The Astrophysical Journal, 611:605–614, 2004 August 10
# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.
THE GAS-PHASE FORMATION OF METHYL FORMATE IN HOT MOLECULAR CORES
Anne Horn,1 Harald Møllendal,1 Osamu Sekiguchi,1 Einar Uggerud,1 Helen Roberts,2 Eric Herbst,2
A. A. Viggiano,3 and Travis D. Fridgen4
Receivved 2004 April 1; accepted 2004 April 21
ABSTRACT
Methyl formate, HCOOCH3, is a well-known interstellar molecule prominent in the spectra of hot molecular
cores. The current view of its formation is that it occurs in the gas phase from precursor methanol, which is
synthesized on the surfaces of grain mantles during a previous colder era and evaporates while temperatures
increase during the process of high-mass star formation. The specific reaction sequence thought to form methyl
formate, the ion-molecule reaction between protonated methanol and formaldehyde followed by dissociative
recombination of the protonated ion [HCO(H)OCH3]+, has not been studied in detail in the laboratory. We
present here the results of both a quantum chemical study of the ion-molecule reaction between [CH3OH2]+ and
H2CO as well as new experimental work on the system. In addition, we report theoretical and experimental
studies for a variety of other possible gas-phase reactions leading to ion precursors of methyl formate. The
studied chemical processes leading to methyl formate are included in a chemical model of hot cores. Our results
show that none of these gas-phase processes produces enough methyl formate to explain its observed abundance.
Subject headingg
s: ISM: molecules — molecular data — molecular processes — radio lines: ISM
1. INTRODUCTION
dances in interstellar sources are determined by chemical kinetics and not by thermodynamics. The chemistry in hot cores
is thought to be a rather complex affair involving both dustsurface and gas-phase processes (Charnley et al. 1995; Millar
et al. 1991). During the era prior to star formation, gas-phase
processes produce a high abundance of carbon monoxide, some
of which is deposited on grain surfaces, where it is partially hydrogenated into formaldehyde (H2CO) and methanol (CH3OH).
Rising temperatures then result in the evaporation of the grain
mantles. Now in the gas phase, methanol, formaldehyde, and
other species previously in the grain mantles can be partially
converted into more complex organic species via gas-phase
ion-molecule and dissociative recombination reactions. For example, the commonly accepted (but poorly studied) reaction
sequence that leads to methyl formate is thought to be
Three isomeric C2H4O2 compounds—methyl formate
(HCOOCH3), acetic acid (CH3COOH), and glycolaldehyde
(HOCH2CHO)—have been detected in quiescent star-forming
regions of dense interstellar clouds. Associated with young
high-mass stellar objects, these regions are known as hot molecular cores and possess temperatures (100–300 K) and densities (106 cm3) somewhat above ambient interstellar values.
While methyl formate has been found in numerous sources
(Ellder et al. 1980; Millar et al. 1997; Nummelin et al. 2000),
acetic acid (Mehringer et al. 1997) and glycolaldehyde (Hollis
et al. 2000) have been found only in the Sgr B2(N-LMH)
source. The relative abundances of acetic acid, glycolaldehyde,
and methyl formate were recently determined to be 1:0.5:26
in that source (Hollis et al. 2001).
Ab initio quantum chemical calculations at the MP2/aug-ccpVTZ level of theory have been reported for the three isomeric
species (Dickens et al. 2001). It was found that acetic acid has
the lowest energy of the three, lying 72 kJ mol1 (1 kJ mol1 =
120 K) below methyl formate, which is in reasonable agreement with the experimental value of 92 kJ mol1 (Affey et al.
2001). Moreover, acetic acid was calculated to lie 118 kJ mol1
lower in energy than glycolaldehyde. No experimental value
is available for the latter species.
If the generation of the three compounds were determined
by thermodynamics alone, acetic acid would have been the
most abundant one, followed by methyl formate and finally by
glycolaldehyde, a result in disagreement with observation in
Sgr B2(N-LMH). But it is well known that chemical abun-
½CH3 OH2 þ þ H2 CO ! ½HC(OH)OCH3 þ þ H2 ;
followed by dissociative recombination with electrons:
½HC(OH)OCH3 þ þ e ! HCOOCH3 þ H:
With the assumption that these reactions occur efficiently,
large amounts of methyl formate can be synthesized within
104 –105 yr (Charnley et al. 1995; Millar et al. 1991; Caselli
et al. 1993).
The amount of experimental work on the first reaction has
been small (see, e.g., Millar et al. 1991 for a discussion), and
it has been unclear whether protonated methyl formate is a major product of the reaction. In this work we report the use of
the methods of quantum chemistry to consider the reaction
between protonated methanol and formaldehyde in detail. As
discussed below, we find that protonated methyl formate
cannot be formed efficiently because of a large potential barrier. Our finding prompted us to pursue additional experimental work on the system. Although the results of this work
are still somewhat ambiguous, we are reasonably convinced
that the reaction does not occur. Consequently, we consider
1
Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern,
NO-0135 Oslo, Norway.
2
Department of Physics, Ohio State University, Columbus, OH 432101106.
3
Air Force Research Laboratory, Space Vehicles Directorate, 29 Randolph
Road, Hanscom Air Force Base, MA 01731.
4
Department of Chemistry, Wilfrid Laurier University, Waterloo, ON N2L
3C5, Canada.
605
606
HORN ET AL.
other gas-phase pathways to methyl formate; these consist of
additional ion-molecule reactions as well as dissociative recombination processes. For one of the ion-molecule reactions
(CHþ
3 þ HCOOH), we have performed experimental work to
determine the branching fraction of the products. Our results
are then used in a model calculation of the gas-phase chemistry
in hot cores.
