J. Phys. Chem. 1996, 100, 4713-4723
4713
NO3 Photolysis Product Channels: Quantum Yields from Observed Energy Thresholds
Harold S. Johnston,* H. Floyd Davis, and Yuan T. Lee
Department of Chemistry, UniVersity of California, and Chemical Sciences DiVision, Lawrence Berkeley
Laboratory, Berkeley, California 94720
ReceiVed: September 13, 1995; In Final Form: January 2, 1996X
The absorption of visible light by NO3 leads to three products: NO + O2, NO2 + O, and fluorescence. We
report a new method for obtaining quantum yields for the NO3 molecule, using measured energy thresholds
separating NO3 and its product channels. The assumptions of this model are the following: (i) NO3 internal
energy (photon plus vibrations plus rotations) gives the necessary and sufficient condition to select each of
the three product channels, as justified by the observed large differences in reaction times for the three products.
(ii) The unresolved complexities of ground-state NO3 spectra and quantum states are approximated by standard
separable ro-vibrational expressions for statistical mechanical probability functions. These results may be of
interest to both physical chemists and atmospheric chemists. The NO3* vibronic precursors of the three
product channels are identified. We evaluate and plot vibrational state-specific absolute quantum yields as
a function of wavelength Φvib(λ) for each product channel. We sum over vibrational states to give the
macroscopic quantum yield as a function of wavelength Φ(λ), obtained here from 401 to 690 nm and at 190,
230, and 298 K. By adding considerations of light absorption cross sections σ(λ) at 230 and 298 K and a
stratospheric radiation distribution I(λ) from 401 to 690 nm, we evaluate the wavelength dependent
photochemical rate coefficients j(λ) for each of the three product channels, and we find the integrated photolysis
constants, jNO, jNO2, and jfluorescence. At 298 K, our Φ(λ) for NO2 + O products agree with the major features
observed by Orlando et al. (1993), but show significant systematic offset in the 605-620 nm wavelength
range. Our Φ(λ) for NO + O2 products at 298 K agree with those observed by Magnotta et al. (1980) within
their experimental scatter. Experimental error in our method for measuring quantum yields arises only from
errors in measuring the wavelengths at which various product yields approach zero; there is no dependence
and, thus, no error arising from light absorption cross sections, light intensities, or species concentrations,
which contribute errors to the method of laser photolysis and resonance fluorescence. The results reported
here are unique in including quantum yields at 190 and 230 K, which may be useful for modeling atmospheric
photochemistry.
Introduction
Absorption of visible light by NO3 yields two product
channels and fluorescence:
NO3 + hν
f NO + O2
f NO2 + O
f NO3 + hν(fluorescence)
rate
jNO[NO3]
jNO2[NO3]
jFL[NO3]
(1)
(2)
(3)
For physical chemical considerations, the quantum state basis
for partitioning the quantum yield among the three channels is
the interesting question, and this article develops new information on the subject. We evaluate state-specific absolute
rotational-vibrational quantum yields for each of the three
channels, sum over rotational states to obtain state-specific
absolute vibrational quantum yields, and sum over vibrational
states to obtain macroscopic quantum yields as a function of
wavelength, which we compare to observed values by others.
For atmospheric problems, the most important quantity is the
photolysis rate coefficient, jNO, since the NO product leads to
destruction of two ozone molecules, whereas product channels
2 and 3 are neutral with respect to ozone:
X
NO3 + hν f NO + O2
NO + O3 f NO2 + O2
NO2 + O3 f NO3 + O2
NO3 + hν f NO2 + O
O + O2 + M f O3 + M
NO2 + O3 f NO3 + O2
net: 2O3 + hν f 3O2
net: null reaction
Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-4713$12.00/0
Previous experimental reports of the quantum yields Φ(λ)
and first-order photolysis rate constants j(λ) for (1) and (2) are
laser-photolysis resonance-fluorescence studies of Magnotta
(1979),1 Magnotta and Johnston (1980),2 and Orlando et al.
(1993).3 Magnotta’s study1,2 was designed to give absolute
quantum yields for product channels 1 and 2. However, as a
result of some systematic error, the NO2 product appeared to
have a maximum quantum yield of about 1.5, and all quantum
yields including those for NO were divided by 1.5, which gives
a 1.00 quantum yield for the NO2 channel between 580 and
585 nm. For this study, we went back to Magnotta’s thesis,1
which has much material that was never published, and in the
upper panel of Figure 1 we present all his directly measured
points for NO2 + O. Magnotta looked for two-photon effects
and found that NO or NO2 products (i) arose only from twophoton effects at 660 nm, (ii) showed one-photon plus weak
two-photon dependence at 623.3 nm, and (iii) showed no twophoton effects at 585 and 589.3 nm. We re-examined all data
between 600 and 625 nm and found no statistically significant
two-photon effects in this region. Orlando et al.3 show
numerous data for NO2 + O in their Figure 2 and include a
line through the points. Values from this average line are listed
between 586 and 639 nm in their Table 1, and we include this
line in the upper panel of our Figure 1 for comparison with
Magnotta’s results. Orlando et al.’s line falls within Magnotta’s
scatter of points, but over the wavelength range 590-615 nm,
most of Magnotta’s points lie below Orlando’s line, and above
620 nm most of Magnotta’s points lie above Orlando’s line.
© 1996 American Chemical Society
4714 J. Phys. Chem., Vol. 100, No. 12, 1996
Johnston et al.
Figure 2. Potential energy profiles (ordinate) of ground-state NO3
(2A2′), photoexcited NO3 (2E′), NO2 + O products in one region of
nine-dimensional configuration space, and NO + O2 products in another
region.5 The NO + O2 products are separated by an energy barrier
from NO3*, and the NO2 + O threshold is determined by thermodynamics.
of states and a congested NO3 absorption spectrum. The state
is 15 105 cm-1 above 2A2′(0,0,0,0), corresponding
to light absorption at 662 nm. (The relations shown between
the electronic states of NO3 and the two product channels are
developed in this article.)
We evaluate the quantum yields as a function of wavelength,
ΦNO(λ), ΦNO2(λ), and ΦFL(λ), for the three channels using (i)
Davis et al.’s recently measured threshold energies,5,6 Θ1 and
Θ2, between ground-state NO3 and its two product channels;
(ii) the fluorescence study of Nelson et al.,7 which gives a sharp
value of the threshold Θ1 for the termination of fluorescence;
(iii) the observed NO and NO2 product formation lifetimes6 from
NO3*; (iv) the observed fluorescence lifetime8 of NO3*; (v) the
NO3 ground-state vibrational frequencies, degeneracies, and
probability distribution functions; and (vi) the NO3 ground-state
rotational energies, degeneracies, and probability distribution
functions.
