]. Conventional transition state theory and tunnelling corrections based on the Wigner expression [2(e)] or the Eckart model [2(d)] have been used to predict rate constants and activation
0166-1280/93/$06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
300
A. Bottoni et a1.l.l. Mol. Strut.
energies and to explain the significant curvature at low temperature observed in experimental Arrhenius diagrams. These studies have shown that the choice of accurate basis sets and the inclusion of correlation energy corrections have a significant effect on transition state vibrational frequencies and are definitely needed to reproduce the experimental activation energies. Since ab initio studies have so far been limited to the oxydryl-methane H-abstraction reaction and no calculations are available which explore on an ab initio basis the effect of systematic structural changes such as halogen substitution near the reaction site, we decided to investigate the potential energy surface associated with the reactions of various fluoro- and chloro-substituted methanes with the OH radical. In the present paper we report the results of ab initio calculations at the unrestricted Hartree-Fock (UHF), UHF second order Moller-Plesset (UHF/MP2) and multiconfigurational self-consistent field (MCSCF) computational levels of the structures and energetics of reactants and transition states for the oxydryl abstraction reaction involving methane and the following halomethanes: CH,Cl, CH, F, CH,Cl,, CH,ClF, CH,F,, CHCl,F and CHF,. For two examples (CH, and CH,Cl) we describe the results obtained with various basis sets of double-zeta quality to establish the minimum computational level required to obtain an accurate description of the reaction surface. Computational
method
All the ab initio molecular computations reported in this paper were performed with the GAUSSIAN 8s [3] and GAUSSIAN 90 [4] series of programs. The restricted Hartree-Fock (RHF) theory was used for closed-shell systems (CH, and the various halomethanes) and the UHF theory for open-shell systems like the OH radical and the transition states. The geometries of the various critical points were fully optimized with the gradient method [5] at the 3-21G* [6] level (3-21G*// 3-21G* computations) and the nature of each
(Theochem) 279 (1993) 299-309
critical point was characterized by computing the harmonic vibrational frequencies. The contribution of dynamic correlation to activation energies was evaluated by an MP2 perturbation treatment [7] and the overall energetics of the reactions was obtained with single-point MP2 computations at the 6-31G* [8] level on the 3-21G* optimized geometries (MP2/6-31G*//3-21G* computations). As suggested by Sosa and Schlegel [9] we used spin-projected MP2 energies to cancel the spin contamination which affects the transition structures and which can be responsible for an overestimation of the reaction barriers. To check the reliability of our computational approach, for both CH, + *OH and CH,Cl + *OH reactions, we also optimized the geometries of reactants and transition states with the 6-31G* and 6-31G** [lo] basis sets (double-zeta plus polarization) and at these levels we carried out single point MP2 computations (in the case of CH4 we considered the 6-3lG** geometry reported in ref. (2(d)). Furthermore, to verify the validity of the UHF approach in describing the transition state region, we investigated the potential energy surfaces for these two reactions with the MCSCF method and the 3-21G* basis set. The MCSCF program that we used is that recently implemented in GAUSSIAN go. The MCSCF active space (three orbitals and three electrons) required to give a correct description of the C-H/O-H bond breaking and forming consisted of the r~ (doubly occupied) and the (T* (vacant) orbitals associated with the C-H bond involved in the abstraction reaction and the singly occupied orbital pa associated with the non-bonding electron of the OH radical (see Scheme 1). Results and discussion
Our first aim is to define a minimal computational level which is capable of providing a reliable description of the potential surface for the series of reactions that we have considered. For this purpose we begin with a detailed discussion of the attacks on CH, and CH,Cl by the OH radical; the related results are collected in Table 1 and Fig. 1, and
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309
‘RCH
pu %H
++
H
X
\
o_
_
_
_
_
_
_
H2
/
‘---z