2. METHODS
2.1. Ab Initio Calculations
The quantum chemical calculations were carried out using
the GAUSSIAN 98 program package (Frisch et al. 1998)
running on an IBM cluster or on the HP SuperDome in Oslo,
Norway. Second-order Møller-Plesset perturbation theory (MP2;
Møller & Plesset 1934) was employed with the 6-31G(d,p)
basis set provided with the GAUSSIAN program (Frisch et al.
1998). All relevant stationary points of the reaction paths, including reactants, intermediates (complexes), transition-state
structures (corresponding to saddle points), and products of the
potential energy surface, were characterized by complete optimization of the molecular geometries.
The proton in protonated methyl formate can be bonded to
either one of the two oxygen atoms. In [HC(OH)OCH3]+ the
proton is bonded to the carbonyl oxygen atom, whereas in
[HC(O)O(H)CH3]+ it is attached to the ester oxygen atom.
Isomeric species such as these, which differ by the placement
of a hydrogen atom, are known as tautomers. Rotational isomerism around the central carbon-oxygen bond is possible for
each of these two tautomeric forms, so that several conformers,
or potential minima in the torsional motion, are possible for
both of them. The energy differences between the various conformers of each of the tautomers were found to be just a few
kJ mol1. The [HC(O)O(H)CH3]+ conformers were found to be
about 40 kJ mol1 less stable than their [HC(OH)OCH3]+
counterparts. The lowest energy [HC(OH)OCH3]+ structure,
labeled ‘‘I’’ and sketched in Figure 1, has a symmetry plane
(CS symmetry). Interestingly, the conformation of structure I is
Vol. 611
TABLE 1
Total Ab Initio MP2/6-31G(d,p) Energies Corrected for
Zero-Point Vibrational Energies
Species
Energy
(kJ mol1)
H2 ......................................................................
H2O ...................................................................
CO .....................................................................
HCO+ ................................................................
H2CO.................................................................
[H2COH]+..........................................................
HCOOH ............................................................
CHþ
3 ...................................................................
CH3OH..............................................................
CH2(OH)2 ..........................................................
[CH3OH2]+ ........................................................
[CH3OCH2]+ .....................................................
[HC(OH)OCH3]+ (I) .........................................
[CH3OH2 O = CH2]+ (II) ..............................
Transition state (III) ..........................................
[H2C = O H O = CH2]+ (IV) .....................
Transition state (V) ...........................................
[H2COCH2OH]+ (VI)........................................
Transition state (VII) ........................................
[CH3OH2 CO]+ (VIII) ...................................
Transition state (IX)..........................................
[H2COCH2OH O = CH2]+ (X)......................
Transition state (XI)..........................................
[H2COCH2OCH2OH]+ (XII) ............................
Transition state (XIII) .......................................
Transition state (XIV)a......................................
[HOCH2O(H)CH2OCH3]+ (XV)a .....................
Transition state (XVI)a......................................
[HOCH2OCH2O(H)CH3]+ (XVII)a ...................
3,011.89
200,057.58
296,724.49
297,334.18
299,716.84
300,430.59
496,818.74
103,218.83
302,796.39
499,794.87
303,569.01
403,243.66
600,356.65
600,407.10
603,158.30
600,288.84
600,220.87
600,264.32
600,062.87
600,349.05
600,240.18
900,062.49
900,029.80
900,051.50
899,959.30
603,290.35
903,144.36
903,079.58
903,185.16
a
Not shown in figures, but used to understand the minor
product at m=z ¼ 61 (63 with 18O) in the experimental study of
reaction (1a).
the same as that found in the crystal structure of the salt
[HC(OH)OCH3]+ [AsF6] (Minkwitz et al. 2000).
No detailed conformational optimizations were carried out
for the other species in our study because relatively small
energy differences are generally associated with conformational isomerism. The complete structures of the species investigated here are available from H. M. upon request.
Harmonic vibrational frequencies were obtained by diagonalizing the mass-weighted Cartesian force constant matrix
calculated from the analytical second derivatives of the total
energy (the Hessian). The harmonic frequencies obtained in
this manner were used to calculate the zero-point vibrational
energies. No scaling was employed. The total energies including zero-point vibrational energies for the species studied
here are listed in Table 1. The energy of structure I has been
used in the calculations of relative energies for the reaction
paths to be described below. The accuracy of the calculated
relative energies has been assessed to be within 30 kJ mol1
(Helgaker et al. 2000).
2.2. Complex Formation
Fig. 1.—Structures of stationary points for the reaction between formaldehyde and protonated methanol with important bond distances. In this and
subsequent figures, C atoms are dark and O atoms are gray.
Several species are found to be intermediate complexes, or
short-lived structures corresponding to potential minima, in
the reaction paths studied below. In addition, several of the
processes, known as association reactions, lead to the formation of a single species as a final product, also referred to as a
No. 1, 2004
METHYL FORMATE IN HOT MOLECULAR CORES
complex. The low pressure of a typical interstellar molecular
cloud will in most cases not permit collisional stabilization by a
third body during the short lifetime of the complex, and the
species is then likely to dissociate back to regenerate the reactants unless it is able to emit enough energy in the form of
radiation to stabilize itself. This latter process, known as radiative association, is only achievable if the complex cannot
dissociate rapidly into products. It is possible to estimate the
rate of radiative association based on the measured analogous
three-body process studied in the laboratory at much higher
pressure. Alternatively, it is possible to estimate the rate of
radiative association via statistical calculations plus an assumption or calculation of the rate of radiative emission of the
complex. We have used the thermal and modified-thermal statistical methods discussed by Bates & Herbst (1988) for several
association reactions below. Complexities arise in each case.