Threshold Energies To Form Each Set of Products. Davis
et al.5 studied the photodissociation of NO3 using the method
of molecular beam photofragmentation translational spectroscopy at laser wavelengths in the range 532-662 nm, and that
study gives threshold energies for channels 1 and 2. A special
nozzle heated a flowing mixture of He and N2O5 to about 573
K for about 1 ms to dissociate the N2O5, then cooled the NO3
and NO2 products to room temperature, and sent the gas into
supersonic expansion to form a molecular beam, where the
vibrational temperature was about 300 K and the rotational
temperature was close to absolute zero. They found an upper
limit to the potential energy barrier height for NO3 f NO +
O2(3Σg-) to be at 594 nm or 16 835 cm-1. With 1 nm spectral
resolution, Davis et al.6 found this threshold to be at 594.2 nm
or 16 829 cm-1. Fluorescence studies by Nelson et al.7,8 and
Ishiwata et al.9 set a sharp lower limit for this threshold Θ1 for
formation of NO + O2 from ground-state NO3. We magnified
and measured the published NO3 fluorescence excitation
spectrum,7 subtracted the NO2 fluorescence excitation spectrum
that they reported, and plotted their observed spectrum, which
gives 594.5 ( 0.5 nm as the threshold wavelength for absence
of fluorescence. With a somewhat greater wavelength uncertainty, Ishiwata et al.9 indicate the same threshold value. Davis
et al.6 directly observed the rate constant for decomposition of
highly excited NO3 to form NO + O2, 1/k ) 0.7 × 10-9 s at
592 nm. Nelson et al.8 found that over 85% of NO3 fluorescence
decayed with a lifetime of 340 ( 20 µs, which is 6 orders of
2E′(0,0,0,0)
Figure 1. Previously measured quantum yields, 298 K. Upper panel:
NO2 + O products; all of Magnotta’s separate experiments1,2 are shown
by dots; Orlando et al.’s3 average values are shown by the line. Lower
panel: NO + O2 products; Magnotta, dots; Orlando et al’s three
observed points are given as a line.
Magnotta’s data for the NO + O2 product channel are given
as points in the lower panel of Figure 1. Orlando et al. obtained
only three quantum yields for the NO + O2 channel, at
wavelengths of 580, 585, and 590 nm (their Figure 2 places
the 590 point at 595 nm, which is inconsistent with their text
and Table 1). They combined their three data with a modification of Magnotta’s NO quantum yields and presented a full set
of values from 586 to 639 nm in their Table 1; but except for
their three points, these values do not represent new results for
the NO + O2 product channel and do not agree with Magnotta’s
actual data. Orlando’s three experimental points for NO + O2
are given by the line in the lower panel of Figure 1, and these
three points do agree with Magnotta’s data over this narrow
wavelength range.
This article presents a different experimental-theoretical
method to obtain the absolute quantum yields for each of the
three channels at any temperature, presented here for 0, 190,
230, and 298 K.
Physical Basis for This Method
A potential energy diagram of this system is given by Figure
2, which gives the energy origin of the ground electronic state
of NO3 (2A2′), an excited electronic state (2E′), the products
NO2 + O, and the products NO + O2 including three electronic
states of molecular oxygen. At a given absolute energy, the
wave function of highly excited NO3 is a combination of terms,
some corresponding to low ro-vibrational energies of the excited
electronic state 2E′ and some corresponding to highly excited
ro-vibrational energies of the ground electronic state 2A2′. The
strong mixing of such states is called the Douglas effect;4 at a
given energy an NO3* is not in one state or the other but has
properties of each state, and this effect produces a high density
NO3 Photolysis Product Channels
J. Phys. Chem., Vol. 100, No. 12, 1996 4715
magnitude longer than the observed6 time to form NO + O2.
Thus, the zero temperature threshold between disappearance of
fluorescence and formation of NO + O2 must be extremely
sharp. From these fluorescence studies and the molecular beam
studies, we assign the threshold Θ1 to be 107/594.5 ( 0.5 )
16 821 ( 14 cm-1.
With respect to the threshold energy, Θ2, for NO3(0,0,0,0)
f NO2(0,0,0) + O(3P), Davis et al.5 (their Figure 10) found no
signal for the NO + O2 channel at 584 nm, the hint of a signal
with signal/noise less than 1 at 585 nm, and a distinct signal at
586 nm. From the directly measured yields and rate constants
for formation of NO + O2, Davis et al.6 found the NO signal to
decrease sharply below 585.5 nm and to become negligible
below 584.8 nm, as the NO2 + O quantum yield becomes unity.
From these observations, we assign the threshold for NO2 + O
production to be 585.5 ( 0.5 nm or 17 079 cm-1. By analyzing
the wavelength range (589-584 nm) over which the NO product
channel gives way to the NO2 product channel, the rate of
forming NO2 was found to be more than 100 times faster than
the rate of forming NO at 584 nm.6 Three significant energy
levels are (compare Figure 2)
NO3(2A′)(0,0,0,0)
Θ1, NO threshold
Θ2, NO2 threshold
594.5 ( 0.5 nm
585.5 ( 0.5 nm
zero of energy
16 821 ( 14 cm-1
17 079 ( 14 cm-1
(4a)
and the orders of magnitude of the observed relaxation times
are
fluorescence
NO3* f NO + O2
NO3* f NO2 + O
300 × 10-6 s
≈10-9 s
<10-11 s
obs, ref 8
obs, ref 6
obs, ref 6
(4b)
Identification of Quantum-State Precursors to Each
Product Channel. These barriers are 1715 and 1974 cm-1
above 2E′(0,0,0,0). We use RRKM theory to calculate the
energy-specific rate constant at 29 cm-1 (energy equivalent of
1 nm) above each barrier. In one calculation NO3 corresponds
to low vibrational quantum numbers of the excited electronic
state 2E′, and we find 1/k ≈ 10-12 s. In the other calculation
the system corresponds to highly excited vibrational states of
the ground electronic state 2A2′, and 1/k ≈ 10-9 s. The observed
lifetimes6 and these RRKM calculations6 identify the Douglas4
components that are NO3* precursors to each of the three
product channels (compare Figure 2):
(i) NO + O2 r NO3(2A2′) ZPE plus
ro-vibrational energy between 16 821 and 17 079 cm-1 (5)
(ii) NO2 + O r NO3(2E′) ZPE plus
ro-vibrational excitation> 1974 cm-1
(iii) NO3 + hν(fluorescence) r NO3(2E′) ZPE plus
ro-vibrational excitation < 1715 cm-1
Rotational-Vibrational States of NO3. The NO3 absorption spectrum contains an enormous number of unresolved lines,
and the detailed electronic-vibrational-rotational states are
uninterpreted (refs 4, 5, 6, 8 and references there). We
approximate these unknown quantum states by the standard
separable spectroscopic and statistical mechanical formulas
(Herzberg,10 pp 22-26, 177-179, 501-510; Atkins,11 pp 472476, 490-494, 571-572, Chapter 20) for vibrational and
rotational energies, degeneracies, partition functions, and normalized probabilities. (NO3 has a D3h potential energy function
with three symmetrically placed shallow minima; each one taken
alone is of C2V symmetry. Since the depth of these shallow
minima is comparable to or less than the zero-point energy,
ZPE, of the fundamental vibrational frequencies, they act merely
as a perturbation to the D3h nature of NO3.12,13 The vibrational
frequencies (ω, cm-1) and degeneracies (g) for NO3 (D3h) are
given by12
ωi ) {ω1(g1), ω2(g2), ω3(g3), ω4(g4)} )
{1061(1), 762(1), 1490(2), 363(2)} (6)
Expressions for the vibrational energy Evib, partition function
qvib, and normalized probability Pvib are slightly different for
the degenerate ω3 and ω4 modes,
Evib ) V(hc/k)ω, gV ) V + 1, V ) 0, 1, 2
(7)
qvib ) (1 - e-hcω/kT)-2
(8)
Pvib ) (gVe-Vhcω/kT)/qvib
(9)
and the nondegenerate ω1 and ω2 modes,
Evib ) V(hc/k)ω, gV ) 1, V ) 0, 1, 2
(10)
qvib ) (1 - e-hcω/kT)-1
(11)
Pvib ) (e-Vhcω/kT)/qvib
(12)
As in (6), the vibrational state is often given by (V1, V2, V3, V4).
