Accelerated chemistry in the reaction between the hydroxyl radical and methanol at interstellar temperatures facilitated by tunnelling

TLDR: It is shown that, despite the presence of a barrier, the rate coefficient for the reaction between the hydroxyl radical (OH) and methanol--one of the most abundant organic molecules in space--is almost two orders of magnitude larger at 63 K than previously measured at ∼200 K.

Abstract: Understanding the abundances of molecules in dense interstellar clouds requires knowledge of the rates of gas-phase reactions between uncharged species. However, because of the low temperatures within these clouds, reactions with an activation barrier were considered too slow to play an important role. Here we show that, despite the presence of a barrier, the rate coefficient for the reaction between the hydroxyl radical (OH) and methanol--one of the most abundant organic molecules in space--is almost two orders of magnitude larger at 63 K than previously measured at ∼200 K. We also observe the formation of the methoxy radical product, which was recently detected in space. These results are interpreted by the formation of a hydrogen-bonded complex that is sufficiently long-lived to undergo quantum-mechanical tunnelling to form products. We postulate that this tunnelling mechanism for the oxidation of organic molecules by OH is widespread in low-temperature interstellar environments.

Figures

Figure 4. Variation of the rate coefficient for the reaction of OH with methanol as a function of total gas density at 82 ± 4 K. The uncertainty for each determination of k1 represents the 2 error from a linear-least squares fit to the variation of the pseudo-first-order rate coefficient k for the removal of OH as a function of methanol concentration (for an example see Figure S5). The bath gas used is nitrogen.

Figure 3. Removal of hydroxyl (OH) radicals and production of methoxy (CH3O) radicals in the reaction of OH with methanol at 82 K. Main figure: The temporal evolution of the decay of OH radicals (blue points) and the production of CH3O radicals (black points) at 82 ± 4 K, for a total gas density of 5×1016 molecule cm-3 and [CH3OH] = 2.06×10 14 molecule cm-3. The red solid lines are fits of the function A exp(-kt) (decay) and Equation 1 (growth) to the data, which yields pseudofirst-order rate coefficients of k = 8600 ± 280 s-1 (decay of OH) and 8870 ± 2800 s-1 (formation of CH3O), respectively. The black points for CH3O are scaled by a factor of 20 to aid comparison. Inset: Bimolecular plot showing the increase in the pseudo-first-order rate coefficients of k for the formation of methoxy radical as a function of [CH3OH], which yields the rate coefficient (3.6±1.4)×10-11 molecule-1 cm3 s-1.

Figure 2. Temperature dependence of the rate coefficient k1 for the reaction of OH radicals with methanol plotted in Arrhenius form together with a theoretical calculation. Data above 200 K are taken from a representative sample of literature data. Black squares Dillon et al. (2005) [5]; Open diamonds Hess et al (1989) [12]; Grey triangles Wallington and Kurylo (1987) [13]. The black filled circles are experimental data from the current study with 2 error bars and the data point at 82 K is an average of the three rate coefficients measured at different [N2]. The solid line is the calculation using the master equation incorporating quantum mechanical tunnelling.

Figure 1. Schematic potential energy surface for the reaction between OH and methanol based on the calculations of Xu and Lin [8] with all energies given in kJ mol-1 relative to the reagents. C refers to the pre-reaction hydrogen bonded complex formed between OH and methanol molecules, and TS-H and TS-M represent transition states located at the barriers to hydroxyl and methylhydrogen atom abstraction, respectively. The macroscopic rate coefficients k1,1 and k1,-1 correspond to the formation and re-dissociation of the complex and k1,2 corresponds to hydrogen abstraction via either of the two transition states.

Figure 5. Rate coefficients for the dissociation back to reactants (black line) and the product forming channel (red line) as a function of energy within the initially formed OH-methanol complex. The microcanonical rate coefficients k1,-1 (black) and k1,2 (red) calculated as a function of energy within the OH-methanol complex using the chemical master equation. The initial relative Boltzmann distribution of energies within the complex at 300 K (cyan line) and 70 K (blue line) (values not shown on axis for clarity) are also shown. The shaded portion represents the fraction of the 70 K Boltzmann population that have energies for which k1,2 > k1,-1. Only the 70 K Boltzmann distribution has a significant population for which for which k1,2 > k1,-1. The energy scale is shown relative to the bottom of the hydrogen bonded complex C (see Figure 1), which is bound by 1715 cm-1 (20.5 kJ mol-1).