2.3. Electron Recombination
In the ion-molecule pathways considered here, methyl formate, HCOOCH3, can be formed in two ways: either by
electron dissociative recombination with simple protonated
methyl formate, [HC(OH)OCH3]+, in which case a hydrogen
atom is ejected, or by electron dissociative recombination involving a larger ionic structure, in which case the fragmentary
pattern is more complex. The more complex ionic structures
require large geometric changes to produce methyl formate
upon recombination. Such processes have been looked at in
detail by Osamura et al. (1999) for the recombination of
HC3NH+ and electrons; these authors found that significant
rearrangements of the skeletal structure could occur before
dissociation into fragments, albeit with small branching fractions. It is therefore prudent to consider such pathways here.
2.4. Experimental Methods
At the Hanscom Air Force Research Laboratory, highpressure experiments were performed on the reaction between
protonated methanol and formaldehyde with the AFRL selected ion flow tube experiment (SIFT). This apparatus has
been described in detail (Viggiano et al. 1990) previously, and
only a brief account is given here. The [CH3OH2]+ ion was
made by ionizing CH3OH in an electron impact ion source
operated in the 0.1 to 1 torr range. The primary [CH3OH]+ ion
reacts with CH3OH to form [CH3OH2]+ (Ikezoe et al. 1987).
The latter was mass selected and injected into a 1 m long flow
tube. The injection energy is not well defined because of stray
fields. Low injection energy resulted in less than 2% breakup
into CHþ
3 . A helium buffer gas maintained at 0.4 torr carried
the ions downstream, where they were sampled, injected into a
quadrupole mass spectrometer, and detected by a discrete
dynode multiplier. The H2CO, made by heating paraformaldehyde, was added through a flow controller midway in the
flow tube. No effort was made to characterize the H2CO, but
previous experiments have shown this method to work well
(Paulson et al. 1983; Viggiano et al. 1994). Rate coefficients
were measured by monitoring the decay of [CH3OH2]+ signal
as a function of H2CO flow. The reaction time was known
from the helium buffer flow rate and previous time-of-flight
measurements (Miller et al. 1984). Products were recorded
and the branching fractions extrapolated to a zero H2CO
concentration in order to account for secondary reactions.
In the low-pressure ion cyclotron resonance (ICR) experiments at Waterloo (Fridgen et al. 2001), additional attempts
were made to study the reaction of protonated methanol with
607
neutral formaldehyde. Gaseous formaldehyde and the vapor
from degassed methanol were introduced to the ICR cell via
heated precision leak valves at (1 2) ; 108 torr for formaldehyde and 5 ; 109 torr for methanol. Ionization was done
inside the ICR cell using 50 ms pulses of 70 eV electrons,
which initially formed the methanol cation and formaldehyde
cation, as well as expected fragments. A delay following ionization resulted in the production of protonated methanol
(mass-to-charge ratio, m=z, of 33). To clarify matters, it was
decided to also use 18O-labeled methanol, and the product of
interest, protonated methyl formate, would then be observed at
m=z ¼ 63 unhindered by any formaldehyde dimer impurity at
m=z ¼ 61.
In Oslo, the gas-phase reactions between CHþ
3 and HCOOH
were investigated using a Fourier transform ion cyclotron
resonance (FT-ICR) mass spectrometer (Apex 47e, Bruker
Daltonics, Billerica, Massachusetts). The methyl cation (CHþ
3)
was formed by electron impact (70 eV) on methane in the
external ion source. The mixture of ions produced in the process was transferred to the ICR cell, which contained the formic acid at a stationary and variable pressure in the range
3:8 ; 109 to 3:7 ; 108 mbar. All ions, except CHþ
3 , were then
ejected from the cell using correlated frequency sweep and
single-frequency shots in order to isolate the CHþ
3 ion. This ion
was then allowed to react with formic acid for a certain time
before the mass spectrum was recorded. By changing the reaction delay, the time development of the system was followed.
In separate experiments, each of the primary reaction products
was isolated by using correlated sweep after an appropriate
reaction time and thereafter allowed to react further with formic acid. This was necessary to determine the reaction scheme
unambiguously. The pressure gauge was calibrated using the
þ
NHþ
3 þ NH3 ! NH4 þ NH2 reaction assuming a rate coefficient k ¼ 2:20 ; 109 cm3 s1.
3. RESULTS CONCERNING REACTION PATHWAYS
3.1. Path (1)
In the first reaction studied,
½CH3 OH2 þ þ H2 C ¼ O ! ½HC(OH)OCH3 þ þ H2 ;
ð1aÞ
protonated methanol reacts with formaldehyde to produce
protonated methyl formate and molecular hydrogen. This reaction pathway has previously been thought to be the major
contributor to the formation of interstellar methyl formate
(Millar et al. 1991). The computed energies relative to the
combined energy of the reactants [CH3OH2]+ and H2C = O
(0 kJ mol1 by definition) of the various stationary species
along the reaction pathway, designated II, III, and I, are shown
in Figure 2. These energies were derived from those in Table 1.
Structures corresponding to these stationary points are depicted
in Figure 1, where bond lengths (in angstroms) of special interest are indicated (as they are in additional figures below).