The separable rotational energies and statistics of D3h NO3
are
Erot ) BJ(J + 1) - (A - B)K2, K e J
) BJ(J + 1) - (B/2)K2 for an equilateral triangle
grot ) (2J + 1) if K ) 0 and 2(2J + 1) if K * 0
(13)
(14)
qrot ) (8π2/6)(I1I2I3)1/2/[h3(2πkT)-3/2] )
(1.0270/6)T3/2/(B3/2)1/2 (15)
Prot ) g(J,K)e-hcE(J,K)/kT/qrot )
g(J,K)e-hcE(J,K)/kT/∑g(J,K)e-hcE(J,K)/kT (16)
where J and K are quantum numbers, B ) 0.458 58 cm-1 for
the planar D3h NO3 (Kawaguchi et al.13), qrot is the rotational
partition function, and Prot is the normalized probability distribution for rotational states. At 190, 230, and 298 K, we calculate
the rotational distributions from (16) for J ) 0-90 in steps of
3 and for all allowed values for K quantum numbers. With
rotational energy Erot(J,K) as the independent variable, the
probability of P(J,K) is shown in the top panel of Figure 3.
The curve of single points is monotonic in J for K ) 0, and the
band of closely spaced points is a complicated mixture of J
and K quantum numbers, such that we have a plot of point
probability as a function of rotational energy. We form the
cumulative sum of P(J,K) as a function of rotational energy,
evaluate it at 0, 40, 80, 120, ..., 1200 cm-1, and demonstrate
that the cumulative sum above about 10 cm-1 is equal to the
cumulative sum of the normalized classical expression (Erot)1/2T-3/2
exp(-Erot/kT). We evaluate the normalized classical expression
(the lower panel in Figure 3) at 10, 30, 50, 70, ..., 1210 cm-1,
and this procedure gives us normalized probability as a function
of rotational energy and temperature, Prot(Erot,T), at 298, 230,
4716 J. Phys. Chem., Vol. 100, No. 12, 1996
Figure 3. Upper panel: Probability distribution of rotational states
with various J and K quantum numbers as a function of the rotational
energy. Lower panel: Normalized classical mechanical distribution
of rotational probabilities that has the same cumulative sum as that of
the upper panel.
and 190 K, each in 61 bins, each bin 20 cm-1 wide. (Calculations and preparation of most figures in this article are done
with the Mathematica 2.1 computer program.14)
Methods of Obtaining Quantum Yields
The Model. The three products, fluorescence, NO + O2,
and NO2 + O, are separated by two thresholds, Θ1 ) 16 821
cm-1 and Θ2 ) 17 079 cm-1 (4). Near absolute zero, the NO3
molecule is in its lowest electronic, vibrational, and rotational
quantum state, and having enough photon energy is a necessary
condition to surmount each threshold. From the large differences (106 in one ratio and more than 100 in the other) in
observed NO3* lifetimes among the three products (4b), we
assume that there are no long-lived metastable states of NO3*
at energies above 15 105 nm, so that photon energy is also a
sufficient condition for product identification. For absolute zero,
the specific assumptions are (i) the quantum yield of NO3
fluorescence is unity at photon energies less than 16 821 cm-1
and zero at energies above 16 821 cm-1; (ii) the quantum yield
of NO formation is unity at photon energies greater than 16 821
cm-1 and below 17 079 cm-1 and zero at energies outside this
258 cm-1 wide energy interval; and (iii) the quantum yield of
NO2 is zero below 17 079 cm-1 and unity above 17 079 cm-1.
These statements are expressed in the top panel of Figure 4 by
the vertical separators of the quantum yield value of unity
between the three product channels.
Johnston et al.
Figure 4. Quantum yields following NO3 light absorption. Upper
panel, T ) 0 K: 401-586.5 nm, NO2 + O products; 585.5-594.5
nm, NO + O2 products; 595.5-690 nm, fluorescence. Lower panel,
T ) 298 K, as found by this article: the same products, but, relative
to 0 K, the quantum yields as a function of wavelength are spread and
overlapped due to thermally excited vibrations and rotations in the
reactant NO3 (2A2′).
At finite temperature, enough internal energy (photon, vibrations, rotations) to surmount its threshold is a necessary
condition for each molecular product formation. The strong
ro-vibronic interactions in photoexcited NO3, the high density
of states,4-6,8 and the widely different rate constants (4b) for
forming the three products justify the assumption that internal
energy provides a sufficient condition for each product channel
identification. At a finite temperature, NO3 in its ground
electronic state has some equilibrium population in excited
vibrational and rotational states, Einternal. In this case, a photon
energy of (Θ1 - Einternal), which is less than the threshold energy,
can access the NO + O2 product channel, leading to photon
wavelength spreads such as those shown around Θ1 by the lower
panels of Figure 4. Similar considerations lead to the spread
of NO2 + O products at energies below Θ2 and to the decrease
of fluorescence to energies below Θ1. Specifically, we assume
that the products following light absorption are
NO2 + O, if Ephoton + Evib + RrErot is greater than Θ2 (17)
NO + O2, if Ephoton + Evib +
RrErot is greater than Θ1 and less than or equal to Θ2
Fluorescing NO3, if Ephoton + Evib +
RrErot is less than or equal to Θ1
where Rr is the fraction of rotational energy effective in
overcoming the energy thresholds, a physical quantity restricted
to the range 0-1.
