A new model for magnesium chemistry in the upper atmosphere

Article abstract of DOI:10.1021/jp211526h

This paper describes the kinetic study of a number of gas-phase reactions involving neutral Mg-containing species, which are important for the chemistry of meteor-ablated magnesium in the upper mesosphere/lower thermosphere region. The study is motivated by the very recent observation of the global atomic Mg layer around 90 km, using satellite-born UV-visible spectroscopy. In the laboratory, Mg atoms were produced thermally in the upstream section of a fast flow tube and then converted to the molecular species MgO, MgO₂, OMgO₂, and MgCO₃ by the addition of appropriate reagents. Atomic O was added further downstream, and Mg was detected at the downstream end of the flow tube by laser-induced fluorescence. The following rate coefficients were determined at 300 K: k(MgO + O → Mg + O₂) = (6.2 ± 1.1) × 10^-10; k(MgO₂ + O → MgO + O₂) = (8.4 ± 2.8) × 10^-11; k(MgCO₃ + O → MgO₂ + CO₂) ≥ 4.9 × 10^-12; and k(MgO + CO → Mg + CO₂) = (1.1 ± 0.3) × 10^-11 cm³ molecule^-1 s^-1. Electronic structure calculations of the relevant potential energy surfaces combined with RRKM theory were performed to interpret the experimental results and also to explore the likely reaction pathways that convert MgCO₃ and OMgO₂ into long-lived reservoir species such as Mg(OH)₂. Although no reaction was observed in the laboratory between OMgO₂ and O, this is most likely due to the rapid recombination of O₂ with the product MgO ₂ to form the relatively stable O₂MgO₂. Indeed, one significant finding is the role of O₂ in the mesosphere, where it initiates holding cycles by recombining with radical species such as MgO ₂ and MgOH. A new atmospheric model was then constructed which combines these results together with recent work on magnesium ion-molecule chemistry. The model is able to reproduce satisfactorily some of the key features of the Mg and Mg⁺ layers, including the heights of the layers, the seasonal variations of their column abundances, and the unusually large Mg⁺/Mg ratio.

Full text of DOI:10.1021/jp211526h

Article
pubs.acs.org/JPCA
A New Model for Magnesium Chemistry in the Upper Atmosphere
John M. C. Plane* and Charlotte L. Whalley
School of Chemistry, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, U.K.
ABSTRACT: This paper describes the kinetic study of a number of gas-phase
reactions involving neutral Mg-containing species, which are important for the
chemistry of meteor-ablated magnesium in the upper mesosphere/lower thermo-
sphere region. The study is motivated by the very recent observation of the global
atomic Mg layer around 90 km, using satellite-born UV−visible spectroscopy. In the
laboratory, Mg atoms were produced thermally in the upstream section of a fast flow
tube and then converted to the molecular species MgO, MgO , OMgO , and MgCO
3
2
2
by the addition of appropriate reagents. Atomic O was added further downstream,
and Mg was detected at the downstream end of the flow tube by laser-induced fluorescence. The following rate coefficients were
−
10
−11
determined at 300 K: k(MgO + O → Mg + O ) = (6.2 ± 1.1) × 10 ; k(MgO + O → MgO + O ) = (8.4 ± 2.8) × 10
;
2
2
2
−
12
−11
3
−1 −1
k(MgCO + O → MgO + CO ) ≥ 4.9 × 10 ; and k(MgO + CO → Mg + CO ) = (1.1 ± 0.3) × 10 cm molecule s .
Electronic structure calculations of the relevant potential energy surfaces combined with RRKM theory were performed to
interpret the experimental results and also to explore the likely reaction pathways that convert MgCO and OMgO into long-
3
2
2
2
3
2
lived reservoir species such as Mg(OH) . Although no reaction was observed in the laboratory between OMgO and O, this is
2
2
most likely due to the rapid recombination of O with the product MgO to form the relatively stable O MgO . Indeed, one
2
2
2
2
significant finding is the role of O in the mesosphere, where it initiates holding cycles by recombining with radical species such
2
as MgO and MgOH. A new atmospheric model was then constructed which combines these results together with recent work
2
on magnesium ion−molecule chemistry. The model is able to reproduce satisfactorily some of the key features of the Mg and
+
+
Mg layers, including the heights of the layers, the seasonal variations of their column abundances, and the unusually large Mg /
Mg ratio.
+
INTRODUCTION
An estimated 10−50 metric tons (t) of interplanetary dust
enters the Earth’s upper atmosphere every day. Most of this
dust undergoes rapid heating and melting, followed by the
evaporation of the constituent elements, a process termed
meteoric ablation. Ablation provides a source of metallic species
in the mesosphere/lower thermosphere region (MLT) of the
atmosphere, at heights between ∼80 and 120 km. Magnesium
is one of the most abundant meteoritic constituents (9.6% by
mass); therefore, meteoric ablation should inject large
metals is the large ion/neutral ratio. The Mg /Mg ratio varies
■
3,5
+
+
from ∼4 to 12 compared to Na /Na and Fe /Fe ratios of
7
,8
+
12
1
∼0.2 and a Ca /Ca ratio of ∼2. This large ion/neutral ratio
+
is even more striking as Mg is not significantly depleted
relative to other metals in the MLT, based on their relative
7
abundances in chondritic meteorites.
Previous work on the mesospheric chemistry of magnesium
has shown that atomic Mg is rapidly oxidized by O to form
MgO, which then goes on to react with O , O , H O, or
CO2 to form the Mg-containing compounds shown in Figure
2
3
1
3
2
3
2
1
4
+
2
quantities of Mg and Mg into the atmosphere. Mg and
+
Mg have been observed via their solar-pumped resonance
fluorescence transitions at 285 and 280 nm, respectively, by
3
4−6
optical spectrometers carried on a rocket and on satellites.
+
Mg has also been measured by rocket-born mass spectrometry
7,8
since the late 1960s.
It is worth pointing out that systematic observations of Mg,
sufficient to establish its chemical climatology, have only
become available in the last 3 years. Observations by the
Figure 1. Schematic diagram showing the role of atomic O in neutral
magnesium chemistry in the upper atmosphere.
4
6,9
GOME and SCIAMACHY satellite instruments show that
9
−2
+
Mg has a column density of ∼2 × 10 cm , with Mg
9
−2
exhibiting column densities between 3 × 10 cm at its winter
1
0
−2
minimum and 1.2 × 10 cm at its summer maximum. The
Mg layer peaks between 90 and 100 km with a peak ion
+
3
−3
Special Issue: A. R. Ravishankara Festschrift
concentration of (1−5)× 10 cm during daytime, decreasing
to 102 cm at night. The Mg layer exhibits lower
−3
10
Received: November 30, 2011
Revised: January 6, 2012
Published: January 9, 2012
6,11
concentrations and a peak altitude at around 88 km.
A
striking difference between magnesium and the other meteoric
©
2012 American Chemical Society
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The Journal of Physical Chemistry A
Article
Figure 2. Schematic diagram of the fast flow tube used to study the reactions of neutral magnesium-containing molecules with atomic O. P =
photomultiplier tube.