Full text

This is a repository copy of Accelerated chemistry in the reaction between the hydroxyl
radical and methanol at interstellar temperatures facilitated by tunnelling..
White Rose Research Online URL for this paper:
http://eprints.whiterose.ac.uk/87629/
Version: Accepted Version
Article:
Shannon, RJ, Blitz, MA, Goddard, A et al. (1 more author) (2013) Accelerated chemistry in
the reaction between the hydroxyl radical and methanol at interstellar temperatures
facilitated by tunnelling. Nature Chemistry, 5 (9). 745 - 749. ISSN 1755-4330
https://doi.org/10.1038/nchem.1692
eprints@whiterose.ac.uk
https://eprints.whiterose.ac.uk/
Reuse
Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright
exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy
solely for the purpose of non-commercial research or private study within the limits of fair dealing. The
publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White
Rose Research Online record for this item. Where records identify the publisher as the copyright holder,
users can verify any specific terms of use on the publisher’s website.
Takedown
If you consider content in White Rose Research Online to be in breach of UK law, please notify us by
emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.

1
Accelerated chemistry in the reaction of OH with methanol at interstellar temperatures
facilitated by tunnelling
Robin J. Shannon
1
, Mark. A. Blitz
1,2
, Andrew Goddard
1
and Dwayne E. Heard
1,2
1
School of Chemistry, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK
2
National Centre for Atmospheric Science, University of Leeds, Woodhouse Lane, Leeds, LS2
9JT, UK

e-mail: d.e.heard@leeds.ac.uk
Understanding the abundances of molecules observed in dense interstellar clouds requires
knowledge of the rates of gas phase reactions between two neutral species. However,
reactions possessing an activation barrier were considered too slow to play any important
role at the low temperatures in these clouds. Here we show that despite the presence of a
barrier the rate coefficient for the reaction between the hydroxyl radical (OH) and methanol,
one of the most abundant organic molecules in space, is almost two orders of magnitude
larger at 63K than previously measured at ~200K. We also observe formation of the
methoxy radical product that was recently detected in space. These results are interpreted
through the formation of a hydrogen-bonded complex that is sufficiently long-lived to
undergo quantum mechanical tunnelling to form products. We postulate that this tunnelling
mechanism for the oxidation of organic molecules by OH is widespread in low temperature
interstellar environments.
The importance of neutral – neutral reactions has been highlighted in low temperature
environments such as the interstellar medium (ISM) and in dense molecular clouds of star forming
regions [1]. However, the chemical databases or networks used to model such environments
contain a relatively small number of this class of reaction [2]. Those reactions that have been
studied at relevant low temperatures (< 200 K) already occur quickly at room temperature, with
k
298K
> 10
-11
molecule
-1
cm
3
s
-1
[3-4], and do not possess any significant barrier to reaction. In this
paper, we show that despite the presence of an energy barrier, the reaction between OH and
methanol proceeds to products rapidly at very low temperatures, which we interpret via a
mechanism involving the formation of a weak hydrogen bonded association adduct, and quantum
mechanical tunnelling, as shown schematically in Figure 1. These two features are present in
many reactions involving hydrogen atom transfer and we propose that this behaviour exhibited by
the reaction of methanol with OH may be widespread under the low temperature conditions found
in space.