NO3 Photolysis Product Channels
J. Phys. Chem., Vol. 100, No. 12, 1996 4717
Nelson’s fluorescence spectrum was in relative, not absolute,
terms, we adjusted the height of the peak near 606 nm to agree
with the corresponding peak in the observed fluorescence
spectrum. (i) In the lowest panel, the rotational energy
contribution toward product formation is set to 0, that is, Rr )
0. It is clear that the assumption of zero contribution by
rotational energy is unacceptable. (ii) In the middle panel, Rr
is taken to be 0.5, which agrees much better with the
fluorescence spectrum, but the approach to 0 between 595 and
600 nm is still too steep. (iii) In the top panel, Rr is taken to be
1, which shows the best agreement with the threshold behavior
and marginally shows the best agreement with the shape of the
band that peaks near 606 nm. The plot with Rr ) 1.00 shows
better agreement than the plot with Rr ) 0.75 (not shown here).
Figure 5 indicates that 100% of rotational energy is available
toward overcoming the energy barriers Θ1 and Θ2, but this
would not be true for a diatomic molecule. For a diatomic
molecule with a known potential energy function, this problem
can be solved in terms of simple algebraic equations, leading
to a “centrifugal barrier” such that less than 100% of the
rotational energy is effective toward breaking the bond.16 A
diatomic molecule has three internal coordinates. Restraints in
matching energy and angular momentum among three coordinates between reactant and products in a diatomic molecule set
up the “centrifugal barrier”. As NO3 (D3h) goes to the transition
state O2N- - -O (C2V) on the way to forming NO2 + O products,
the direct pseudo-diatomic molecule probably has a centrifugal
barrier. Both the NO3 reactant and the NO2 + O products have
nine internal coordinates relative to center of mass, and there
may be complex paths in nine dimensions where all the
rotational energy of the reactant contributes to the energy
required to reach the threshold of reaction. Some of these
multidimensional reaction paths may take a longer time to get
to products than a direct route, but the direct route for forming
NO2 + O is so fast that substantial delay along some paths
would not lead to NO + O2 formation or to collisional
deactivation. Except as stated otherwise, we assign Rr to be
1.0 in subsequent evaluations.
Rotational-Vibrational State-Specific Quantum Yields.
The statements (17), expressed as the logical “If” function, give
our most fundamental expression for quantum yields:
Figure 5. Calculated and observed fluorescence spectrum as a function
of wavelength. The solid line in each panel is that observed by Nelson
et al.7 derived from their Figure 1. The dotted spectra are those
calculated according to different assumptions about the effectiveness
of rotational energy in overcoming barriers. Upper panel: Rotational
energy is assumed to be fully as effective as vibrational and photon
energy in overcoming the energy barriers between ground-state NO3
and photolysis products (Rr ) 1.00). Middle panel: Only half the
rotational energy is assumed to be effective in overcoming the energy
barriers between ground-state NO3 and photolysis products (Rr ) 0.50).
Lowest panel: Rotational energy is assumed to be totally ineffective
in overcoming the energy barriers between ground-state NO3 and
photolysis products (Rr ) 0.0).
Empirical Method for Estimating the Nominal Fraction
of Effective Rotational Energy. Nelson et al.7 corrected their
fluorescence excitation spectrum for variation of excitation light
intensity and provided the separately measured NO2 fluorescence
spectrum to give a true base line between 585 and 616 nm.
Assigning a light source uniform over wavelength and using
Sander’s15 298 K NO3 cross sections, we carry through our
procedure (described below) to calculate the fluorescence
excitation spectrum over the 585-616 nm range for four
different assignments of Rr, 0, 0.50, 0.75, and 1.00, three of
which are shown by the dotted curves in Figure 5. Since
[(
[ (
NO2
Φr,v
(λ) ) If
NO
(λ) ) If θ1 <
Φr,v
FL
(λ) ) If
Φr,v
[(
)
]
107
+ Ev + Er > θ2, 1, 0 ) 1 or 0 (18)
λ
)
]
107
+ Ev + Er e θ2, 1, 0 ) 1 or 0
λ
(19)
)
]
107
+ Ev + Er e θ1, 1, 0 ) 1 or 0
λ
(20)
where the photon energy is given by Ephoton/cm-1 ) 107/(λ/
nm), and the If function is 1 if the conditional statement is true
and 0 if the statement is false. When Erot is given by (13),
shown as the top panel of Figure 3, eq 18-20 give the
vibrational-rotational state-specific quantum yield, 0 or 1. In
practice, we use a 20 cm-1 bandwidth of the classical probability
distribution function (lower panel of Figure 3) as the unit of
rotational energy. For the full range of vibrational states,
rotational states, and wavelength bins, the above expressions
yield a three-dimensional (λ, Ev, Er) array where all elements
are either 0 or 1.
Vibrational State-Specific Absolute Quantum Yields. At
each wavelength interval, λ - 1/2 to λ + 1/2 nm, the probability
(9) or (12) of a selected vibrational state multiplied by the sum
4718 J. Phys. Chem., Vol. 100, No. 12, 1996
Johnston et al.
of (18)-(20) over all rotational energy intervals gives the
vibrational quantum yields as a function of photon wavelength:
Φvib(λ) ) Pvib∑Φr,v(λ)Prot
(21)
rot
where Prot is the normalized rotational distribution function and
the summation is the average of Φr,v over all rotational sates.
Our Quantum Yields To Be Compared with Observed
Quantum Yields. Over each 1 nm radiation band, the quantum
yield is the average of Φr,v over rotational and vibrational states,
formally given by
Φ(λ) ) ∑∑Φr,v(λ)PvibProt ) 〈Φr,v〉ave: λ-1/2 to λ+1/2 nm (22)
vib rot
These quantum yields are the ones to compare with observed
quantum yields. The wavelength dependent quantum yield
expressions for each of the three photolysis channels are, in
detail,
ΦNO2(λ) ) ∑∑PrPv If
vib rot
[(
107
λ
[ (
ΦNO(λ) ) ∑∑PrPv If θ1 <
vib rot
ΦFL(λ) ) ∑∑PrPv If
vib rot
[(
107
λ
)
]
+ Ev + Er > θ2, 1, 0 (23)
107
λ
)
]
+ Ev + Er e θ2, 1, 0
)
]
+ Ev + Er e θ1, 1, 0
(24)
(25)
Note: quantum yields found from observed thresholds have no
dependence on absorption cross sections or light intensity. At
each temperature, we do a separate ro-vibrational calculation
for V ) (0,0,0,0), V4 ) 1, V4 ) 2, and V2 ) 1, applying
appropriate probability factors for each of four vibrational
energies and for each of 61 rotational energies.
Quantum Yield Results
Vibrational State-Specific Absolute Quantum Yields. In
Figure 6, we show vibrational state-specific absolute quantum
yields for the following conditions: (i) for four different
vibrational states, (0,0,0,0), (0,0,0,1), (0,0,0,2), and (0,1,0,0),
with respective energies of 0, 363, 726, and 762 cm-1 and with
respective vibrational probabilities Pvib (9) or (12) of 0.666,
0.237, 0.062, and 0.025; (ii) for the three product channels (1,
2, 3); and (iii) at 298 K. Higher vibrational energies give less
than 1% contribution to the quantum yields at temperatures
below 300 K.