bY Scheme 1. Table 2 and Fig. 2 respectively. In Tables 1 and 2 we give the absolute and relative energies computed at the UHF and UHF/MP2 levels with the 3-21G*, 6-3 lG* and 6-3 lG** basis sets. In Tables 1 and 2 we have also collected the zero-order vibrational energy corrections (ZPE) and the computed activation energy values Ea.These activation energies include net zero-point vibrational energies, thermal energy corrections at 300K and an RT value of 0.59 kcalmol-‘; they can be compared with the experimental Arrhenius activation energies. In all cases the ZPE and the thermal corrections are those determined for a given reference optimized geometry: for example, the activation energies determined at the 3-21G*//3-21G* level and at the MP2/3-21G*//3-21G* level include the same ZPE (- 1.79 kcalmol-’ ) and the same thermal corrections (- 0.94 kcal mol-‘) obtained for the 3-21 G* optimized geometry. For both reactions a transition state corresponding to the attack on the C-H bond has been located. The geometry of the transition state for the reaction involving CH, is shown in Fig. 1, where we have reported the optimum values of the geometrical parameters determined at the various computational levels. As has already been pointed out in refs. 2(d) and 2(e), the methyl fragment is staggered with respect to the O-H bond at all the computa-
301 tional levels that we have considered, the eclipsed conformation being a second-order saddle point (SOSP). The three atoms involved in the transfer .C)are nearly collinear, with the O-H’(0 ...H'.. C angle assuming the values 171.7” (3-21G*), 175.9” (6-31G*) and 176.1” (6-31G**). Furthermore, the other geometrical parameters do not change dramatically when we compare the results obtained with the 3-21G*, 6-31G* and 6-31G** basis sets. The most significant differences can be found in the lengths of the breaking C-H and forming O-H bonds: the optimum lengths of the C-H bonds are in fact 1.364 A, 1.314A and 1.299 A at the 3-21G*, 6-31G* and 6-31G** levels respectively; the corresponding values of the O-H bond are 1.172 A, 1.2OOAand 1.205 A. Thus the reactantlike character of the transition state increases with the increasing accuracy of the basis set. To examine the product or reactant-like character of the transition states it is useful to define the quantity 8 = 6R,,/dR,_,where SRoH = R,_,/&-,,, and R,_, In these expressions S&n = Ro-n I&W,. and R,, are the lengths of the breaking C-H and forming O-H bonds respectively, and RC_H,eq and are the corresponding equilibrium distances %-H&q in the reactant (halomethane) and product (H,O) molecules. A value of unity for 8 corresponds to a transition state in which one bond is broken to the same extent as the other one is formed; a value greater than unity is associated with a product-like character of the transition state; a value lower than unity corresponds to a more reactant-like transition state. In the previous case the value of 0 decreases on passing from the 3-21G* to the 631G* and 6-31G** basis sets (0 = 1.039,0.979 and 0.938 respectively). The analytical Hessian has been computed for this transition structure at all computational levels and it is always characterized by a negative eigenvalue. The normal coordinate corresponding to the imaginary frequency is a linear combination of the new forming O-H’ bond and the breaking C-H’ bond. The first real frequency is associated with a normal coordinate which describes an almost free
302
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309
TABLE 1 Absolute energy E, relative energy 6E, zero-point vibrational energy correction ZPE and activation energy E, computed for the reaction CH, + *OH + *CH, + Hz0 at various computational levels (E,,,pt = 3.92 kcal mol-‘)
;.u.,
6E (kcalmol-I)
ZPE (kcalmol-‘)
E, (kcal mol- ’)
3-21G*//3-21G* Reactants Transition state
- 114.947106 - 114.900461
0.00 29.27
35.28 33.54
27.71
MP2/3-21G*//3-21G* Reactants
- 115.131132
Transition
-115.111918
12.06
10.50
MCSCF/3-21G*//MCSCF/3_2lG* Reactants Transition state
- 114.945784 - 114.920854
0.00 15.64
14.08
MP2/6-31G*//3-21G* Reactants
- 115.854969
0.00
Transition
state
- 115.842640
7.74
6-31G*//6-31G* Reactants Transition state
- 115.577447 - 115.527663
0.00 31.24
MP2/6-31G*//6-31G* Reactants Transition state
- 115.854562 - 115.839825
0.00 9.25
6-31G**//6-31G** Reactants Transition state
- 115.590036 - 115.543524
0.00 29.19
MP2/6-31G**//6-31G** Reactants Transition state
- 115.897854 - 115.886133
0.00 7.35
state
0.00
_
_ 6.18 34.99 33.89
30.33
10.16 35.58 33.77
_
27.58
5.74
“See ref. l(b).