2
In the field of chemical kinetics, the rate at which a reaction proceeds is governed by the potential
energy surface (PES) upon which that reaction occurs. If there is an overall barrier, this acts as a
bottleneck to reaction and only molecules with sufficient energy are able to surmount this barrier
and proceed to products. The relationship between the rate coefficient, k, and temperature is often
represented by the Arrhenius equation:
T
Ea
eTk
R
A)(


(1)
where E
a
is an empirical parameter which is related to the overall barrier for reaction and A is
related to the frequency of reactant collisions that have the correct geometry for reaction. The rate
coefficient for the reaction between OH and methanol is relatively small at room temperature [5],
increasing at higher temperature as shown in Figure 2. Therefore, the reaction of OH with
methanol and other reactions with a significant barrier to products have hitherto been considered
too slow to be important in low temperature environments such as the ISM, dense molecular
clouds of star-forming regions, or the atmospheres of other planets. However, closer inspection of
Figure 2 reveals that the Arrhenius plot is curved, with the apparent activation barrier to reaction
decreasing as temperature is lowered. Deviation from Arrhenius behaviour is not uncommon and it
is often explained by the reaction not proceeding via a single-step, involving a weakly bound
intermediate [4], or due to the presence of quantum mechanical tunnelling (QMT) [6].
Weakly bound complexes have also been invoked to explain rate coefficients that increase
as the temperature is lowered [7]. Electronic structure calculations by Xu and Lin [8] for the
reaction between OH and methanol have shown the presence of a weakly-bound (~ 20 kJ mol
-1
)
hydrogen-bonded complex prior to the barrier to reaction, as shown in Figure 1. However, around
room temperature and above this weakly bound complex has too short a lifetime to significantly
influence the reactions kinetics. Experimental [9] and theoretical [10] studies have shown that the
reaction of OH with HNO
3
proceeds through tunnelling via an association complex at low
temperatures, with a modest negative temperature dependence of the rate coefficient being
observed below 300K. However, at the lowest temperature studied, 240 K, the measured rate
coefficient (2×10
-13
molecule
-1
cm
3
s
-1
) is still three orders of magnitude lower than would be
expected for a barrierless reaction. In a theoretical study, Herbst [11] showed that tunnelling in the
C
2
H + H
2
reaction leads to an observed negative temperature dependence in the rate coefficient,
but in the limit of 0 K the rate coefficient for this reaction was still predicted to be many orders of
magnitude lower than would be expected for a barrierless process. We postulate that a mechanism
involving a weakly bound complex may lead to rate coefficients at low temperature which are
similar in magnitude to those expected for an entirely barrierless reaction. Such a mechanism
could then play an important role in cold temperature environments such as in space. In this work
we show experimentally that the rate coefficient for the reaction of OH with methanol increases
dramatically as the temperature is lowered to 63 K. We also use the PES of Xu and Lin [8] and

3
statistical rate theory calculations using a master equation approach to show that the formation of
the OH-methanol complex and QMT can explain these findings.
Results
Figure 3 shows an example of the decay of OH radicals as they are removed by reaction with
methanol at 82 K. Kinetic analysis (see Methods and Supplementary Information Figures S4 and
S5) yields the removal rate coefficient, k

, and the rate coefficient for the reaction of OH and
methanol, k
1
, the latter obtained from the dependence of k

on the methanol concentration. Figure
2 compares values of k
1
measured here at 63 K and 82 K with previous results at higher
temperatures [5,12-13], demonstrating a significant enhancement in k
1
at lower temperatures, with
k
1,T=63K
/ k
1,T=210 K
= 72. Figure 4 shows that k
1
is essentially independent of the density of N
2
used.
The reaction of OH with methanol proceeds by abstraction of a hydrogen atom at either the
methyl or the hydroxyl site, with activation barriers of 4.2 and 15.0 kJ mol
-1
, respectively [8]:
OH + CH
3
OH  CH
2
OH + H
2
O (R1a)
OH + CH
3
OH  CH
3
O + H
2
O (R1b)
However, this reaction is not a single step. A schematic of the PES for the OH + CH
3
OH reaction
calculated by Xu and Lin [8] is shown in Figure 1, where it can be seen that the reaction consists of
three elementary reactions:
OH + CH
3
OH