A graphical, physical interpretation can be given to each curve
in Figure 6, presented here only for the (0,0,0,0) vibrational
state and the formation of NO2 + O, upper panel of Figure 6.
The probability Pv of this vibrational state at 298 K is 0.666
(9), and the threshold wavelength is 585.5 nm. At any photon
wavelength below 585.5 nm, the photon energy 107/λ cm-1 is
greater than the threshold energy, and all rotational states (the
area under the curve in the lower panel of Figure 3, which has
a value of 1.00) are carried along to give NO2 + O products,
and Φ ) (0.666)(1.00) ) 0.666. At any photon wavelength
above 585.5 nm, the photon does not have enough energy to
surmount the barrier by a deficit energy δ ) Θ2 - 107/λ. Any
rotational state that has energy less than this deficit energy will
not contribute to reaction, and only those rotational states with
energy greater than δ will lead to reaction, that is, the area under
the curve in Figure 3 from Erot ) δ to Erot ) ∞, which is less
Figure 6. Vibrational state-specific, absolute, quantum yields deduced
from observed thresholds, 298 K. In order of area under the curves,
the quantum yields are for vibrational states V ) (0,0,0,0), (0,0,0,1),
(0,0,0,2), and (0,1,0,0). The sum of these quantum yields at each photon
wavelength is the deduced macroscopic quantum yield as a function
of wavelength, Φ(λ), which is to be compared with empirical quantum
yields, found by the relation j(λ)/[σ(λ) I(λ) ∆(λ)].
than 1.00. The quantum yield is the product of the fraction of
vibrational states that have only the zero-point energy (0.666)
and the fraction of rotational states that have energy greater
than the energy deficit: Φ ) (0.666)(∑Pr < 1.00) < 0.666. As
the photon wavelength increases, the energy δ increases, the
area under the rotational probability curve from δ to ∞ decreases,
and the quantum yield decreases. By 630 nm the contribution
of the (0,0,0,0) vibrational state is almost zero since it requires
very high degrees of rotational excitation. This pattern is
followed by the other three vibrational states included here.
These effects quantitatively follow the equation
Erot)1200 cm-1
ΦVNO2(λ)
) Pv
∑
P(Erot)
(26)
Erot)Θ2-107/λ?
The summation is simply the cumulative sum of rotational
NO3 Photolysis Product Channels
J. Phys. Chem., Vol. 100, No. 12, 1996 4719
Figure 8. Comparison of quantum yields with NO2 + O products at
298 K: deduced from thresholds (dashed line) and observed by Orlando
et al.3 (open circles and average line). The filled circles and error bars
represent conditions where absolute calibrations were made3 by way
of ozone photolysis.
Figure 7. Comparison of quantum yields deduced from thresholds
(lines) and quantum yields observed by Magnotta1,2 at 298 K: Upper
panel, NO2 + O products, all observed points; lower panel, NO + O2
products, all observed points (compare Figure 1).
probability from the photon energy deficit δ to 1200 cm-1 in
the lower panel of Figure 3, which is readily calculated, stored,
and recalled to give a simple alternate way to calculate quantum
yields by our method.
Comparison with Observed Quantum Yields. The upper
panel of Figure 7 compares all of Magnotta’s observed quantum
yields,1,2 for NO2 + O products with our deduced line for 298
K (23). Within Magnotta’s scatter of points, these two
determinations of ΦNO2(λ) agree between 580 and 608 nm and
agree again at 637.5 nm, and Magnotta’s data lie above our
results between 609 and 627 nm. The lower panel of Figure 7
compares all of Magnotta’s observed quantum yields1,2 for NO
+ O2 products with our deduced line (24). Our curve and
Magnotta’s observed points indicate the same general shape and
size of the contribution of this product channel, but Magnotta’s
values show large scatter and tend to be higher than our line at
short wavelengths and lower at long wavelengths.
A detailed comparison between our quantum yields for
forming NO2 and Orlando et al.’s observations3 is given by
Figure 8 (based on Orlando’s Figure 2), where the circles are
their observed points, the solid squares with error bars locate
the wavelengths of their absolute calibration against ozone
photolysis, the solid line is their fit to the data, and the dashed
line is our result. In the important feature, the break below Φ
) 1.0 at 585 nm and the fall to 0 at about 635 nm, our results
and Orlando’s results are in good agreement. In view of the
wide range, 585-401 nm, where the quantum yield of NO2 +
O is 1.00, the detailed agreement of disagreement between our
two “falloff” curves is of minor atmospheric importance, but
of some physical-chemical interest. The average magnitude of
the error bars at the calibration points is 0.14 quantum yield
unit. Our line agrees with their line within 0.14 unit, except
between about 605 and 620 nm, where our line is systematically
low. Orlando et al. show detailed structure in their quantum
yields above 620 nm, but this structure is qualitatively incompatible with our model (compare Figure 6), for which fundamental physics suggests only monotonic decrease as wavelength
increases (26). Some of this structure is correlated with the
NO3 absorption cross section, which may indicate some error
in the cross section used to translate their measured j values
into quantum yields; this error could be a small offset between
the wavelength scale used to measure j(λ) and the wavelength
scale used to make the separate measure of σ(λ).
The systematic separation between our quantum yield line
and that of Orlando et al. between 595 and 635 nm is of
physical-chemical interest in that it may have implications for
the NO3 (2A2′) quantum states. This discrepancy appears to be
either a systematic error in Orlando’s experiment or a wrong
assignment of quantum states in our model. With our quantumstate assignments, Orlando’s results appear to contradict the
principle of conservation of total probability. There is not
enough ro-vibrational energy at 298 K to account for Orlando’s
line in the 595-635 nm region, since our model gives an upper
bound value (energy is assumed to be the necessary and
sufficient condition for reaction) to the calculated quantum yields
for NO2. A conceivable explanation is that our results are low
because there is a very low lying electronic state that gives extra
“hot band” population relative to the zero state of NO3 (2A2′).
A conceivable explanation with respect to Orlando et al’s
experiment is that there was a systematic error in their
wavelength extension of their absolute calibrations via successive overlaps.