rotation of the CH3 fragment around the C-H’ direction. Let us now discuss the energetics of this reaction. An activation energy of 27.71 kcalmoll’ has been obtained at the 3-21G*//3-21G* level. Thus this computational level largely overestimates the value of the activation energy (experimental value of 3.92 kcalmol-‘). A more realistic estimate of the barrier is obtained when correlation energy is taken into account: at the MP2/3-21G*//3-21G* level in fact the energy barrier significantly decreases (12.06 kcal mol-’ ) and the resulting activation energy becomes 10.50 kcal molli . The importance
of correlation energy in providing a value of the activation barriers in good agreement with experiment is stressed by the results obtained with the 6-31G* basis set, which in addition includes polarization d functions on carbon atoms and can give a better description of the correlation contribution. With this basis set we obtain an activation energy of 6.18 kcalmol-’ (MP2/6-31G*//3-21G* level), a value which is quite close to that determined experimentally. Very similar results were obtained using the 6-31G* and the 6-31G** optimized geometries. In these cases the activation energies are likewise overestimated when we neglect the contribution of
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309 0
=
f59.80
0
(60.10)
[60.15] c59.902
102.15
171.70
(100.17)
(175.93)
l99.911
[176.10] z
-
1.1719 (1 .1998) [1.2052] <1.2081>
1.0778
<103.61>~~
-kO (1.3135)
"*I"='
\w
1.0779
101.89
[1.2986]
(104.81) \
<1.3799>
[103.11]
(1.0791) Il.07951 H"
<1.0775>
<105.42> 0
Fig. 1. Structure of the transition state for H abstraction by *OH from CH, computed at the UHF/3-21G*, (UHF/631G*), [UHF/6-31G**] and (MCSCF/3-21G*) levels (Q is the dihedral angle between the two planes H-C-O and H-O-C).
correlation energies: 30.33 kcalmol-’ at the 631G*//6-3 lG* level and 27.58 kcalmol-’ at the 63 1G**//6-3 1G** level. These values significantly decrease when the correlation corrections are included and become 10.16 kcal mol-’ and 5.74 kcal mol- ’respectively. The results obtained in the study of the reaction between *OH and CH,Cl are very similar to those just described for methane. The transition state located in this case (Fig. 2) is almost identical to that found for CH, even if the C-Cl bond is now eclipsing the O-H bond: in this case the conformation in which the two C-H bonds are staggered to the O-H bond is a SOSP only 1.2 kcal mol- ’higher in energy (3-21G* value) with respect to the transition state. The three atoms involved in the transfer are almost collinear and the 0-H’-C angle does not change dramatically at the various computational levels (< OH’C is 172.2”, 176.1” and 175.2” at the 3-21G*, 6-31G* and 6-31G** levels respectively). Also the variations of the other geometrical parameters are fairly small on passing from the 3-21G* to the 6-31G* and 6-31G** basis sets. Again, the most significant change can be found in the value of the breaking C-H’ bond which is 1.367A at the 3-21G* level and becomes 1.313A and 1.299A at the 6-31G* and 6-31G** levels respectively (the parameter 8 changes from 1.058 to 0.970 and 0.966, in agreement with increas-
303
ing reactant-like character of the transition state). Only one imaginary frequency has been found, indicating that the structure represented in Fig. 2 is a real transition state. The analysis of the values collected in Table 2 shows that, as for CH,, at all computational levels, when correlation energy is neglected, the activation energy is largely overestimated. Furthermore, as in the case of CH,, the best values (3.13 kcalmol-‘, 5.08 kcal mol- ’and 3.16 kcal mol-’ at the MP2/63 1G*//3-21G*, MP2/6-3 1G*//6-3 1G* and MP2/631G**//6-31G ** levels respectively) are obtained when 3d polarization functions on carbon and oxygen atoms are included in the basis set; the effect of p polarizations functions on hydrogen atoms (6-31G** level) seems to be less important. The optimum geometries of the two transition states obtained at the MCSCF level using the 321G* basis set are also reported in Figs. 1 and 2 (values in angle brackets). They are ,:uite similar to those obtained at the UHF level with the same basis set. This finding is in agreement with the fact that the MCSCF wavefunction is dominated by the SCF configuration: the configuration interaction coefficients of this configuration are 0.983 and 0.985 in the two cases. This means that the contribution of the structure-dependent correlation