The structure for the protonated methyl formate product labeled
by ‘‘I’’ represents the global minimum compared with other
conformers/tautomers.
In the first step of this mechanism, [CH3OH2]+ and H2C = O
combine to form a hydrogen-bonded complex [CH3OH2 O =
CH2]+ (complex II), where the dots indicate the H bond. The
formation of this complex occurs with no activation energy, a
common property of protonated molecules in the gas phase
(Uggerud 1992). We are unaware of any prior studies on the
existence of this complex, although its calculated structure is
608
HORN ET AL.
Fig. 2.—Potential energy surface (path [1a]) for the reaction between
formaldehyde and protonated methanol.
what is expected for a complex of this type. The H bond is
comparatively strong, since the potential energy is lowered by
118 kJ mol1 according to the calculations (Fig. 2).
The second reaction step leads to the formation of protonated
methyl formate, [HC(OH)OCH3]+ (product I) and H2. This
involves passage over a transition state (structure III), calculated to lie 128 kJ mol1 (15,000 K) higher in energy than the
reactants, before leading to the exothermic products. The energy of the transition state roughly corresponds to the activation energy of the total reaction; such a large activation energy
indicates that this reaction path cannot lead to the formation
of [HC(OH)OCH3]+ at any reasonable temperature. Thus the
standard reaction invoked to form methyl formate in hot cores
cannot take place according to our theoretical analysis.
Past experimental results do indicate a small product
channel for an ion of m=z ¼ 61, equivalent to that of protonated methyl formate, without determination of the structure
of the ion (D. K. Bohme 1990, private communication). It was
this result that was seized on by Millar et al. (1991) in support
of the importance of the reaction, which was first mentioned
by Blake et al. (1987). Indeed, Millar et al. (1991) noted with
an element of hopefulness that an inverse temperature dependence could, at low temperatures, lead to the formation of
the m=z ¼ 61 product with a near-Langevin rate. Because of
the importance of corroborating the existence of the m=z ¼ 61
product and possibly determining its structure, we undertook
additional experiments on the reaction, using both the highpressure SIFT apparatus and the low-pressure ICR device.
The experimental results from the SIFT, which show a minor
(5%) channel for m=z ¼ 61 at temperatures down to 193 K,
indicate that the dominant product ion under high-pressure
conditions is the associative product (m=z ¼ 63), presumably
the hydrogen-bonded complex [CH3OH2 O = CH2]+ (complex II), and also indicate, in agreement with older work
(Ikezoe et al. 1987), a significant channel with an ionic product
of m=z ¼ 45, presumably due to the products ½CH3 OCH2 þ þ
H2 O. Subsequent calculations show that this channel can indeed be reached from complex II followed by a transition state
that lies 65 kJ mol1 under the energy of reactants.
Experimental results from the Waterloo ICR apparatus at
room temperature and much lower pressure show that there is
no production of a cluster ion and that the m=z ¼ 45 ion
Vol. 611
product is dominant, but that there is a small channel at
m=z ¼ 61 of unknown structure. Earlier ICR work (Karpas &
Meot-Ner 1989) had also found the m=z ¼ 45 ion product to
dominate. The lack of existence of a cluster ion product at low
pressure is typical, since at these pressures three-body association is inefficient, especially if there is a competing barrierless exothermic channel. To determine if the small ion
channel at m=z ¼ 61 results from some impurity or secondary
reaction not involving methanol in the system, 18O-enriched
methanol was used, and a small amount of m=z ¼ 63 product
(1%) obtained. So, the results of both experiments confirm
that there is indeed a minor channel leading to an ion that
might be protonated methyl formate or some other isomer.
Given this result, we again tried with quantum theoretical
methods to find a reaction pathway from reactants to an ion
product + H2. Unsuccessful searches for more favorable transition structures for the indicated transformation than the one
reported shown in Figure 1 were made. We conclude that formation of protonated methyl formate via reaction (1a) is most
unlikely.
But what process or processes cause the experimental findings of an ion of the correct mass to be protonated methyl
formate? Paraformaldehyde, the laboratory source for formaldehyde, is likely to be contaminated by small amounts of water.
Heating of the contaminated paraformaldehyde will generate
the gaseous hydrate of formaldehyde, CH2(OH)2, known as
methanediol. Detailed calculations show that methanediol, in
turn, can react with the product [CH3OCH2]+ to form an isomer
of protonated methyl formate via the exothermic process
½CH3 OCH2 þ þ CH2 (OH)2 ! ½HOCH2 OCH2 þ þ CH3 OH:
According to our calculations, an initial complex is first
formed between methanediol and [CH3OCH2]+, lowering the
energy by 106 kJ mol1. A transition state with an energy
41 kJ mol1 less than that of the starting species is then passed
to produce [HOCH2OCH2O(H)CH3]+, which is 147 kJ mol1
more stable than the starting species. Its dissociation then
yields [H2COCH2OH]+ (structure VI), shown in Figure 3, and
methanol. The combined energies of these two species are
22 kJ mol1 less than the combined energies of CH2(OH)2 and
[CH3OCH2]+. If m=z ¼ 61 (63 if 18O-enriched methanol is
used) is in fact produced by the reaction of CH3OCH2+ and
Fig. 3.—Structures of stationary points for the reaction between formaldehyde and protonated formaldehyde with important bond distances.
No. 1, 2004
METHYL FORMATE IN HOT MOLECULAR CORES
609
methanediol in the laboratory experiments, then this would be
consistent with the calculations that show that protonated
methyl formate cannot be formed via reaction (1a).