1
. These compounds can potentially undergo the following
EXPERIMENTAL SECTION
■
significantly exothermic reactions with atomic O
Reactions 1−5 were studied using a fast flow tube, which has
been used previously to study the reactions of neutral Fe- and
Ca-containing species with atomic O.
15,16
MgO + O → Mg + O2
The stainless steel
ΔH0K = −245 kJ mol−1
flow tube, shown schematically in Figure 2, has an internal
diameter of 37.5 mm and consists of sections of tube, cross
pieces, and nipple sections connected by conflat flanges sealed
with copper gaskets. The tube has a total length of 1130 mm
from the upstream entry point of the carrier gas (designated as
I1 in Figure 2) to the downstream LIF detection cell.
Magnesium atoms were produced continuously by heating
magnesium pellets (Aldrich, 99.5%) to a temperature between
(1)
(2)
(3)
(4)
2
MgO + O → MgO + O2
ΔH0K = −161 kJ mol−1
OMgO + O → MgO + O
2
2
2
7
00 and 800 K. The pellets were located in an aluminum oxide
crucible placed inside of a tungsten basket heater, positioned
120 mm upstream of the LIF cell. The Mg atoms were
ΔH0K = −125 kJ mol−
1
1
MgCO + O → MgO + CO
entrained in the main carrier flow of N , which entered the tube
3
2
2
2
upstream of the crucible. All reactant flows were injected via
side ports (I2 and I3) downstream of the crucible. The gas flow
exited the tube through a throttle valve to a booster pump
backed by a rotary pump, providing a volume displacement rate
ΔH0K = −127 kJ mol−
1
where the standard reaction enthalpies at 0 K are determined
from electronic structure calculations (see below). Because the
atomic O mixing ratio above 85 km in the MLT can approach
−1
of 110 L s . Typically, a total gas flow rate of 3200 sccm was
used at a pressure of 1.2 Torr, creating a flow velocity of 33.1 m
1
−1
1
%, this sequence of reactions could recycle these compounds
s . The Reynolds number was always below 80, ensuring
laminar flow within the tube. Mg was detected by LIF at 285.2
back to Mg very efficiently. These reactions are therefore key to
determining the effectiveness of these Mg-containing com-
pounds as reservoirs (or permanent sinks) for magnesium in
1
1
nm (Mg(3 P −3 S )) using a frequency-doubled Nd:YAG-
1
0
pumped dye laser (pulse rate, 10 Hz; pulse energy, 10 mJ),
frequency doubled with a BBO crystal.
the MLT.
Atomic O was produced by the microwave discharge of N to
2
In this paper, we describe a kinetic study of reactions 1−4,
which do not appear to have been studied previously. The rate
coefficients were measured using a fast flow tube with detection
of Mg by laser-induced fluorescence (LIF) and atomic O by
chemiluminescence (following titration with NO). In order to
establish the technique, the reaction
generate N atoms, which were then titrated with NO (N + NO
→
O + N ). As shown in Figure 2, the microwave cavity was
2
mounted on a side arm, which consisted of a 150 mm quartz
tube that projected 10 mm into the flow tube, in order to
decrease the time taken for the atoms to become well mixed in
the flow and to avoid large initial wall losses. The O atom flow
entered 750 mm downstream of the magnesium source. The
MgO + CO → Mg + CO2
1
[O] was determined by titration with NO , where the NO + O
2
17
ΔH0K = −272 kJ mol−
recombination generates electronically excited NO *. The
resulting chemiluminescence from NO * was measured by a
2
(5)
2
was also studied as CO is a useful surrogate for atomic O in
reaction 1. The experimental results were then interpreted
using electronic stucture calculations and rate theory, which
was also used to explore other possible reaction pathways for
species such as OMgO and MgCO in the atmosphere. Finally,
these results were incorporated into a new atmospheric model
of magnesium and compared with the satellite observations
described above.
photomultiplier tube with an interference filter at 590 ± 5 nm,
situated 260 mm downstream of the microwave discharge. The
first-order loss of O atoms to the flow tube walls was
determined by measuring the [O] at different flow velocities at
constant pressure (and hence different flow times in the flow
tube). The change in relative [O] was monitored via the
addition of NO just upstream of the photomultiplier tube and
measurement of the relative intensity of the resulting NO2*
2
3
6
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The Journal of Physical Chemistry A
Article
1
3
−3
chemiluminescence. The [O] was ∼10 atom cm at the point
of injection.
Table 1. Flow Tube Wall Loss Rates at 300 K for Mg
(measured) and Mg-Containing Molecules (estimated using
the listed dipole moments and polarizabilities to calculate
corresponding diffusion coefficients)
Materials. N (99.999%, BOC Gases), O (99.999%. BOC
Gases), CO (99.995%, BOC Gases), and CO (99.999%, BOC
2
2
2
Gases) were used without further purification. O was produced
3
wall
by flowing O through a commercial ozonizer. The resulting 5−
2
dipole
ionization
potential
eV
diffusiona
coefficient
loss
b
8
% O in O mixture was collected on silica gel held at 156 K
moment polarizability
rate
3
2
−
24
3
2
−1
−1
species
debye
10 cm
Torr cm s
s
by an ethanol slush bath, and the O was pumped off at the
2
c
same temperature to produce a 10−20% O /O mixture.
Mg
0
10.6
7.65
136
117
119
127
89
96
83
75
90
63
3
2
d
e
f
MgO
6.2
7.7
8.0
e
e
e
MgO2
OMgO2
MgCO3
3.1
5.2
8.05
RESULTS
■
e
e
e
0.4
5.5
10.4
Kinetic Analysis in the Flow Tube. The Mg-containing
e
e
e
11.6
6.3
9.10
species (MgX) were produced in situ from atomic Mg by
addition of appropriate reactants downstream of the Mg source.
Atomic O was added further downstream in order to convert
MgX back to Mg, either directly or via an intermediate such as
a
20
Calculated using the standard formalism in Maitland et al.
b
Measured in the present system for Mg and scaled for the Mg-
c
34
d
35 e
containing species (see text). Measured.
at the B3LYP/6-311+g(2d,p) level of theory. Measured.
Measured. 4C6alculated
2
5 f
MgO or MgO. Therefore, experiments were monitored by
2
measuring the relative intensity of Mg in the presence and
absence of atomic O. As the gas-phase chemistry in the flow
tube is complex, the rate coefficients of interest had to be
determined using a model that described all of the processes
that occurred between the Mg source and the LIF detection
point, including diffusion and loss to the walls of Mg, MgX, and
O and also any additional reactions occurring between reactants
and products. The model has been described in detail in
than a 5% change in the pertinent rate coefficient retrieved
from fitting the model to the experimental data.