is very small and that the UHF method can provide a satisfactory description of the topology of this reaction surface. Even if the MCSCF corrections to the wavefunction are very small, the multireference wavefunction partially introduces a dynamic correlation energy contribution, which causes a decrease of the energy barriers (from 27.71 to 14.08 kcalmol-’ for CH, and from 28.21 to 23.68 kcal mol-’ for CH,Cl). Since a limited active space has been used (three electrons in three orbitals) this contribution is small and the barriers are still significantly higher than the experimental values. The results obtained for these two reactions clearly demonstrate that the inclusion of correlation energy is essential to obtain reasonable activation energies, as already pointed out in refs. 2(d)
304
A. Bottoni et al./J. Mol. Struct. (Theochem) 279 (1993) 299-309
TABLE 2 Absolute energy E, relative energy 6E, zero-point vibrational energy correction ZPE and activation energy E, computed for the reaction CH,Cl + *OH + *CH,Cl + H,O at various computational levels (I&,,, = 2.61 kcalmol-r)
3-21G*//3-21G* Reactants Transition state
t.u.,
6E (kcal mol-r )
ZPE (kcalmol-r)
2calmolV’)
- 571.765225 - 571.719176
0.00 29.90
30.65 28.59
28.21
MP2/3-21G*//3-21G* Reactants
- 572.076763
0.00
Transition
- 572.060957
9.92
MCSCF/3-21G*//MCSCF/3-2lG* Reactants Transition state
- 571.779966 - 571.739532
0.00 25.37
-
MP2/6-31G*//3-21G* Reactants
- 574.876551
0.00
_
Transition
-
state
state
- 574.868869
4.82
6-31G*//6-31G* Reactants Transition state
- 574.475428 - 574.426097
0.00 30.95
MP2/6-31G*//6-31G* Reactants
- 574.876434
0.00
Transition
- 574.865546
6.83
6-31G**//6-31G** Reactants Transition state
- 574.48623 1 - 574.440246
0.00 28.86
MP2/6-31G**//6-31G** Reactants Transition state
- 574.911326 - 574.903561
0.00 4.87
state
_ 11.94
31.16 29.06
23.68
3.13
29.20
5.08 31.16 29.09
_
27.15
3.16
“See ref. l(b).
and 2(e). Furthermore, they suggest that the MP2/ 6-3 lG*//3-21 G* level is an adequate computational approach for studying the reactions of the OH radical with halomethanes. Consequently we have decided to study all the remaining reactions using single-point MP2 computations at the 3-21G* optimized geometries. Figures 3-8 show the optimized geometries of the transition structures (all characterized by one imaginary frequency) for the various reactions. Table 3 lists the corresponding total and relative energies for reactants and transition states and the computed activation energies. In all cases the transition structures that we have located are very similar to those determined for
CH4 and CHCl. These structures are all characterized by a nearly collinear arrangement of the C, H’ and 0 atoms with the lengths of the breaking C-H’ bond and of the newly forming O-H’ bond almost constant in the various cases and close to the values determined for CH, and CH,Cl (about 1.37 A for C-H’ and 1.16-l. 17 A for O-H’). This result is reflected by the almost constant value of the parameter 8 (in the range 1.05-l .09). Only for CHF, is the C-H’ distance larger (1.407 A), the O-H’ distance becoming shorter (1.121 A). This corresponds to a value of 1.140 for the parameter 8 and to a more pr’onounced product-like character of the transition state.
A. Bottoni et al/J. Mol. Struct. (Theochem) 279 (1993) 299-309
@
= f118.38
305
(118.98) [118.78] <118.22>
1.0738 (1.0756) [1.0763] d.0733,
Fig. 2. Structure of the transition state for H abstraction by -OH from CH,Cl computed at the UHF/3-21G*, (UHF/631G*), [UHF/6-31G**] and (MCSCF/3-21G*) levels (@ is the dihedral angle between the two planes H-C-O and H-O-C).
of Figs. 3-8 shows that the halogenInspection carbon bond is eclipsed to the O-H bond in the OH * - - CH,F and OH. . * CHF, transition states (Figs. 3 and 8 respectively). For CHCl,F the situation is different: two transition states, TS, and TS, (see Fig. 7), have been located. The energies of the two transition states are almost identical, TS, being only 0.3 kcalmoll’ lower than TS,. While the TS, structure has a plane of symmetry (C, symmetry) with the C-F bond eclipsing the O-H bond, no symmetry element characterizes the TS, structure, in which the C-F and C-Cl’ bonds are approximately staggered with respect to the O-H bond. Furthermore, a more pronounced geometrical distor-
Fig. 4. Structure of the transition state for H abstraction by *OH from CH,Cl, computed at the UHF/3-21G* level (a is the dihedral angle between the two planes Cl-C-O and H-O-C).