If the complete reaction does not occur, the radiative association might be competitive, as long as the collision complex
does not dissociate too quickly to form [CH3OCH2]+. The rate
coefficient for the radiative association to form the intermediate
complex in reaction (1a),
½CH3 OH2 þ þ H2 C ¼ O ! ½CH3 OH2 O ¼ CH2 þ þ h;
ð1bÞ
which we label process (1b), can be estimated from the threebody rate coefficient we have measured with the SIFT or calculated from first principles (Bates & Herbst 1988). The former
method yields a rate coefficient of 3:1 ; 1015 (T =300)3 cm3
s1, where the temperature dependence is taken from the
modified thermal approach of Bates & Herbst. The purely
theoretical thermal method of Bates & Herbst yields a somewhat smaller value of 1:8 ; 1016 (T =300)3:5 cm3 s1. We
use the former rate coefficient in our model calculations (x 4),
where it is assumed that, upon dissociative recombination,
the product ion yields at least some neutral methyl formate
(Osamura et al. 1999). In the purely theoretical approach to
radiative association, we have neglected the channel leading
to the ion [CH3OCH2]+. More detailed calculations of the radiative association rate should take this competitive channel
into account.
Since the reaction thought to lead to methyl formate in hot
cores possesses a large barrier according to our calculations,
and since the radiative association between the reactants will
not be very efficient even if the subsequent recombination
produces some methyl formate, it is necessary to consider alternate pathways. In doing so, we consider species that are
known either to exist in reasonable abundance in hot cores or
to be likely inhabitants of such regions.
A variant of the path in reaction (1a) is to start with methanol and protonated formaldehyde:
CH3 OH þ ½H2 C ¼ O Hþ ! ½HC(OH)OCH3 þ þ H2 : ð1cÞ
The energy of CH3 OH þ ½H2 C ¼ O Hþ (Table 1) is higher
than the energy of ½CH3 OH2 þ þ H2 C ¼ O by 59 kJ. For
reaction (1c), the first step leads, as in reaction (1a), to
complex II, while the rest of the path is identical with reaction (1a). The thermodynamic advantage of starting with the
proton on formaldehyde does not, however, completely remove the activation energy, which results from the unfavorable barrier in the exit channel, now reduced to 69 kJ mol1
(8000 K). In addition, it is much more likely that the reactants
in reaction (1c) just undergo a proton transfer reaction to
produce the reactants in reaction (1a), which are exothermic
by 59 kJ mol1.
3.2. Path (2)
In this reaction, formaldehyde and protonated formaldehyde react to give protonated methyl formate in an association
reaction:
H2 C ¼ O þ ½H2 C ¼ O Hþ ! ½HC(OH)OCH3 þ þ h:
ð2Þ
Experimental information concerning reaction (2) is mixed.
Low-pressure ICR studies show a variety of exothermic
Fig. 4.—Potential energy surface (path [2]) for the reaction between
formaldehyde and protonated formaldehyde.
channels but no adduct (Karpus & Klein 1975), while higher
pressure work does show an adduct (Bone & Garrett 1976),
presumably formed by ternary association. The ternary association rate coefficient has not been determined.
Reaction (2) is calculated to take place in three steps, with the
relative energies of the stationary points shown in Figure 4.
Some of the intermediate species involved in this reaction
are depicted in Figure 3. An H-bonded complex, [H2C =
OHO = CH2]+ (complex IV; Fig. 3), with energy lowered by
141 kJ mol1 relative to the energy of the reactants (Fig. 4)
is formed initially; the energy is in reasonable agreement
with the experimentally determined room temperature enthalpy change of 115 kJ mol1 found in gas-phase equilibrium experiments (Cunningham et al. 1972; Fehsenfeld et al.
1978; Larson et al. 1982a, 1982b) and presumed to refer to
complex IV.
The second step goes through a transition state (TS1, structure V; Fig. 3) with potential 73 kJ mol1 less than the energy
of the reactants to form a covalently bonded dimer of the two
reactants, the cation [H2COCH2OH]+ (complex VI). The energy of [H2COCH2OH]+ (complex VI) is 117 kJ mol1 lower
than the energy of the reactants (H2 C ¼ O þ ½H2 C ¼ O Hþ ).
The molecular system then passes through a second transition
state (TS2, structure VII) to form protonated methyl formate
(product I) in the third step. Despite the fact that the product is 209 kJ mol1 lower in potential energy relative to the
reactants (H2 C ¼ O þ ½H2 C ¼ O Hþ ), the second transition state represents an effective barrier against reaction because it is 85 kJ mol1 higher in potential energy than the
reactants.
In conclusion, is likely that the only reaction between formaldehyde and protonated formaldehyde is a radiative association to form the H-bonded complex IV and/or [H2COCH2OH]+
(complex VI). It is also possible that HCOOCH3 is formed
directly from complexes IV or VI by electron dissociative recombination despite the need for significant structural alteration.
We have calculated the rate coefficient for the radiative association to form complex IV to be 8:1 ; 1015 (T =300)3:5 cm3
s1 with the thermal theory of Bates & Herbst (1988) and an ab
initio approach to the actual rate of infrared emission of the
complex.
3.3. Path (3)
Because protonated methanol and CO are abundant species
in hot cores; it is reasonable to consider how rapidly these
610
HORN ET AL.
Vol. 611
Fig. 5.—Potential energy surface (path [3a]) for the reaction between
carbon monoxide and protonated methanol.