Photolysis Rate Constant Results
Unlike the quantum yields found by this method, the
photolysis constants depend on NO3 cross sections and the
radiation distribution. The photolysis constant j(λ) spanning 1
nm width is defined as
j(λ) )
Φ(λ) σ(λ) I(λ) ∆λ for the range ∆λ ) λ - 1/2 to λ +
1/2 nm (27)
and a photochemical rate constant j is the integral under the
curve
4720 J. Phys. Chem., Vol. 100, No. 12, 1996
Johnston et al.
j ) ∫401 Φ(λ) I(λ) σ(λ) dλ
690
(28)
where Φ(λ) is the quantum yield as a function of wavelength,
σ(λ) is the light absorption cross section of NO3, and I(λ) is the
light intensity, photons s-1 cm-2/∆nmrange. In (23)-(25) we
derive expressions for Φ(λ), and we use here the σ measurements by Sander15 between 401 and 690 nm and at 298 and
230 K, as modified by Wayne17 et al., p 38. The top panel of
Figure 9 gives these cross sections, σ(λ), at 230 K. We use
solar irradiance obtained in the stratosphere by Arveson18 et
al., converting their values in watts m-2 ∆nm-1 to photons s-1
cm-2 ∆nm-1 by
I(λ) )
photons s-1
)
cm2 (∆nm)range
( )[
5.03411 × 1011
]
λ
watts
(29)
nm m2 (∆nm)
range
This midday solar irradiance, I(λ), between 401 and 690 is the
lower panel of Figure 9. In evaluating the photolysis constants,
the integral (28) is approximated by a summation with 1 nm
steps. Using Sander’s15 cross sections measured at 230 K, we
show the NO + O2 j values as a line and NO2 + O j values as
points between 401 and 690 nm in the lower panel of Figure
10, and the approximate j value for NO production at absolute
zero is given by the top panel. As temperature increases, the
envelope of NO production decreases in height, broadens over
wavelengths, and reveals structure arising primarily from the
cross sections.
We present in Table 1 the 298 K photolysis constants using
quantum yields as reported by Magnotta et al.1,2 and by Orlando
et al.3 and σ(λ)15 and I(λ)18 as we use here. Our photolysis
constant for forming NO2 is 7% lower than that of Orlando et
al., and our photolysis constant for forming NO is 18% larger
than that of Magnotta et al. In view of the recognized scatter
in the experimental results, these comparisons show that these
two different methods of finding photolysis constants are in
reasonably good agreement.
Table 2 gives our evaluated photolysis constants for three
product channels as a function of temperature (298 and 230 K)
and the sensitivity of the photolysis constants to assigned
rotational energy efficiency, Rr, at 298 K. The values of jNO at
298 K for the three values for Rr average 0.0203 with standard
deviation 0.0003, which is 1.5% of the average. Uncertainty
in the rotational energy parameter has only a small effect on
the nitric oxide photolysis constants. Between 230 and 298 K
the value of jNO2 decreases by 1.4%, jNO decreases by 10%,
and jFL decreases by 4.5%. The photolysis constants change
only slowly with temperature.
As a study of the sensitivity of j values to uncertainties in
the assigned threshold energies, we carry out our procedure with
many pairs of Θ1 and Θ2, expressed in Table 3 as threshold
wavelengths, λ1 ) 107/Θ1 and λ2 ) 107/Θ2. The maximum
and minimum values of λ1 - λ2 between our assigned thresholds
594.5 ( 0.5 and 585.5 ( 0.5 are 10 and 8 nm, respectively;
that is, our estimated uncertainty in the spread of the two
thresholds is (1 nm. The differences λ1 - λ2 in Table 3
includes values 8, 9, and 10 nm. The quantity β gives a
convenient measure of the importance of jNO relative to that of
NOx ) NO + NO2:
β ) jNO/(jNO + jNO2)
(30)
Regardless of the individual values of λ1 and λ2, the value of
Figure 9. Upper panel: Sander’s15 light absorption cross sections at
230 K for NO3 as modified by Wayne et al.17 Lower panel: Solar
intensity measured in the lower stratosphere (Arveson, et al.18).
Figure 10. Photolysis rate constants as a function of wavelength for
NO2 + O (dots) and for NO + O2 (lines). Upper panel: 0 K and only
the NO products are shown. Lower panel: 298 K. The apparent scatter
of the NO2 product channel is caused by real structure in the crosssection function and in solar radiation.
the ratio β is largely determined by the difference λ1 - λ2, and
∆β/∆(λ1 - λ2) averages 0.0011 nm-1, which is 10% per nm.
NO3 Photolysis Product Channels
J. Phys. Chem., Vol. 100, No. 12, 1996 4721
TABLE 1: Integrated Photolysis Constants (s-1) at 298 K: (A) Two Experimental Investigations As Reported in the
Literature and As Recalculated To Include the Cross Sections and Solar Radiation Used Here; and (B) As Obtained Here from
Interpreted Observed Thresholds
as reported in reference
-1
jNO2/s
(A) Magnotta et al. (1979, 1980)
Orlando et al. (1993)
(B) this study, standard case, Rr ) 1.0
difference between our values and observed values
0.18
0.19
jNO/s
as recalculated here
-1
0.022
(0.016b)
jNO2/s-1
jNO/s-1
0.167
0.156
-7.1%
0.0165a
b
0.0201
+18%
a Based on Magnotta’s (1979), p 166, averaged and interpolated NO + O quantum yields. b Based on only three experimental points and a long
2
extrapolation, partially fitted to Magnotta’s data.
TABLE 2: Integrated Photolysis Rate Constants j/s-1
Calculated from Observed Thresholds: (A) The Change of
j’s as a Function of rr, the Fraction of Rotational Energy
Effective in the Dissociation Processes; (B) The Effect of
Temperature on Derived Photolysis Rate Constants, with rr
) 1.00
Rr
T/K
jNO2
jNO
jFL
298
1.00
0.75
0.50
A. Effect of Assigned Rr
0.156
0.0201
0.130
0.150
0.0202
0.135
0.144
0.0207
0.141
298
230
1.00
1.00
B. Effect of T, with Rr ) 1.00
0.156
0.0201
0.130
0.158
0.0223
0.157
β ) jNO/jNOx
0.114
0.118
0.125
0.114
0.123
TABLE 3: Sensitivity of Calculated Integrated Photolysis
Constants (j/s-1) to Assigned Energy Thresholds at 230 and
298 Ka
T/K λ2/m λ1/nm jNO2/s-1 jNO/s-1 β ) jNO/jNOx ΦNOmax λ1 - λ2
298 586.5
585.5
584.5
230 586.5
585.5
585
594.5
594.5
594.5
594.5
594.5
595
0.158
0.156
0.151
0.161
0.158
0.156
0.0177
0.0201
0.0221
0.0195
0.0223
0.0243
0.101
0.114
0.128
0.108
0.123
0.135
0.34
0.36
0.42
0.48
0.52
0.56
8
9
10
8
9
10
The thresholds are expressed as wavelengths: λ1 ) 107/Θ1 and λ2
) 107/Θ2. The fraction β ) jNO/JNOx ) jNO/(jNO2 + jNO) and the
maximum value of the NO quantum yield are included. The results
based on the selected thresholds are printed in boldface. Note: ∆β/
∆(λ1 - λ2) is about 0.1 or 10%.
a
On this basis, we estimate our error in the accuracy of β )
jNO/(jNO + jNO2) to be (10% due to uncertainty in assigning
the threshold energies, Θ1 and Θ2. This percentage uncertainty
in the photolysis constant applies to results at both 298 and
230 K. The uncertainty of jNO itself is larger since it includes
errors associated with light intensity and NO3 cross sections.