1,1
k
C (R1,1)
C

1,1
k
OH + CH
3
OH (R1,-1)
C

2,1
k
products (either R1a or R1b) (R1,2)
The increase in the overall rate coefficient, k
1
, at low temperature can be understood by examining
how the relative contributions from these three elementary reactions change with temperature. At
high temperatures the complex (C) will be formed with a significant amount of internal energy and
will rapidly re-dissociate back to reactants. The reaction then appears to be a single step process
over a barrier to products with k
1
displaying a normal Arrhenius behaviour, as observed at higher
temperatures (Figure 2). However, as the temperature decreases C will be formed with less
internal energy on average and as such its lifetime with respect to re-dissociation will increase.
Therefore at very low temperatures, the rate coefficient k
1
will then be determined not by the
barrier associated with process R1,2, but instead by the barrierless association R1,1, i.e. the
reaction is complete once the complex is formed. The temperature at which this transition occurs is

4
controlled by the binding energy of the complex and the rate of tunnelling through the abstraction
barrier. The OH-methanol complex binding energy is ~ 20 kJ mol
-1
, and at room temperature the
kinetics are close to the high temperature regime and the rate coefficient is relatively small with k
1
= k
1a
+ k
1b
= 9 × 10
-13
cm
3
molecule
-1
s
-1
[5]. However, at the very low temperatures of the present
study the complex is relatively long-lived, and thus the measured rate coefficients are closer to the
collision encounter limit.
There are two possible fates for the complex at low temperatures when dissociation to
reactants is very slow. Either C is stabilised through unreactive collisions with the buffer gas (N
2
in
these experiments), which is not particularly interesting as this does not lead to chemical products.
Alternatively the OH moiety bound in C may abstract a hydrogen atom to form products, which is
chemically of greater interest. Abstraction via channels R1a and R1b over the barriers shown in
Figure 1 would appear to be ruled out as there is insufficient energy. However, in the case of
abstraction of light hydrogen atoms there is a significant probability of going through the barrier
rather than over it via quantum mechanical tunnelling (QMT) [6]. In a single-step process, QMT
normally manifests itself via non-Arrhenius behaviour being displayed at low temperatures, though
still with a positive activation energy and the rate coefficient decreasing at lower temperatures.
However, for the present system, QMT is not occurring in a single-step reaction from reactants to
products, rather from the hydrogen-bonded complex C, which has a lifetime that is rapidly
increasing as the temperature is lowered.
If the complex C were just being collisionally stabilised under our experimental conditions,
the rate coefficient k
1
would be expected to be strongly dependent on the total gas number density.
However, as shown in Figure 4, k
1
is almost independent of the total gas density, providing strong
evidence for the proposed QMT mechanism. Tunnelling corrections to rate coefficients calculated
by classical transition state theory (transmission coefficients) are now calculated routinely [14-15],
and Figure 2 shows the overall rate coefficient k
1
calculated by a chemical master equation
incorporating QMT using a parabolic Eckhart type barrier (see Methods and Supplementary
Information). Although there are more detailed approaches to calculating transmission coefficients
[16], the approach adopted here is to simply demonstrate that the weakly-bound complex/QMT
mechanism is capable of showing a marked increase in the rate coefficients at lower temperatures,
as seen in the experimental data in Figure 2.
To emphasize further the crucial role of tunnelling in this reaction, Figure 5 shows the
calculated individual rate coefficients, k
1,-1
and k
1,2
as a function of energy, together with the initial
Boltzmann distribution of energies within the complex, C, formed in the OH reaction with methanol
at both 300 K and 70 K. It is important to note the crossover of the rate coefficients k
1,-1
and k
1,2
at
~1750 cm
-1
, below which tunnelling becomes more favourable than re-dissociation of the complex.
At 300 K, the Boltzmann energy distribution has a negligible population of molecules below the k
1,-1
and k
1,2
crossing point, however, at 70 K, midway between the two experimental temperatures of

Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, the authors used a chemical master equation incorporating quantum mechanical tunnelling ( QMT ) using a parabolic Eckhart type barrier ( see Methods and Supplementary Information ). 

Q2. What is the effect of QMT on the rate coefficient of a complex?