Rate coefficients were obtained for reactions 1−5 by
integrating the pertinent coupled ordinary differential equations
21
using a fourth-order Runge−Kutta numerical scheme. The
rate coefficient of interest, k , was obtained by minimizing the
x
sum over N data points of the squared difference between the
meas
1
8
16
measured relative Mg
i
(obtained by averaging the LIF signal
Woodcock et al. and Broadley and Plane.
The first-order loss rates of Mg and O due to deposition on
the flow tube walls were measured by the relative changes in
3
model
from ∼10 laser shots) and the modeled Mg
i
2
N
∑
i
⎛
Mg im eas − Mg im odel
⎞
[
Mg] and [O] as a function of flow time (which was varied by
χ2 =
⎜
⎜
⎝
⎟
⎟
⎠
changing the total flow rate at a fixed pressure). The measured
O loss rate varied day-to-day, most likely due to a buildup of
surface coatings on the flow tube walls, and therefore was
measured prior to each experimental run. The average O loss
rate was 207 ± 24 s , where the stated error is the standard
deviation of the measurements. The error of an individual
measurement of the wall loss rate was typically 11%.
SDi
(II)
meas
where SD is the standard deviation of Mg
when averaging
i
i
−1
2
the Mg LIF signal of each data point. χ was calculated over a
range of k values in order to locate its minimum and thus the
x
optimized value of k . The uncertainty in k was set equal to the
x
x
If loss of Mg to the flow tube walls is assumed to occur with
an uptake efficiency close to unity, then the diffusion coefficient
standard deviation of the difference between the value of kx
obtained by carrying out a fit to each experimental point
separately and the value obtained from the global fit using eq II.
This uncertainty was then combined in quadrature with the
systematic error arising from the rate coefficients and diffusion
coefficients in the model. The systematic error was estimated
of Mg in N , DMg−N2, can be calculated using the following
2
expression, which describes the diffusion out of a cylinder of
1
9
radius, r
r2
.81
D
= kDiffMg 5
P
by using a Monte Carlo procedure that calculated the standard
Mg−N2
(I)
4
deviation of k from 10 model fits in which these model
x
parameters were randomly sampled within their 1σ uncertain-
ties. The systematic errors that arose from calibrations of the
pressure, temperature, and mass flow rates were minor (<2%)
in comparison.
where P is the total pressure and kDiffMg is the measured first-
order loss rate of Mg. D was measured to be 70 ± 12 Torr
Mg−N
2
2
−1
cm s , which is significantly less than an estimated value of
2
−1
1
36 Torr cm s , calculated via the long-range dispersive force
MgO + O, MgO + O. MgO was produced by the addition
2
between Mg and N (relevant parameters are listed in Table
2
13
2
0
of O3 downstream of the Mg oven
1
). This result indicates that Mg atoms were not lost with
unity efficiency on the flow tube walls, probably again due to
the surface coating. The long-range dispersion and dipole−
Mg + O3 → MgO + O2
induced dipole forces between the MgX species and N were
2
ΔH0K = −147 kJ mol−1
(6)
then calculated using the polarizabilities, ionization energies,
and dipole moments listed in Table 1. Diffusion coefficients
2
0
In previous work on CaO and FeO kinetics, we used the
reactions of Ca and Fe with NO to produce CaO and FeO,
were calculated and converted into wall loss rates using eq I,
scaled by the factor of 0.52 (=70/135) to be consistent with the
observed Mg loss rate. The estimated wall loss rates for the
MgX species are listed in Table 1. In fact, the numerical model
used to obtain the rate coefficients was fairly insensitive to these
parameters; a 50% change in any one wall loss rate caused less
2
1
5,16
respectively.
However, at room temperature, Mg is
; hence, it is not a suitable oxidant in
the flow tube. The problem with using O as the oxidant is
unreactive toward NO
2
22
3
13
that MgO then reacts to produce MgO2
6
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The Journal of Physical Chemistry A
Article
MgO + O → MgO + O
3
2
2
ΔH0K = −231 kJ mol−
1
(7)
13
However, as k and k have been measured previously, it was
6
7
possible to retrieve k and k simultaneously using a two-
1
2
2
23
dimensional (2D) χ minimization model. Reactions 1 and 2
were studied by measuring the relative [Mg] in the presence
and absence of a fixed [O], as a function of varying [O ]. The
3
1
1
12
−3
[
O ] varied between 5 × 10 and 9 × 10 molecules cm
during these experiments, which was too small to measure
3
directly in the flow tube. [O ] was therefore determined from
3
the measured first-order decay rate of Mg in the presence of O3
(
without addition of atomic O), using the value for k
6
13
determined previously. The 2D minimization model solved
the following coupled differential equations
Figure 3. Plot of relative [Mg] in arbitrary units (measured by LIF)
against [O ] in the presence and absence of atomic O at 300 K and 1.2
3
d[Mg]
dt
=
−kDiffMg[Mg] − k [Mg][O ]
Torr. The open triangles and solid line are the experimental data and
model fit in the presence of atomic O. The dashed lines show the
model fit when k and k are varied within their uncertainties. The
6
3
1
2
+
k1[MgO][O]
−kDiffMgO[MgO] − k [MgO][O]
(III)
filled triangles and dotted line are the experimental data and model fit
in the absence of O. Laminar flow velocity along the tube axis = 52.9 m
d[MgO]
−1
16
−3
13
s ; [N ] = 3.9 × 10 molecules cm ; [O] = 1.9 × 10 molecules
=
2
1
−3
dt
cm injected 260 mm upstream; O
3
injected 720 mm upstream of the
LIF cell.
−
+
k [MgO][O ] + k [MgO ][O]
7
3
2
2
production of MgO . [Mg] was measured as a function of O ,
2
2
k [Mg][O ]
(IV)
(V)
6
3
while [O] and [O ] were fixed. The minimization model solved
3
the following differential equations, in addition to eqs III and
VI
d[MgO2]
=
−kDiffMgO2[MgO ] − k [MgO ][O]
2
2 2
dt
d[MgO]
+
k [MgO][O ]
= −kDiffMgO[MgO] − k
1
[MgO][O]
7
3
dt
d[O]
=
−
+
k [MgO][O ] − k [MgO][O ]
7
3
8
2
−kDiffO[O]
(VI)
dt
k [MgO ][O] + k [Mg][O ]
2
6
3
(VII)
(VIII)
(IX)
2
The wall loss rates and rate coefficients (k and k ) are listed in
6
7
Tables 1 and 2, respectively. An example of an optimized model
d[MgO2]
=
−kDiffMgO2[MgO ] − k [MgO ]
2
2
2
dt
Table 2. Rate Coefficients Used to Model the Flow Tube
Chemistry at 300 K and a Pressure of 1.2 Torr
[O] + k [MgO][O ]
7
3
3
−1 −1
reaction
rate coefficient cm molecule s
+
k [OMgO ][O]
3
2
10
11
13
12
a
a
b
b
Mg + O → MgO + O
1.4 × 10−
3
2
−
MgO + O → MgO + O
3.5 × 10
3
2
2
d[OMgO2]
MgO + O → OMgO
6.8 × 10−
1.3 × 10−
= −kDiffOMgO2[OMgO2]
2
2
dt
MgO + CO → MgCO
2
3
a
13
b
24
Plane and Helmer Rollason and Plane.