NO + O2: 10-26% at ground level, 2-6% at 15 km altitude,
and 1-3% at 20 km. Present indication is that in the
stratosphere reduction of NO + O2 by collisional quenching is
a small effect, and collisional quenching of NO2 + O production
is negligible.
Tabulation of Quantum Yields. For possible use by
modelers of atmospheric chemistry, we give in Table 4 the
quantum yields (times 1000) to three figures for two product
channels, NO + O2 and NO2 + O, in the wavelength range
640-401 nm at the three temperatures 190, 230, and 298 K.
Overall, as T increases, the fluorescence signal loses intensity
to both NO and NO2 formation, the NO product channel gains
intensity from the fluorescence channel but loses intensity to
the NO2 product, and the NO2 product gains intensity from both
fluorescence and NO.
Error Estimate. There is no error in our quantum yields
arising from absorption cross sections, the light intensities,
species concentrations, or calibration against a reference substance of known quantum yield, all of which contribute errors
to the method of laser photolysis and resonance fluorescence.
Experimental error in our method for measuring quantum yields
arises only from errors in measuring the wavelengths at which
various product yields approach zero. A systematic error of
unknown magnitude would be present if there is an unidentified
low lying electronic state of NO3. A random uncertainty, of
unknown magnitude, is introduced from our using simple
separable spectroscopic and statistical mechanical expressions
instead of realistic ones, for which we have no knowledge of
the needed parameters. We identify (10% error in photolysis
constant ratio β ) jNO/(jNO2 + jNO) due to uncertainty in location
of the energy thresholds, which are assigned from considerations
other than observed quantum yields. We identify a (3% error
in jNO from uncertainty in assigning the rotational energy
parameter Rr. The two experimental studies give quantum yields
agreeing with the general pattern of our results (Table 1 and
Figures 7 and 8), but there are differences in quantitative details.
Discussion
Collisional Quenching of Product Formation. The quantum yields obtained by this method are for low pressure,
collision-free conditions. The experimental measurements of
quantum yields were done at 10 Torr N21,2 or at 2-5 Torr He.3
The pressure of air is 760 Torr at ground level and 76 Torr at
about 18 km altitude in the atmosphere. We consider here the
possibility of collisional deactivation affecting the laboratoryobserved quantum yields or decreasing product yields in the
atmosphere. In their Discussion section, Nelson et al.8 give a
detailed account of ro-vibronic coupling, density of states, and
excited-state dynamics of NO3. In their Table 1, Nelson et al.8
present bimolecular rate constants for collisional quenching of
fluorescence (excited at 662 nm) by He, N2, O2, C3H8, and
HNO3. These rate constants imply negligible collisional
quenching of NO + O2 production under the experimental
conditions,1-3 and in the atmosphere they imply reduction of
Conclusions
Summarizing Figure. As a broad picture of our results for
the three product channels over the wavelength interval 580640 nm at 298 K, we show our quantum yields Φ(λ) and
photolysis constants j(λ) in units of s-1 nm-1 in Figure 11.
Of Physical-Chemical Interest. Our method sets up the
problem in terms of its true physics, but carrying out the
derivations and computations necessarily involves approximations and simplifications, which contribute unknown errors in
the final results. The dominating feature that determines the
quantum yields is the location of the energy thresholds, which
we obtain from a critical review of recent direct determinations.5-7,9 The physical feature that determines quantum yields
as a function of temperature is the thermal buildup of excited
rotational and vibrational states in the ground-state NO3
molecule. In this analysis, we confirm6 the electronic-
4722 J. Phys. Chem., Vol. 100, No. 12, 1996
Johnston et al.
TABLE 4: Quantum Yields Multiplied by 1000 for Product
Channels NO + O2 and NO2 + O between 640 and 585 nm
and at 298, 230, and 190 K, Where Barrier Heights Are
16 821 and 17 079 cm-1, Corresponding to 594.5 and 585.5
nm (For Wavelengths Less than 585 nm, the Quantum Yield
of NO is 0 and that of NO2 is 1; at and Greater than 641
nm, the Quantum Yields of NO and NO2 are 0)
Φ(NO)
Φ(NO2)
nm
298 K
230 K
190 K
298 K
230 K
190 K
585.0
586.0
587.0
588.0
589.0
590.0
591.0
592.0
593.0
594.0
595.0
596.0
597.0
598.0
599.0
600.0
601.0
602.0
603.0
604.0
605.0
606.0
607.0
608.0
609.0
610.0
611.0
612.0
613.0
614.0
615.0
616.0
617.0
618.0
619.0
620.0
621.0
622.0
623.0
624.0
625.0
626.0
627.0
628.0
629.0
630.0
631.0
632.0
633.0
634.0
635.0
636.0
637.0
638.0
639.0
640.0
0.0
15.2
39.1
97.1
128.0
190.0
220.0
249.0
303.0
328.0
359.0
357.0
318.0
323.0
314.0
291.0
296.0
291.0
283.0
280.0
264.0
271.0
268.0
250.0
248.0
236.0
205.0
200.0
190.0
166.0
166.0
160.0
141.0
143.0
139.0
131.0
127.0
122.0
117.0
106.0
98.5
92.3
84.8
73.9
69.9
64.9
57.8
50.8
46.6
42.6
37.3
32.3
29.4
26.6
23.5
20.3
0.0
26.4
66.7
161.0
209.0
300.0
343.0
383.0
455.0
487.0
517.0
501.0
430.0
421.0
396.0
346.0
338.0
322.0
294.0
282.0
253.0
251.0
243.0
217.0
208.0
193.0
159.0
150.0
138.0
114.0
110.0
102.0
85.5
83.5
78.4
71.5
66.0
61.9
57.6
49.6
44.5
40.6
36.0
29.9
27.4
24.7
21.3
17.8
15.9
14.2
12.0
9.86
8.7
7.66
6.53
5.38
0.0
37.9
94.4
221.0
283.0
397.0
448.0
495.0
575.0
610.0
630.0
598.0
493.0
468.0
429.0
355.0
335.0
310.0
267.0
249.0
213.0
205.0
194.0
167.0
155.0
140.0
111.0
101.0
90.6
71.2
66.1
59.7
47.5
44.8
40.9
36.0
32.0
29.2
26.5
21.9
19.0
16.8
14.5
11.5
10.2
9.01
7.52
6.02
5.23
4.54
3.73
2.93
2.52
2.16
1.78
1.41
983.0
967.0
943.0
885.0
854.0
793.0
763.0
734.0
680.0
654.0
608.0
587.0
567.0
531.0
509.0
472.0
438.0
415.0
371.0
351.0
323.0
296.0
280.0
259.0
238.0
226.0
210.0
193.0
181.0
166.0
147.0
137.0
124.0
108.0
99.3
89.7
76.9
70.4
64.3
55.2
48.7
44.2
39.3
33.9
29.4
26.4
23.6
19.5
17.7
16.1
14.6
11.9
10.7
9.57
8.56
7.15
996.0
970.0
930.0
836.0
788.0
696.0
653.0
614.0
542.0
510.0
453.0
429.0
406.0
367.0
345.0
307.0
275.0
254.0
215.0
198.0
176.0
155.0
143.0
128.0
113.0
105.0
94.7
84.0
77.3
68.4
58.3
52.7
46.5
38.6
34.6
30.3
24.8
22.1
19.7
16.2
13.8
12.2
10.5
8.67
7.23
6.29
5.45
4.29
3.8
3.36
2.97
2.3
2.02
1.77
1.54
1.24
999.0
961.0
905.0
779.0
716.0
602.0
551.0
505.0
424.0
390.0
332.0
307.0
285.0
249.0
229.0
196.0
170.0
153.0
123.0
111.0
94.4
80.0
71.9
62.1
53.0
48.1
42.2
36.2
32.6
28.0
22.9
20.2
17.3
13.8
12.1
10.2
8.03
6.99
6.07
4.8
3.94
3.39
2.83
2.26
1.81
1.53
1.29
0.969
0.838
0.724
0.624
0.462
0.396
0.338
0.288
0.224
vibrational states (that is, the Douglas4 effect components) of
the excited NO3* precursors for each of the three product
channels (5). We give expressions for and evaluate absolute
ro-vibrational state-specific quantum yield (18, 19, 20). For
vibrational state-specific absolute quantum yields, we present
an equation (21) and plot several examples in Figure 6. We
sum over these interesting microscopic-state quantum yields to
obtain useful values as a function of wavelength and temperature.