In a single-step process, QMTnormally manifests itself via non-Arrhenius behaviour being displayed at low temperatures, thoughstill with a positive activation energy and the rate coefficient decreasing at lower temperatures. 

Q3. What is the rate coefficient of the complex C at low temperatures?

If the complex C were just being collisionally stabilised under their experimental conditions,the rate coefficient k1 would be expected to be strongly dependent on the total gas number density. 

Q4. What is the rate coefficient of the OH-methanol complex at low temperatures?

The OH-methanol complex binding energy is ~ 20 kJ mol-1, and at room temperature thekinetics are close to the high temperature regime and the rate coefficient is relatively small with k1 = k1a + k1b = 9 × 10 -13 cm3 molecule-1 s-1 [5]. 

Q5. What is the temperature in some star forming environments?

Although the temperatures in some star forming environmentsare close to 80 K [22], for other stellar and interstellar environments the temperatures areconsiderably lower, and the gas density is extremely low. 

Q6. What is the rate coefficient for the reaction of OH with methanol at a low?

In a theoretical study, Herbst [11] showed that tunnelling in theC2H + H2 reaction leads to an observed negative temperature dependence in the rate coefficient, but in the limit of 0 K the rate coefficient for this reaction was still predicted to be many orders ofmagnitude lower than would be expected for a barrierless process. 

Q7. What is the rate coefficient of the complex at low temperatures?

at the very low temperatures of the presentstudy the complex is relatively long-lived, and thus the measured rate coefficients are closer to thecollision encounter limit. 

Q8. What is the effect of QMT on the rate coefficient of the complex at low temperatures?

for the present system, QMT is not occurring in a single-step reaction from reactants toproducts, rather from the hydrogen-bonded complex C, which has a lifetime that is rapidlyincreasing as the temperature is lowered. 

Q9. What is the effect of the temperature on the ratecoefficient of the reaction between OH and?

In conclusion, this study has shown that for the reaction between OH and methanol the ratecoefficient displays a large negative dependence on temperature below 200 K, with an increase ofabout two orders of magnitude at ~70 K. 

Q10. What is the importance of neutral – neutral reactions in interstellar clouds?

The importance of neutral – neutral reactions has been highlighted in low temperatureenvironments such as the interstellar medium (ISM) and in dense molecular clouds of star formingregions [1]. 

Q11. What is the role of a pre-reaction hydrogen bonded OH complex in low?

Theseresults further highlight the role that a pre-reaction hydrogen bonded OH complex plays in lowtemperature kinetics, in this case the adduct is sufficiently long lived to facilitate tunnelling, themajority proceeding via the higher activation barrier to form CH3O. 

Q12. What is the relationship between the rate coefficient and temperature?

The relationship between the rate coefficient, k, and temperature is oftenrepresented by the Arrhenius equation:TEaeTk RA)( (1)where Ea is an empirical parameter which is related to the overall barrier for reaction and A is related to the frequency of reactant collisions that have the correct geometry for reaction. 

Q13. What is the rate coefficient for a OH-methanol reaction at a low temperature?

The authors postulate that a mechanisminvolving a weakly bound complex may lead to rate coefficients at low temperature which aresimilar in magnitude to those expected for an entirely barrierless reaction. 

Q14. At what temperature is the branching ratio for the channel forming CH3O?

At 298 K the master equation predicts(see Supplementary Information Figure S7) that the branching ratio for the channel forming CH3O is 0.36, which is consistent with experimental measurements which show CH2OH is the dominant product [18]. 

Q15. What is the significance of the reaction of OH with methanol?

Currently this reaction is not included in astrochemical networks and given the high abundances ofboth methanol and OH in star-forming regions, these results indicate that the reaction of OH withmethanol may provide a significant loss for methanol at low temperatures. 

Q16. What is the effect of QMT on the rate coefficients at low temperatures?

Although there are more detailed approaches to calculating transmission coefficients[16], the approach adopted here is to simply demonstrate that the weakly-bound complex/QMTmechanism is capable of showing a marked increase in the rate coefficients at lower temperatures,as seen in the experimental data in Figure 2.