− k [OMgO ][O] + k [MgO]
3
8
2
fit to one experimental data set is shown in Figure 3.
Experiments were repeated with different [O] (ranging from
[O2]
13
1
2
13
−3
In this case, an apparent upper limit of k
3
≤ 5 × 10− cm3
5
.5 × 10 and 1.8 × 10 molecules cm ), which showed that
molecule−
compares a selection of model runs using a range of k with an
experimental data set. In fact, this measurement of k is very
3
1
s
−1
was found. This is shown in Figure 4, which
there was no systematic change in the retrieved values of k and
1
−10
3
k . The average values are k = (6.2 ± 1.1) × 10 and k = (8.4
2
±
1
2
2.8) × 10− cm molecule s , respectively (1σ errors).
11
3
−1 −1
likely compromised by the subsequent recombination of MgO2,
OMgO + O. OMgO was produced via the recombination
2
2
2
4
produced by reaction 3, with O
Discussion).
2 2 2
to form O MgO (see the
reaction
MgCO + O. MgCO was produced via the recombination
reaction
3
3
MgO + O + (N ) → OMgO
2
2
(8)
24
2
3
with O added to first produce MgO from Mg. Sufficient O2
MgO + CO + (N ) → MgCO
2
2
(9)
3
was added in the same port as the O so that reaction 8
3
dominated (by a factor of at least 80 in their relative rates) over
with O added to produce MgO from Mg. Sufficient CO was
3 2
the reaction of MgO with O (reaction 7), in order to minimize
added in the same port as the O to allow reaction 9 to
3
3
6
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The Journal of Physical Chemistry A
Article
Figure 4. Plot of the relative [Mg] in arbitrary units (measured by
Figure 5. Plot of the relative [Mg] in arbitrary units (measured by
LIF) against [O ] in the presence of atomic O at 300 K and 1.2 Torr.
LIF) against [CO ] in the presence of atomic O at 300 K and 1.2 Torr.
2
2
The lines show the expected [Mg] for different values of k . Laminar
The solid line is the model fit to the experimental data. The dashed
3
−1
16
flow velocity along the tube axis = 52.9 m s ; [N ] = 3.9 × 10
molecules cm ; [O] = 7.5 × 10 molecules cm injected 260 mm
upstream; [O ] = 2.9 × 10 injected 720 mm upstream; O injected
lines show the model fit when k is varied within its uncertainty.
2
4
−
3
12
−3
−1
Laminar flow velocity along the tube axis = 52.9 m s ; [N ] = 3.9 ×
10 molecules cm ; [O] = 7.8 × 10 molecules cm injected 260
mm upstream; [O ] = 2.5 × 10 injected 720 mm upstream; CO2
injected 720 mm upstream of the LIF cell.
2
11
16
−3
12
−3
3
2
11
7
20 mm upstream of the LIF cell.
3
dominate (by at least a factor of 12 in relative rates) the
reaction of MgO with O . [Mg] was measured as a function of
basis set. This is a large, flexible basis set that has both
polarization and diffuse functions added to the atoms. At this
level of theory, the expected uncertainty in the calculated
3
[
CO ] at fixed [O] and [O ]. The minimization model solved
2
3
the following differential equations in addition to eqs III and VI
−1
26
reaction enthalpies is ±20 kJ mol . Molecular geometries
were first optimized and checked for wave function stability,
and their respective vibrational frequencies were calculated.
d[MgO]
=
−kDiffMgO[MgO] − k [MgO][O]
1
dt
More accurate energies (±12 kJ mol− ) were then determined
1
26
−
+
k [MgO][O ] − k [MgO][CO ]
7 3 8 2
using the Complete Basis Set (CBS-Q) method of Petersson
27
k [MgO ][O] + k [Mg][O ]
and co-workers.
2
6
3
(X)
(XI)
2
The molecular parameters and heats of formation of the Mg-
containing molecules relevant to this study are listed in Table 3.
The molecular geometries of the compounds in Table 3 are
illustrated in Figure 6. Heats of formation were calculated from
the experimental heats of formation listed in the footnote to the
table and by using the CBS-Q reaction enthalpies at 0 K. In the
d[MgO2]
=
−kDiffMgO2[MgO ] − k [MgO ]
2
2
2
dt
[O] + k [MgO][O ]
7
3
+
k [MgCO ][O]
1 +
4
3
case of the smallest molecules MgO(X Σ ) and MgOH, more
accurate bond energies were calculated using the coupled
d[MgCO3]
25
cluster CCSD(T) method with the aug-cc-pVQZ basis set at
=
−kDiffMgCO3[MgCO3]
the B3LYP/6-311+g(2d,p) geometries, giving D (Mg−O) =
dt
0
−1
2
49 and D (Mg−OH) = 306 kJ mol (from which the heats of
0
−
+
k [MgCO ][O]
4
3
formation of these species were determined). The theoretical
bond lengths, dipole moments, vibrational frequencies, and
heats of formation of these two species are generally in very
good agreement with the available experimental data (Table 3).
MgOH is a quasi-linear molecule, predominantly ionic (i.e.,
k [MgO][CO ]
(XII)
8
2
The model fit for reaction 4, illustrated in Figure 5, yielded k =
4
12
3
−1 −1
(
6.7 ± 1.8) × 10− cm molecule s . As discussed below, this
+
−
is in fact most likely a lower limit.
Mg −OH ) but with some covalent character. It has a quartic
28
MgO + CO. This reaction was studied by measuring the
bending potential, which is probably why our theoretical
bending frequency is somewhat lower than the measured
frequency. The theoretical results from the present study are in
1
2
relative [Mg] as a function of [O ] (0−5.2 × 10 molecules
3
−3
12
−3
cm ), with [CO] fixed (at 9.0 × 10 molecules cm ). A value
−11
3
−1 −1
13,24,29
of k = (1.1 ± 0.3) × 10 cm molecule
s
was obtained
satisfactory agreement with previous theoretical work.
5
from a kinetic plot analogous to that shown in Figure 3.
In the discussion below regarding reactions 3−5 and also for
elucidating atmospheric pathways that are beyond the scope of
the experimental technique in the present study, we have used
Rice−Ramsperger−Kassel−Markus (RRKM) theory to esti-
mate rate coefficients. We employ a solution of the master
equation (ME) based on the inverse Laplace transform
DISCUSSION
■
In order to interpret the experimental results and to explore
additional atmospheric pathways, a set of electronic structure
calculations was performed on the relevant Mg-containing
molecules. The hybrid density functional/Hartree−Fock
B3LYP method was employed from within the Gaussian 09
30
method, which we have applied previously to reactions of
metal-containing species where a stable intermediate is present
25
31
suite of programs, combined with the 6-311+G(2d,p) triple-ζ
on the potential energy surface (PES). These reactions
6
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6
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Article
The ME describes the evolution with time of the grain
populations of the adduct. The probability of collisional transfer
between grains was estimated using the exponential down
model, where the average energy for downward transitions was
−1
33
set to ⟨ΔE⟩
= 300 cm , typical of N . The ME was
down
2
expressed in matrix form and then solved to yield the
recombination rate constant at a specified pressure and
temperature.