tion with respect to a collinear arrangement of the 0, H’ and C atoms can be observed in TS, , in which the 0-H’-C angle becomes 164.7”. A similar distortion is found in the OH. . . CHF, transition state, in which this angle has a value of 167.2”. When only two halogen atoms are bonded to carbon, as in CH,Cl, (Fig. 4) and CH,F, (Fig. 6), the transition state is characterized by a staggered arrangement of the two halogen-carbon bonds with respect to the O-H bond, the transition state structure again possessing a C, symmetry. This symmetry disappears in the case of the OH * . . CH,ClF transition state (Fig. 5). In this case the O-H and C-F bonds become almost eclipsed, the dihedral angle H-O-C-F (Q) 0
=-9.18
O’= -126.49 a’=
109.31
104.85 t,H_j
Fig. 3. Structure of the transition state for H abstraction by *OH from CH,F computed at the UHF/3-21G* level (@ is the dihedral angle between the two planes H-C-O and H-O-C).
Fig. 5. Structure of the transition state for H abstraction by -OH from CH,ClF computed at the UHF/3-21G*, level (a, W and W’ are the dihedral angles between the two planes F-C-O and H-O-C, Cl-C-O and H-O-C, and H-C-O and H-O-C respectively).
306
A. Bottoni et al.lJ. Mol. Struct. (Theochem) 279 (1993) 299-309 (a)
TS2
0 = 38.18
4, 0 =
-78.6
QP’ =
157.12
Cl”
Fig. 6. Structure of the transition state for H abstraction by *OH from CH,F, computed at the UHF/3-21G* level (Q is the dihedral angle between the two planes F-C-O and H-O-C).
being
9.2”. A further
investigation
of the potential
CH,F, simiCH,Cl, the conformation with the two C-H bonds staggered to the O-H bond corresponds to an SOSP, whereas for CH,Cl, , CH,ClF and CH, F, an SOSP has been found when the C-H bond is eclipsed to the O-H bond. This SOSP is only slightly higher in energy than the transition state, the energy difference at the 3-21 G* level being 0.98 kcalmol-’ for CH,Cl, and 2.19 kcalmol-’ for CH,ClF. These small energy differences are in agreement with the very low value of the first real frequency, which characterizes all these transition structures, and which suggests an almost free rotation around the C-H’ direction (24cm-’ for CH,Cl, and 82cm-’ for CH,ClF). The activation energies computed at the various computational levels show the same behaviour already pointed out for CH, and CH,Cl and again emphasize the importance of the correlation contribution: they are in fact overestimated when this contribution is neglected, but become much more realistic at the MP2/6-31G*//3-21G* level. However, even if the MP2 activation energies are in reasonable agreement with experiment (except for CHCl, F, for which the computed activation energy is abnormally low and indicates a barrierless process), their trend is not always satisfactory when compared with the experimental values. For surface
larly
has shown
to what
that
occurs
in the case of
in
Fig. 7. Structure of the two transition states TS, (a) and TS, (b) for H abstraction by -OH from CHCl,F computed at the UHF/3-21G* level (for TS,, @ is the dihedral angle between the two planes Cl-C-O and H-O-C; for TS,, a’, @’and W’ are the dihedral angles between the two planes F-C-O and H-O-C, Cl’-C-O and H-O-C, and Cl”-C-O and H-O-C respectively).
Q
=*117.57
1.3336
Fig. 8. Structure of the transition state for H abstraction by *OH from CHF, computed at the UHF/3-21G* level (@ is the dihedral angle between the two planes F-C-0 and H-O-C).
A. Bottoni et al/J.
Mol. Strut.