Fig. 7.—Potential energy surface (path [3b]) for the reaction between the
formyl cation and methanol.
species can radiatively associate to form protonated methyl
formate:
½CH3 OH2 þ þ CO ! ½HC(OH)OCH3 þ þ h:
ð3aÞ
The potential pathway for this reaction is shown in Figure 5. An
H-bonded complex, [CH3OH2CO]+ (complex VIII; Fig. 6)
between protonated methanol and CO is formed in the first step.
The potential energy is lowered by the rather small amount of
55 kJ mol1. The complex then passes over a transition state
(structure IX) to form protonated methyl formate (product I).
The energy of the transition state is 53 kJ mol1 higher than
the combined energy of the reactants (½CH3 OH2 þ þ CO). Such
an activation energy barrier makes the overall association
unfeasible. The rate coefficient for the association to form
complex VIII is small because of the small binding energy.
Moreover, it is unlikely that the weakly bound complex VIII
can produce a significant amount of methyl formate upon dissociative recombination.
An alternative pathway is the association between methanol
and the formyl cation:
CH3 OH þ ½HCOþ ! ½HC(OH)OCH3 þ þ h:
Fig. 6.—Structures of stationary points for the reaction between carbon
monoxide and protonated methanol with important bond distances.
ð3bÞ
The energy of the reactants is now 163 kJ mol1 higher than in
the previous case (reaction [3a]). It was found in our calculations that the H-bonded complex VIII is again produced in
the first step. From then on, as can be seen in Figure 7, the
reaction follows the same route as in reaction (3a), except that
transition state IX now lies considerably below the energy of
reactants, so that radiative association is theoretically possible.
The problem with this possibility, however, is that the reaction
between the formyl ion and methanol has been studied and
found to undergo only exothermic proton transfer (Bohme
1979). For radiative association to occur with a nonnegligible
rate coefficient, three-body association must be apparent in the
high-pressure experiments of Bohme (1979).
No. 1, 2004
METHYL FORMATE IN HOT MOLECULAR CORES
611
The potential energy surface for the reaction is depicted in
Figure 8, while the stationary structures are shown in Figure 9.
Although the surface is rather complex, the key feature is the
second transition state, TS2 (structure XIII), which lies 22 kJ
mol1 higher in energy than the reactants. The energy of
transition state XIII is relatively small compared with the uncertainty of the calculations (30 kJ mol1), so that there is a
small possibility that reaction (4) may take place without a
barrier. Since the abundance of the initial ionic reactant is
likely to be quite low compared with the major organic ions in
hot cores such as protonated methanol, and since it is likely
that the reaction possesses at least some activation energy, we
do not consider this reaction further.
3.5. Path (5)
Fig. 8.—Potential energy surface (path [4]) for the reaction between
formaldehyde and [H2COCH2OH]+.
The final reaction that we consider is the radiative association between methyl ion and formic acid:
3.4. Path (4)
þ
CHþ
3 þ HCOOH ! ½HC(OH)OCH3 þ h:
It was seen in path (2) that the radiative association reaction
between formaldehyde and protonated formaldehyde to form
the stabilized complex [H2COCH2OH]+ (complex VI) is likely
to occur with zero activation energy, although the overall rate
coefficient will not be large at hot core temperatures and there
will be competition between products VI and IV. Even so, we
investigate the possibility that an additional association reaction between [H2COCH2OH]+ and another formaldehyde
molecule can result in protonated methyl formate (structure I)
and formaldehyde:
½H2 COCH2 OHþ þ H2 CO ! ½HC(OH)OCH3 þ þ H2 CO:
ð4Þ
ð5Þ
The methyl cation is found to attach itself either to the carbonyl oxygen atom or to the hydroxyl group oxygen atom
of the formic acid with no activation energy. The result is
the production of one of the several forms possible for protonated methyl formate (see the discussion in x 2.1). Conformational relaxation plus proton tunneling through low
barriers will ultimately lead to the global minimum I, which
is calculated to be 325 kJ mol1 more stable than the reactants. This is a very deep well, and the possibility that an
association reaction occurs must be investigated. It should be
noted, however, that another channel for reaction has been
studied experimentally by Freeman et al. (1978) in a flowing
afterglow apparatus. This channel, leading to the products
Fig. 9.—Structures of stationary points for the reaction between formaldehyde and [H2COCH2OH]+ with important bond distances.
612
HORN ET AL.
TABLE 2
Fractional Molecular Abundances in Hot Cores
Molecule
Orion Compact Ridge
4(8)a
1(7)b
9(9)b
1(8)b
9.5(9)f
H2CO...............
CH3OH............
HCOOCH3 ......
CH3OCH3 ........
HCOOH ..........
a
b
c
d
e
f
G34.26
Sgr B2(N-LMH)
...
3–14(8)c
1(10)c
...
1(9)f
...
4(8)d
1(8)e
...
1(9)e
Mangum et al. (1990).
Blake et al. (1987).
Hatchell et al. (1998).
Pei et al. (2000).
Snyder et al. (2002).
Liu et al. (2001).
Vol. 611
Extrapolation of the measured results to zero pressure gives
an estimate for the radiative rate coefficient of approximately
1 ; 1011 cm3 s1 at room temperature. With the standard
modified thermal (Bates & Herbst 1988) temperature dependence of T 3, we obtain that the rate coefficient at 100 K is
3 ; 1010 cm3 s1. Given the large uncertainty, we utilize a
value of 109 cm3 s1 in our model calculations below, to
estimate the largest possible effect for the association.