MgO + O, MgO + O. The rate coefficient for reaction 1, k
2
1
(6.2 ± 1.1) × 10− cm molecule , is larger than the typical
10
3
−1
=
hard-sphere collision frequency by a factor of ∼2. The long-
range forces governing this reaction include the dispersion force
(
the ionization energy and calculated polarizability for MgO are
−25
3
34
listed in Table 1; α(O) = 8.0 × 10 cm ), the dipole−
induced dipole force arising from the large permanent dipole of
MgO (6.2 D = 2.1 × 10− C·m ), and the dipole−quadrupole
29
35
3
force arising from the quadrupole moment of O( P) (Θ
=
xx
4.3 × 10− and Θ = 2.2 × 10 C·m2 ). Using these
40
−40
36
−
zz
parameters in the analytic expressions derived by Georgievskii
32
and Klippenstein from long-range variational transition-state
theory, the respective capture rate coefficients at 300 K are 4.9
×
−10
−10
−10
3
−1 −1
10 , 3.7 × 10 , and 3.1 × 10 cm molecule s . The
overall rate that would result from a potential that incorporated
all three of these forces would not be a simple sum but up to
about 1.4 times the rate calculated for the dominant interaction
32
alone. That would indicate an overall capture rate for reaction
of about 6.5 × 10− cm molecule s , which agrees well
10
3
−1 −1
1
with our measurement. The dispersion (and dipole−induced
dipole) force gives rise to a T1 dependence in the capture rate,
/6
which we apply to k in the atmospheric model.
1
Reaction 2 involves MgO . The triplet forms of this molecule
2
Figure 6. Optimized geometries (at the B3LYP/6-311+g(2d,p) level
3
are either the triangular superoxide MgO ( A ) or linear
of theory) of magnesium-containing molecules likely to form in the
2
2
3
−
3
3
−
OMgO( Σ ) where the Mg is inserted into the O (Figure 6a
and b). The heats of formation of both isomers are very similar
(Table 3), and these molecules are about 110 kJ mol more
stable than singlet MgO ( A ). There is a significant barrier on
upper atmosphere: (a) MgO ( A ); (b) OMgO ( Σ ); (c) OMgO
g
2
2
2
g
2
3
3
2
+
2
(
B ); (d) O MgO ( B ); (e) MgOH ( Σ ); (f) OMgOH ( Π); (g)
1
2
2
2
2
1
3
−1
HOMgO2 ( A ); (i) MgCO ( A ); (j) OMgCO ( A″); (k)
2
3
1
3
2
1
Mg(OH)CO2 ( A′); (l) HOMg(OH)CO ( A′) ; (m) MgCO H
A′); (n) HOMgCO H ( A′). Color scheme: Mg (yellow); O (red);
1
2
3
2
1
1
1
(
3
−1
3
the A″ surface between the isomers, which lies 183 kJ mol
C (gray); H (white).
above MgO at an O−Mg−O angle of 60.1°. In the present
2
study, MgO2 is produced via reaction 7, and therefore,
formation of either triplet is spin-allowed, and a mixture of
the triplet isomers may well be formed. The rate coefficient
measured here for reaction 2 would then describe the overall
loss of both isomers (treated as a single species in the kinetic
proceed via the formation of an excited adduct, which can
either dissociate back to reactants or forward to products or be
stabilized by collision with a third body. The internal energy of
this adduct was divided into a contiguous set of grains (width
typically 30 cm ), each containing a bundle of rovibrational
states. Each grain was then assigned a set of microcanonical rate
coefficients for dissociation, which were determined using
−1
model). In fact, most MgO in the upper mesosphere is made
2
via reaction 7, and therefore, the value of k obtained here
2
should be valid for atmospheric modeling. Reaction 2 is
inverse Laplace transformation to link them directly to krec,∞
the high-pressure limiting recombination coefficient. For these
neutral reactions, k was set to a typical capture rate
,
relatively fast, although k is a factor of 4 below a typical capture
2
rate constant. This may reflect the fact that the products
rec,∞
10
1
+
3
−
−
1/6
3
−1 −1 32
MgO( Σ ) + O ( Σ ) occur on a triplet surface, whereas the
coefficient of 3 × 10 (T/300 K) cm molecule s ,
where the small positive temperature dependence is character-
istic of a long-range potential governed by the dispersion force.
For reactions involving two radical species that could therefore
take place on surfaces of different spin multiplicities, the
capture rate was then multiplied by the appropriate statistical
factor. The density of states of the adduct was calculated using
the Beyer−Swinehart algorithm for the vibrational modes
2
g
reactants generate additional singlet and quintet surfaces that
do not lead to reaction.
OMgO + O. There is a barrier on the quintet surface for
2
−1
this reaction that is 22 kJ mol above the reactants; therefore,
this surface should not play a role. In contrast, reaction on the
triplet surface involves addition of the O to form O
MgO ,
2
2
followed by dissociation to MgO + O over a barrier that lies
2
2
45 kJ mol− below the reactants. This is not in accord with the
1
(
without making a correction for anharmonicity) and a classical
33
−13
3
densities of states treatment for the rotational modes. The
vibrational frequencies and rotational constants were taken
from the electronic structure calculations (the data are listed in
Table 3).
measured rate coefficient being less than 5 × 10
cm
molecule− s . The likely reason for this is that the MgO
1
−1
2
product from reaction 3 recombines with the O present in the
2
flow tube
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3
11+g(2d,p) level of theory) and the O, which is both
MgO + O ( + M) → O MgO
ΔH0K = −253 kJ mol−1
A RRKM estimate of k10 using the molecular parameters for
2
2
2
2
polarizable and has a significant quadrupole moment (see the
earlier discussion regarding MgO + O), there is no obvious
reason why k is only (6.7 ± 1.8) × 10 cm molecule s . In
fact, it seems likely that once OMgO forms, it then recombines
with the large excess of CO in the flow tube (which was added
to make MgCO via reaction 9), that is, the reverse reaction
illustrated in Figure 7
(10)
−12
3
−1 −1
4
−27
MgO and O MgO in Table 3 yields k = 6.4 × 10 (T/3003
2
2
2
rec,0
2
−3.3
6
−2 −1
−10
K) cm molecule s , k
= 1.8 × 10 exp(−46/T) cm
rec,0
rec,∞
3
molecule− s , and F = 0.30 (k is the rate coefficient at the
1
−1
C
low-pressure limit, krec,∞ is that at the higher-pressure limit, and
31
F is the broadening factor ). At the experimental conditions
OMgO + CO → OMgCO3
C
2
in the present study (1.2 Torr, 300 K), k = 3.2 × 10− cm
11
3
rec
ΔH0K = −118 kJ mol−
1
molecule− s , that is, within an order of magnitude of the
1
−1
(11)
capture rate coefficient. As shown in Figure 4, the O2
Application of RRKM theory to this reaction indicates k = 1.8
1
1
concentrations required to generate OMgO via reaction 8 in
2
−11
3
−1 −1
×
10 cm molecule
Reaction 11 would therefore compete effectively with reaction
because [O]/[CO ] ranged from 0.5 to 8% (Figure 5).
s under the experimental conditions.
the flow tube were a factor of 30−120 times larger than the O
atom concentration. Thus, even if k is close to the capture rate
3
2
2
coefficient between OMgO and O, the MgO product would
2
2
OMgCO must then be recycled to MgCO (or OMgO ) by
3
3
2
likely react with O via reaction 10 rather than reaction with O
2
reaction with O, which slows down the overall rate at which Mg
is produced. We therefore conclude that the measured value for
k4 is most likely a lower limit.
via reactions 2 and then 1 to yield Mg. This holding cycle
would then account for the small measured value for k3.