(Theochem)
307
279 (1993) 299-309
TABLE 3 Absolute energy E, and relative energy 6E, zero-point vibrational energy correction ZPE, and activation energy E, computed for the reaction between various substituted halomethanes and the OH radical at various computational levels 6E
(kcalmol-I)
k.U.,
(A) CH,F + -OH + *CH*CH,F
+ H,O
-213.252121 -213.208213
MP2/6-31G*//3-21G* Reactants Transition state
- 214.857984 -214.851071
3-21G*//3-21G* Reactants Transition state
(E,,,,,
0.0 27.54
MP2/6-31G*//3-21G* Reactants
- 1033.898030
0.0
Transition
- 1033.894253
2.37
- 670.072042 - 670.026783
0.0 28.40
MP2/6-31G*//3-21G* Reactants Transiton state
- 673.887331 - 673.883152
0.0 2.62
3-21G*//3-21G* Reactants Transition state
0.00 29.45
MP2/6-31G*//3-21G* Reactants
-313.886075
0.0
Transition
- 313.879371
4.20
(E) CHCl,F
+ *OH + - CCI,F + H,O
3-21G*//3-21G* Reactants
26.72
_ 0.71
26.22 23.93
26.67
0.89
27.55 24.92
27.44
_ 2.19
(Ea,expt= 2.10kcalmol-‘)
T%
- 1126.882655 1126.837747 - 1126.837162
0.00 28.23 28.52
MP2/6-31G*//3-21G* Reactants
- 1132.913267
0.00
=I
25.05 22.70
(E,,_p, = 3.52 kcalmol-‘)
- 311.579332 -311.532359
state
2.71
(Ea,enpt= 2.28 kcal mol-‘)
3-21G*//3-21G* Reactants Transition state
(D) CH,F, + *OH + - CHF, + H,O
25.91
= 2.08 kcalmol-‘)
0.0 28.38
(C) CH,ClF + *OH + * CHClF + H,O
31.67 29.78
0.0 4.34
- 1028.576486 - 1028.531248 .-
state
E, (kcal mol-I)
(E._,,, = 3.75 kcalmol-‘)
3-21G*//3-21G* Reactants Transition state
(B) CH,C12 + - OH + - CHCl, + H,O
ZPE (kcal mol-‘)
-
19.78 17.43 17.26 -
26.59
26.81
308
A. Bottoni et al.lJ. Mol. Struct.
(Theochem)
279 (1993) 299-309
TABLE 3 (continued)
TSI
E
SE
(a.u.)
(kcal mol-‘)
- 1132.910742 - 1132.910303
TS, (F) CHF, + *OH + - CF, + H,O 3-21G*//3-21G* Reactants Transition state
(E,,e,,
1.58 1.86
E, (kcal mol-‘)
_
- 0.06 0.13
22.69 19.57
32.23
= 5.79 kcalmol-‘)
- 409.921956 - 409.866814
0.00 34.60
MP2/6-31G*//3-21G* Reactants
-412.928833
0.00
Transition
-412.917293
7.24
state
ZPE (kcalmol-‘)
_ 4.87
BSee ref. 1(b).
example, the value for CH,F, (2.19 kcalmol-‘) is with CH,Cl too small when compared (3.13 kcal mol-‘) and the value for CH, (6.18 kcal mol-‘) is in general too large. Furthermore, for CH,Cl, and CH,ClF, even if the computed activation energies parallel the experimental trend, their absolute values are too low. All these results indicate that, even if the MP2/631G*//3-21G* computational approach can provide a satisfactory description of the transition state geometries and reasonable values for the activation energies, a more accurate computation of the energetics of these reactions probably requires a further geometry optimization with a correlated wavefunction and a more extended basis set, a higher level of Moller-Plesset theory, and, possibly, tunnelling corrections. Conclusions In this paper we have reported ab initio UHF and MCSCF computations for the reaction of *OH with methane and various halomethanes. Two reactions (-OH + CH, and *OH + CH,Cl) have been investigated in detail using a UHF and an MCSCF wavefunction, and various basis sets of different accuracy. These computations have shown the following. (i) The UHF scheme can provide a satisfactory description of these reaction
surfaces. The MCSCF wavefunction is in fact dominated by the SCF configuration, and the MCSCF optimized geometries do not differ significantly from the UHF optimized geometries with the same basis set. (ii) The UHF optimized geometries of the transition states do not change dramatically using basis sets of different accuracy (3-21G*, 6-31G*, 6-31G**). (iii) To obtain reasonable values of the activation energies it is essential to take into account the dynamic correlation energy contributions on reactants and transition states. We have also shown that this contribution can be satisfactorily included by performing single-point MP2 computations at the 3-2 1G* optimized geometries with the 6-31G* basis set, and we have indicated the MP2/6-3 1G*//3-21 G* approach as the minimal computational level required to obtain a reasonable description of these reactions. Thus we have used this approach to investigate all the remaining reactions. In all cases we have found that in the absence of the correlation contribution the activation energies are overestimated with respect to the experimental values and only when this contribution is included do these values come into reasonable agreement with the experiment. Acknowledgements S.S.E. acknowledges support from Minister0 dell
A. Bottoni et al./J. Mol. Strut.
309
(Theochem) 279 (1993) 299-309
Universita’ e della Ricerca Scientifica e Tecnologica, 40% programs.
3
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