Another possible process of interest involving HCOOH is
the alkylation reaction
þ
CH3 OHþ
2 þ HCOOH ! ½HC(OH)OCH3 þ H2 O;
CHþ
5 þ CO2 , was found to occur at the collisional rate coefficient (2:1 ; 109 cm3 s1) despite the unusual nature of the
process. Unless the two channels are parallel in nature, i.e.,
do not involve any of the same intermediate structures, the
reactive channel may significantly depress the rate of radiative association.
We have reinvestigated the reactions between CH3+ and
HCOOH in the Oslo laboratory and find that a variety of
processes occur, including association, implying that parallel
mechanisms do indeed happen. In contrast to the report by
Freeman et al. (1978), we could not observe CHþ
5 (m=z ¼ 17).
The reaction kinetics were analyzed on the basis of the following major reactions:
(i); ki ¼ 5:7 ; 1010 ;
þ
CHþ
3 þ HCOOH ! HCO þ CH3 OH
þ
10
CHþ
;
3 þ HCOOH ! ½CH3 OH2 þ CO (ii); kii ¼ 7:6 ; 10
þ
11
CHþ
;
3 þ HCOOH ! ½HC(OH)OCH3 (iii); kiii ¼ 2:2 ; 10
HCOþ þ HCOOH ! ½HC(OH)2 þ þ CO (iv); kiv ¼ 2:8 ; 109 ;
HCOþ þ HCOOH ! H3 Oþ þ 2CO
(v); kv ¼ 6:7 ; 1011 ;
where the rate coefficients, in cm3 s1, were obtained by a
simultaneous nonlinear least-squares fit (O. Sekiguchi et al.
2004, in preparation). The association reaction occurs, under
the conditions of the experiment, via both three-body and
radiative mechanisms.
but experimental investigations show that only protonation to
form protonated formic acid, [HC(OH)2]+, occurs in this
system (Freeman et al. 1978).
4. MODEL RESULTS
We have run a gas-phase chemical model for a hot-core
source. Some relevant molecular abundances with respect to
H2 in three such sources—the Orion compact ridge, G34.26,
and Sgr B2(N-LMH)—are listed in Table 2. Although the
abundances of the molecules shown—formaldehyde, methanol, methyl formate, dimethyl ether, and formic acid—are not
constant from source to source, they all show a considerable
abundance of methyl formate. In our model, molecules on
grain mantles are injected into the gas when temperatures rise
at the onset of high-mass star formation (Charnley et al. 1995).
The injected molecules and their fractional abundances with
respect to n( H ), mainly taken from Charnley et al. (1995), are
listed in Table 3. Among the injected species are formaldehyde and methanol, for which grain-surface syntheses from
CO have some basis in laboratory studies (Hiraoka et al. 2000;
Watanabe & Kouchi 2002).
We assume a subsequent temperature of 100 K and a gas
density n(H2) of 106 cm3, and follow the gas-phase chemistry
for 106 yr. The reaction network is based on the UMIST compilation (Le Teuff et al. 2000). Additional reactions and rate
coefficients based on the calculations here are shown in Table 4
along with the previous ‘‘standard’’ reaction to form the protonated precursor to methyl formate (reaction [1a]). We have
assumed that the large H-bonded complex formed in reaction
(1b) can dissociatively recombine into methyl formate, H2, and
H on approximately 10% of collisions, since a large structural
TABLE 3
Selected Calculated Fractional Abundances
Molecule
H2O .........................
CO ...........................
N2 ............................
NH3 .........................
O2 ............................
CH4..........................
C2H4 ........................
C2H6 ........................
H2CO.......................
CH3OH....................
HCOOCH3 ..............
CH3OCH3 ................
HCOOH ..................
Injected [0 yr]
2(5)
1(4)
2(5)
1(5)
2(7)
1(7)
8(8)
1(8)
1.2(7)
1(6)
...
...
...
Charnley et al. (1995)
Model 1 [8(4) yr]
Model 2 [8(4) yr]
Model 3 [1.3(5) yr]
...
...
...
...
...
...
...
...
4(8)
8(7)
1.5(8)
1.7(8)
...
...
...
...
...
...
...
...
...
5.1(7)
4.1(7)
5.4(9)
4.2(9)
1.6(8)
...
...
...
...
...
...
...
...
5.2(7)
4.1(7)
1.3(10)
4.3(9)
1.6(8)
...
...
...
...
...
...
...
...
3.6(7)
2.3(7)
1.3(11)
3.7(9)
1.8(8)
Note.—Abundances are listed at those times where methyl formate is at its peak. See text.
No. 1, 2004
613
METHYL FORMATE IN HOT MOLECULAR CORES
TABLE 4
Rate Coefficients k (109 cm3 s 1) for Additional Reactions Used in 100 K Models
Reaction
Model 1
Model 2
Model 3
þ
CH3 OHþ
2 þ H2 CO ! HC(OH)OCH3 þ H2 (1a) ........................
CH3 OHþ
þ
H
CO
!
CH
OH
O
¼ CHþ
2
3
2
2
2 þ h (1b) ............
þ
CH3 OH2 O ¼ CH2 þ e ! HCOOCH3 þ H2 þ H .................
CH3 OH2 O ¼ CHþ
2 þ e ! CH3 OH þ H2 CO þ H .................
H2 COHþ þ H2 CO ! H2 COHOCHþ
2 þ h .................................
H2 COHOCHþ
þ
e
!
HCOOCH
þ
H........................................
3
2
þ
CHþ
3 þ HCOOH ! HC(OH)OCH3 þ h (5)..............................