Atomic O should reduce O MgO to OMgO
2
2
2
MgO + CO. The PES of this reaction is characterized by a
−1
weakly bound MgO−CO complex (well depth = 4.8 kJ mol ),
O MgO + O → OMgO + O
2
2
2
2
which then dissociates to Mg + CO over a barrier that is 2.6 kJ
2
ΔH0K = −116 kJ mol−
1
−1
mol below the reactant entrance channel. The measured rate
−
11
3
−1 −1
coefficient, k = (1.1 ± 0.3) × 10 cm molecule s , can be
5
since there do not appear to be barriers on the triplet and
quintet surfaces of this reaction. Hence, this reaction together
with reactions 3 and 10 would just cycle between OMgO2,
MgO , and O MgO . We therefore conclude that the apparent
reproduced using RRKM theory if the energies of the complex
−1
and barrier are both lower by 3 kJ mol with respect to the
reactants.
2
2
2
Atmospheric Implications. An important objective of this
study is to identify stable magnesium reservoirs that account for
the removal of atomic Mg on the underside of the Mg layer.
The OMgO −MgO −O MgO cycle discussed above is one
small upper limit measured for k results from this recycling of
3
MgO , preventing atomic Mg from being generated via
2
reactions 2 and 1. This indicates that the RRKM estimate for
2
2
2
2
k is reasonable (it is used in the atmospheric model described
10
possibility. However, this cycle will be less efficient above 85
below) and that k is probably close to the capture rate
−5
3
km, where the low pressure (<10 bar) slows down reaction 10
coefficient.
1
and the [O]/[O ] ratio approaches 10%, so that reaction 2
2
MgCO + O. The triplet PES of this reaction is illustrated in
3
becomes a more competitive route for MgO . Hence, the Mg
oxides are probably not effective reservoirs above 85 km. The
2
Figure 7. It is characterized by a strongly bound OMgCO3
present study has also shown that MgCO reacts efficiently with
3
O (reaction 4). Therefore, we now consider how the
magnesium oxides and the carbonate can be converted to
hydroxide species, such as those illustrated in Figure 6. The
magnesium hydroxides may be more effective reservoirs, first
because these species tend to be more stable thermodynami-
cally (see below) and second because the hydroxides are
destroyed by reaction with H (in contrast to O, which destroys
the oxides and carbonate), and the ratio of [H]/[O] is only
1
about 1%. We have previously studied the formation of
24
Mg(OH) from MgO
2
MgO + H O ( + M) → Mg(OH)
2
2
ΔH0K = −448 kJ mol−
1
(12)
Figure 7. Potential energy surface for the reaction MgCO + O,
3
calculated at the B3LYP/6-311+g(2d,p) level of theory.
Although this reaction is fast, there is much less H O in the
2
1
upper atmosphere than O , so that MgO will tend to form
2
−1
complex (well depth = 257 kJ mol ; see Table 3 and Figure
j), which then dissociates to OMgO + CO over a barrier that
24
OMgO predominantly. We therefore now explore theoret-
2
6
2
ically how magnesium hydroxides can be produced from
OMgO and MgCO . Figure 8a illustrates the PES for the
−1
is submerged 150 kJ mol below the reactant entrance channel.
The transition state, illustrated in Figure 7, actually leads to a
2
3
addition of H O to OMgO2
2
weakly bound OMgO−CO complex before the products,
2
−1
H O + OMgO → Mg(OH) + O
2 2 2
2
which are 21 kJ mol above the transition state. Given the large
capture rate coefficient that might be expected between the
highly polar MgCO (μ = 11.6 D, calculated at the B3LYP/6-
ΔH0K = −240 kJ mol−1
3
D
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MgCO + H O → Mg(OH) + CO
2
2
2
3
ΔH0K = −242 kJ mol−
1
This reaction starts with the formation of a strongly bound
complex between MgCO and H O, driven by the strong
3
2
dipole−dipole interaction of the reactants. Rearrangement by
transfer of a H atom from the H O to the nearest O atom on
2
the carbonate leads to a more stable intermediate designated as
HOMg(OH)CO in Figure 8 (the structure is shown in Figure
2
6
l). This intermediate can dissociate directly to the products or
undergo further rearrangement by the H atom migrating to the
terminal O of the carbonate, yielding the more stable
HOMgCO H (see Figure 6n). Note that the barrier to this
3
final rearrangement is well below the reactant energy, and
therefore, there should be facile exchange of the H atom
between the carbonate oxygens until all of the HOMg(OH)-
CO has dissociated to Mg(OH) + CO . Although not shown
2
2
2
in Figure 8, we have also demonstrated that the reaction of
MgCO with atomic H
3
MgCO + H → MgOH + CO2
3
ΔH0K = −277 kJ mol−
1
should occur without any significant barriers. It therefore
appears that there are several potentially rapid reactions
involving H O and H that produce magnesium hydroxides
2
from OMgO and MgCO .
2
3
Now, consider the subsequent chemistry of these hydroxides.
One potential pathway is the addition of CO , for example
2
Mg(OH) + CO ( + M) → HOMg(OH)CO
2
2
2
ΔH0K = −42 kJ mol−
1
MgOH + CO ( + M) → Mg(OH)CO
2
2
ΔH0K = −32 kJ mol−
1
where the resulting hydrogen carbonates are illustrated in
Figure 6k and l. However, the theoretical enthalpy changes
listed above show that CO does not bind strongly enough to
2
these hydroxides. Subsequent rearrangements to form the more
Figure 8. Potential energy surfaces calculated at the B3LYP/6-
stable isomers HOMgCO H and MgCO H involve barriers of
3
11+g(2d,p) level of theory for (a) OMgO + H O, (b) OMgO + H,
3
3
2
2
2
−1
and (c) MgCO + H O.
131 and 127 kJ mol , respectively. The barrier for HOMg-
OH)CO ↔ HOMgCO H is illustrated in Figure 8c. Hence,
3
2
(
2
3
This significantly exothermic reaction proceeds through the
rearrangement of two weakly bound intermediates to yield the
products; there are no significant barriers, and therefore, this
reaction should be rapid. Figure 8b shows the PES for the
reaction of H with OMgO2
addition of CO is unlikely to play a role in further stabilizing
2
these hydroxides.
15
By analogy with the mesospheric chemistry of iron and
16
calcium, the route back to Mg is very likely to be through the
reactions of Mg(OH) and MgOH with H
2
Mg(OH) + H → MgOH + H O
H + OMgO → MgOH + O2
2
2
2
ΔH0K = −35 kJ mol−
1
ΔH0K = −275 kJ mol−1
(13)
(14)
MgOH + H → Mg + H O
H can add to either end of the molecule, forming two very
2
stable intermediates. However, it is only HOMgO that can
ΔH0K = −186 kJ mol−1
2
then dissociate to two sets of exothermic products; on the basis
of a density of states argument, MgOH + O should be the
major products because these products are 218 kJ mol more
Given that Mg(OH) is not a radical and reaction 13 is only
2
2
−1
modestly exothermic, k13 may be relatively slow, and the
dihydroxide could be the major neutral magnesium reservoir. In
fact, even if this is not the case, the MgOH product is likely to
be involved in another holding cycle initiated by recombination
exothermic than MgO + OH.
2
Figure 8c illustrates the PES for the addition of H O to
2
MgCO3
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The Journal of Physical Chemistry A
Article
with O to form HOMgO (see Figure 6g)
2
2
MgOH + O ( + M) → HOMgO
2
2
ΔH0K = −249 kJ mol−
1
(15)
A scan on the PES for this reaction shows that there is no
barrier to forming HOMgO2 (apart from when the O2
approaches orthogonal to the MgOH axis close to the C2v
symmetry axis). Applying RRKM theory (with the parameters
for HOMgO in Table 3) and treating the two low-frequency
2
vibrational modes as free rotors (i.e., HO−MgO ), we estimate
2
−26
−4.07
6
−2 −1
k
1
= 1.2 × 10 (T/200 K)
cm molecule s , k
=
rec,0
rec,∞
.2 × 10− exp(−48/T) cm molecule s , and F = 0.24.
10
3
−1 −1
C
13
Under typical conditions at 85 km (T = 200 K, [M] = 5 × 10
−3
−13
3
−1 −1
cm ), k = 4.9 × 10 cm molecule s . Because [O ]/[H]
15
2
5
is ∼10 , reaction 15 is likely to compete very effectively with
reaction 14, although HOMgO should then be recycled to
2
MgOH via exothermic reactions with O
HOMgO + O → HOMgO
2
ΔH0K = −128 kJ mol−
1
(16)
(17)
HOMgO + O → MgOH + O2
ΔH0K = −117 kJ mol−
1
1
Because the [O]/[H] ratio is about 100 above 80 km, these
reactions are likely to be more important than the reactions of
atomic H with HOMgO and HOMgO to yield MgO and
Figure 9. Schematic diagram of magnesium chemistry in the upper
mesosphere/lower thermosphere region. Major magnesium species are
shown in boxes with bold outlines. Important reaction pathways are
indicated with thicker arrows. Reactions with measured rate
coefficients are indicated with solid arrows; broken arrows indicate
pathways for which rate coefficients are estimated or fitted. Note the
role of O in the MgO −O MgO −OMgO and MgOH−HOMgO −
2
2
MgO (which are less exothermic, ΔH = −25 and −58 kJ
0
K
−1
mol , respectively).
To summarize, the neutral chemistry of magnesium in the
mesosphere is complex. In fact, there may not be a dominant
reservoir species. The most likely candidate is Mg(OH) , but
2
2
2
2
2
2
2
even if this is not the case, O should play an important role in
OMgOH holding cycles.
2
creating holding cycles for MgO and MgOH, which slow down
the regeneration of Mg via reactions 2 (followed by reaction 1)
and 14, respectively.
2
+
1
+
and O . Above 90 km, Mg mostly reacts with O , although
2 3
+
+
the resulting MgO is overwhelmingly recycled back to Mg by
reaction with O. Below 90 km, recombination of Mg with N
becomes more rapid; the resulting Mg ·N ions then switch
+
A New Atmospheric Model for Magnesium Chem-
istry. The reaction scheme illustrated in Figure 9 brings
together the results of this study with our recent work on the
2
+
2
+
3
1,37,38
with O
2
, so that Mg·O
2
is the major molecular ion below 85
ion−molecule chemistry
and earlier work on the neutral
1
3,24
km. These molecular ions either react with atomic O, first to
chemistry
of magnesium. Solid arrows in Figure 9 indicate
+
+
form MgO and then Mg , or undergo dissociative recombi-
nation with electrons, yielding neutral Mg. The rate coefficients
for all of the ion−molecule reactions in Table 4 have been
measured, apart from the dissociative electron recombination
reactions to which we have assigned a single rate coefficient
k ) that is typical of small molecular ions.
26
reactions for which rate coefficients have been measured, and
thicker arrows indicate the likely more important pathways.
This reaction scheme is significantly more complex than the
scheme in our previous magnesium model published 15 years
1
3
ago. In order to make this complexity tractable in the model,
we simplistically assign the neutral reservoir species to be
40
(
Mg(OH) and assume that this is produced whenever OMgO2
2
In the model, the concentrations of the three major gas-
phase magnesium species, Mg, Mg(OH) , and Mg , are
or MgCO3 form (via reactions 8 and 9) or directly via
+
2
recombination of MgO and H O (reaction 11). A single rate
2
determined by full solution of their respective continuity
equations. All other magnesium species whose reactions are
listed in Table 4 are short-lived intermediates and are therefore
treated in the chemical steady state. The continuity equations
of the major species are then given by
coefficient k is then varied in the model to produce an optimal
12
fit to the satellite observations described in the Introduction.
The small positive temperature dependence assigned to
reaction 12 is that for the analogous reaction Ca(OH) +
2
1
6,39
H.