1.0
8.4(5)
2.6(1)
2.3(2)
3.8(4)
2.6(1)
1.0
2.1(2)
8.4(5)
2.6(1)
2.3(2)
3.8(4)
2.6(1)
1.0
2.1(6)
8.4(5)
2.6(1)
2.3(2)
3.8(4)
2.6(1)
1.0
change is required. A similar assumption was made for the
dissociative recombination of [H2COHOCH2]+ (path [2]).
Three models have been run. In model 1 we adopt the old,
large rate coefficient for reaction (1a), while in model 2 we use
a rate coefficient approximately 50 times smaller, based on our
room-temperature experimental results with the assumption
that the small amount of product at the mass of protonated
methyl formate is indeed this isomer and is produced via reaction (1a). In model 3 we reduce the rate coefficient for reaction (1a) to essentially zero. Results for some large organic
molecules in all three models plus the results of Charnley et al.
(1995) are shown in Table 3 with respect to n(H2). These results
are chosen at the time of peak abundance for methyl formate,
which occurs at times in the range (1 2) ; 105 yr in our models.
Our results for model 1 should be closest to those of
Charnley et al. (1995) since these authors also used the large
rate coefficient for reaction (1a). Our model requires more time
for methyl formate to reach its peak abundance; in addition,
differences of factors of 2–4 exist for the largest molecules
shown. Still, both model 1 and the earlier Charnley et al. results
are generally in reasonable (order of magnitude) agreement
with observation. The results for model 2 show distinctly that
reaction (1a) is the key reaction for methyl formate production:
when the rate coefficient is dropped by a factor of 50, the
abundance of methyl formate drops by the same factor! The
peak calculated abundance of methyl formate is now well below the observed value in two out of the three sources. When
the rate coefficient for reaction (1a) is dropped to an insignificantly low value, which is what theory indicates to be the
case, the calculated peak abundance of methyl formate drops
only 1 order of magnitude more, because reaction (5) becomes
the dominant synthetic process. Still, the peak value of methyl
formate is now below the detected value in all three sources
listed.
One possibility for producing more methyl formate is to
consider that its precursor formic acid might be synthesized on
grain surfaces and desorbed into the gas phase (Hudson &
Moore 1998). Reaction (5) followed by dissociative recombination would then play a significant role. Assuming that
formic acid is injected into the gas with a fractional abundance
of 107, we are able to increase the abundance of methyl
formate somewhat, but the amount of formic acid becomes
much too large in models 2 and 3. The detailed results are
shown in Table 5 and compared with the best-studied hot core
of the three: the Orion compact ridge. For this source, our peak
predicted abundance of methyl formate is still between 1 and 2
orders of magnitude too low.
5. CONCLUSIONS
With a combination of theoretical and experimental studies,
we have raised grave doubts that the standard synthesis of
methyl formate from methanol in hot cores is the correct one.
In particular, the reaction between protonated methanol and
formaldehyde to produce protonated methyl formate and hydrogen has been calculated to have a significant activation
energy barrier. Moreover, experimental studies at both low
and high pressure show that the product branching fraction is
small. Finally, we have suggested that all of the laboratory
product at the correct mass to be protonated methyl formate is
an isomer coming from a sequence of secondary reactions that
do not occur in a hot-core environment.
Assuming that the standard approach to the formation of
methyl formate in hot cores is incorrect, we have looked at
alternative possibilities. Based on model calculations reported
TABLE 5
Selected Calculated Fractional Abundances: HCOOH Injection
Molecule
H2O ...............................
CO .................................
N2 ..................................
NH3 ...............................
O2 ..................................
CH4................................
C2H4 ..............................
C2H6 ..............................
H2CO.............................
CH3OH..........................
HCOOCH3 ....................
CH3OCH3 ......................
HCOOH ........................
Injected [0 yr]
2(5)
1(4)
2(5)
1(5)
2(7)
1(7)
8(8)
1(8)
1.2(7)
1(6)
...
...
1(7)
Model 2 [8(4) yr]
Model 3 [8(4) yr]
...
...
...
...
...
...
...
...
5.2(7)
4.1(7)
3.2(10)
4.4(9)
1.5(7)
...
...
...
...
...
...
...
...
6.2(7)
6.0(7)
2.0(10)
4.5(9)
1.6(7)
Note.—Abundances are listed at those times where methyl formate is at its peak.
Orion Compact Ridge
...
...
...
...
...
...
...
...
4(8)
1(7)
9(9)
1(8)
9.5(9)
614
HORN ET AL.
here, it appears that the next best possibility lies in the radiative association reaction between methyl ions and formic acid
(HCOOH), for which we have obtained some positive laboratory evidence at 300 K. Even this reaction, while calculated
to be rapid at 100 K, does not produce enough methyl formate
to agree with observations in hot cores, especially the Orion
compact ridge, even if an abnormally large amount of formic
acid is present in the warm gas.
Given the difficulty in producing large amounts of methyl
formate by gas-phase syntheses, it is reasonable to ask whether
or not this and other large saturated organic molecules in hot
cores may be produced at least in part directly on cold grain
surfaces during the era before star formation. An assortment
of suggestions to this effect has been made in the literature
(Charnley et al. 1995; Ehrenfreund & Charnley 2000).
Thanks are due to the Norwegian Research Council
(Programme for Supercomputing) for a grant of computer
time. Astrochemistry at Ohio State is supported by the National Science Foundation. A. A. V. thanks the United States
Air Force Office of Scientific Research for support under
project 2303EP4. We thank A. Hjalmarson for his interest in
the initial phase of this work.
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