In reality, this rate coefficient most likely encapsulates
the role of several reservoir species. The set of reactions
required for this simplified neutral chemistry scheme, along
with their rate coefficients, is listed in Table 4.
d[Mg]
+
= Iabl + A[Mg(OH) ] + B[Mg ]
2
dt
Figure 9 also illustrates the ion−molecule chemistry of
+
− (C + D)[Mg] − ∇ΦMg
magnesium. Mg ions are mostly formed in the atmosphere by
(XIII)
charge transfer with the dominant lower E region ions, NO+
6
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The Journal of Physical Chemistry A
Article
Table 4. Gas-Phase Neutral and Ion−Molecule Reactions of
Magnesium-Containing Species in the Time-Resolved
Atmospheric Model
⎧
⎩
D = k [O ]⎨(k [O ] + k [CO ][M] + k [O ][M])
6
3
7
3
9
2
8
2
a
number
reaction
rate coefficient
reference
⎛
⎜
⎝
⎞
⎫
⎭
k [O ][M]
10
2
⎟ + k [H O][M]⎬/E
Neutral Chemistry
11
2
k [O] + k [O ][M]⎠
2.3 × 10−10 exp(−139 K/T) Plane and13
2
10
2
(
(
(
(
(
(
(
(
(
R6)
R1)
R7)
R2)
R8)
R9)
Mg + O → MgO
3
+
O
Helmer
2
Mg + O → Mg +
5.8 × 10−10(T/200 K)1/6
this study
E = k [O] + (k [O ] + k [CO ][M] + k [O ][M])
1 7 3 9 2 8 2
O
2
2.2 × 10− exp(−548 K/T) Plane and13
10
⎛
⎞
MgO + O →
k [O ][M]
10 2
⎝ k [O] + k [O ][M]⎠
3
MgO + O
Helmer
⎜
⎟ + k [H O][M]
2
2
11
2
MgO + O →
7.9 × 10−11(T/200 K)1/6
this study
2
10
2
2
MgO + O
2
X
3.8 × 10−29(T/200 K)−1.59
and ∇Φ is the divergence of the vertical flux of species X. The
transport of all of the magnesium constituents is assumed to be
governed by the same eddy diffusion coefficient up to the
turbopause around 100 km, and the vertical flux of species X at
height z is given by
MgO + O (+M)
Rollason and
2
2
4
→
OMgO2
Plane
MgO + CO (+M) 5.9 × 10−29(T/200 K)−0.86
Rollason and
2
24
→
MgCO3
Plane
Rollason and
R12) MgO + H O (+M) 1.1 × 10−26(T/200 K)−1.59
2
24
→
Mg(OH)2
Plane
R10) MgO + O (+M)
1.8 × 10−26(T/200 K)−2.50
see text
⎛
⎞⎞
2
2
⎛
∂[X]
1
⎝H
1 ∂T
X
→
O MgO
2 2
⎜
⎟
Φ = −K ⎜
+ [X]
+
⎟
zz
1 × 10−11 exp(−600 K/T) fitted, see
⎝ ∂z
T ∂z ⎠⎠
R13) Mg(OH) + H →
(XVI)
2
Mg
text
where Kzz is the vertical eddy diffusion coefficient, H is the
atmospheric scale height, and T is the temperature. Above the
turbopause, molecular diffusion dominates over eddy diffusion,
and Kzz and H in eq XVI are replaced by D and H , the
Ion−Molecule Chemistry
+
+
1.2 × 10−9
(
(
(
(
(
(
(
R18) Mg + O + → Mg
Rutherford et
51
2
+
O
al.
Rutherford et
2
+
8.2 × 10−10
R19) Mg + NO → Mg
NO
51
X
X
+
al.
molecular diffusion coefficient and the scale height of the
+
1.2 × 10−9
R20) Mg + O →
Whalley et
41
3
+
31
individual species X, respectively.
MgO + O
al.
2
+
2.4 × 10−30(T/200)−1.65
The model is one-dimensional (1D), extending from 65 to
110 km with a height resolution of 0.5 km. Equations XIII−XV
are integrated with a 10 min time step using a time-implicit
R21) Mg + O (+M) →
Whalley et
2
+
31
Mg·O2
al.
R22) Mg + N (+M) → 1.8 × 10−30(T/200)−1.72
+
Whalley et
2
Mg·N2+
31
42
al.
integration scheme. The changing diurnal concentration
+
4.6 × 10−29(T/200)−1.42
2.3 × 10−28(T/200)−2.53
R23) Mg + CO (+M)
Whalley and
2
profiles of Kzz and the background mesospheric species that
+
52
→
+
Mg·CO2
Plane
+
−
control the magnesium chemistry (H, O, O , NO , e , etc.) are
3
R24) Mg + H O (+M)
Martinez-
Nunez et
43
2
+
read in every 20 model minutes. All model runs shown here
→
Mg·H O
2
53
al.
were integrated over 20 model days, for the conditions of
January, 40° N.
+
+
5.9 × 10−10
(
(
R25) MgO + O → Mg
Whalley and
52
+
O
Plane
2
+
There are only two adjustable parameters in the model, k12
and the meteoric ablation flux of Mg. The annual average flux
−
−7
−1/2
R26) Mg·X + e → Mg
X (X = N ,
3 × 10 (T/200)
see text
+
2
−2 −1
CO , H O, O)
was set to 8200 Mg atom cm s , equivalent to a global daily
2
2
a
3
−1 −1
6
−2
input of 30 t of cosmic dust. The corresponding height profile
Units: bimolecular, cm molecule s ; termolecular, cm molecule
−
1
of the Mg injection rate (I in eq XIII) is taken from our
s .
abl
2
chemical ablation model and peaks at 85 km with a maximum
injection rate of 0.012 atom cm− s . The ablation flux was
2
−1
d[Mg(OH)2]
44
=
D[Mg] − A[Mg(OH)2]
then varied seasonally according to the radio meteor rate.
+
dt
Figure 10 illustrates the model predictions of Mg , Mg, and
∇ΦMg(OH)2
Mg(OH) in the MLT, for January and July at midlatitudes.
(XIV)
2
−
+
This shows a two-fold increase in the Mg column abundance
9
9
−2
+
from 3.0 × 10 in winter to 6.1 × 10 cm in summer. This i9s
d[Mg ]
+
4
=
C[Mg] − B[Mg(OH) ] − ∇ΦMg
in very good agreement with the GOME and SCIAMACHY
2
(
XV)
dt
satellite measurements (see the Introduction). The peak height
+
of the Mg layer is between 90 and 100 km, with peak densities
where Iabl is the rate of injection of Mg from meteoric ablation
−3
between 2000 and 5000 cm , in accord with rocket-born mass
8
,45
A = k [H]
spectrometric measurements.
13
The neutral Mg layer, in contrast, exhibits little seasonal
9
variation, with a small decrease from 2.1 × 10 in January to 1.5
B = (k [O ] + k [O ][M] + k [N ][M]
20
3
21
2
22
2
9
−2
×
10 cm in July. Again, this agrees well with the satellite
4,9
record, and the predicted peak of the Mg layer around 88 km
is in accord with Mg profiles retrieved recently from
SCIAMACHY limb-scanning measurements.
+
k [CO ][M] + k [H O][M])
23 2 24 2
−
⎛
⎜
⎝
⎞
6
k [e ]
2
6
⎟
−
k [O] + k [e ]⎠
2
5
26
CONCLUSIONS
This study has used a combination of laboratory experiments,
theory, and atmospheric modeling to develop a significantly
■
+
+
C = k [O ] + k [NO ]
1
8
2
19
6
250
dx.doi.org/10.1021/jp211526h | J. Phys. Chem. A 2012, 116, 6240−6252

The Journal of Physical Chemistry A
Article
Council for a research studentship (for C.L.W.). We thank Dr
Miriam Sinnhuber (Karlsruhe Institute of Technology) and
Prof. John Burrows (University of Bremen) for helpful
discussions regarding the SCIAMACHY data set.
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