Figure 11. Summary of our results at 298 K and between 580 and
640 nm: NO2 + O (line decreasing from left), NO + O2 (dots), and
fluorescence (line increasing to the right); upper panel, quantum yields
Φ(λ); lower panel, photolysis constants j(λ).
Of Atmospheric Interest. This article presents a different
experimental method of obtaining quantum yields for NO3
photolysis. Our results are applicable to stratospheric temperatures, and we present quantum yields as a function of
wavelength at 298, 230, and 190 K, and we evaluate the sunlit
stratospheric photolysis rate constants, jNO, jNO2, and jFL at 230
and 298 K. We regard our results (Table 4) to give the best
available room temperature quantum yields for the NO + O2
channel: Magnotta’s results1,2 had an imposed correction factor
and showed large experimental scatter; and Orlando et al. made
only three measurements for this channel. Our results for NO2
+ O quantum yields at 298 K agree with those of Orlando et
al.3 in major features such as wavelength of initial quantum
yield falloff below a value of 1 and the wavelength where the
quantum yield has dropped essentially to 0, but at intermediate
wavelengths there are systematic disagreements (Figure 8). Since
these disagreements cause only a 7% difference between the
photolysis constants, we think one could equally accept either
set of quantum yields for this channel at this temperature. There
are no measured quantum yields for NO2 + O or NO + O2
production at other than room temperature; our quantum yields
at 190 and 230 K are in the range of stratospheric temperatures;
and for internal consistency our quantum yields at three
temperatures (Table 4) are, we think, the currently best available
data set for atmospheric modeling. The uncertainty of the NO3
photolysis coefficients is now much less than the factor of 2
cited by a recent critical survey19 in 1994.
Acknowledgment. This work in the Chemistry Department
of the University of California and at the Lawrence Berkeley
Laboratory was supported by the Director, Office of Energy
Research, Office of Basic Energy Sciences, Chemical Sciences
Division, of the U.S. Department of Energy under Contract No.
DE-AC03-76SF00098.
NO3 Photolysis Product Channels
References and Notes
(1) Magnotta, F. Absolute Photodissociation Quantum Yields of NO3
and N2O5 by Tunable Laser Flash Photolysis-Resonance Fluorescence. Ph.D.
Thesis, University of California, Berkeley, CA, 1979.
(2) Magnotta, F.; Johnston, H. S.; Geophys. Res. Lett. 1980, 7, 769.
(3) Orlando, J. J.; Tyndall, G. S.; Moortgat, G. K.; Calvert, J. G. J.
Phys. Chem. 1993, 97, 10996.
(4) Douglas, A. E. J. Chem. Phys. 1966, 45, 1007.
(5) Davis, H. F.; Kim, B.; Johnston, H. S.; Lee, Y. T. J. Phys. Chem.
1993, 97, 2172.
(6) Davis, H. F.; Ionov, P. I.; Ionov, S. I.; Wittig, C. Chem. Phys. Lett.
1993, 215, 214.
(7) Nelson, H. H.; Pasternack, L.; McDonald, J. R. J. Phys. Chem.
1983, 87, 1286.
(8) Nelson, H. H.; Pasternack, L.; McDonald, J. R. J. Chem. Phys.
1983, 79, 4279.
(9) Ishiwata, T.; Fugiwara, I.; Naruge, Y.; Obi, K.; Tanaka, I. J. Chem.
Phys. 1983, 87, 1349.
(10) Herzberg, G. Molecular Spectra and Molecular Structure II.
Infrared and Raman Spectra of Polyatomic Molecules; D. Van Nostrand
Co., Inc.: New York, NY, 1945.
(11) Atkins, P. W. Physical Chemistry, 4th ed.; W. H. Freeman and
Co.: New York, 1990.
J. Phys. Chem., Vol. 100, No. 12, 1996 4723
(12) Kim, B.; Hunter, P. L.; Johnston, H. S. J. Chem. Phys. 1992, 96,
4057.
(13) Kawaguchi, K.; Hirota, E.; Ishiwata, T.; Tanaka, I. J. Chem. Phys.
1990, 93, 951-956.
(14) Wolfram, S. Mathematica, 2nd ed.; Addison-Wesley Publishing
Co., Inc.: Redwood City, CA, 1991.
(15) Sander, S. P. J. Phys. Chem. 1986, 90, 4135.
(16) Johnston, H. S. Gas Phase Reaction Rate Theory; The Ronald Press
Co.: New York, 1966; pp 107-108.
(17) Wayne, R. P.; et al. The Nitrate Radical: Physics, Chemistry, and
the Atmosphere. Air Pollution Research Report 31, Commission of the
European Communities, 1990.
(18) Arveson, J. C.; Griffin, R. N., Jr.; Pearson, B. D., Jr. Appl. Opt.
1969, 8, (11).
(19) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.;
Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E. Molina, M.
J. Jet Propulsion Laboratory Publication 94-26, NASA, 1994. Chemical
Kinetics and Photochemical Data for Use in Stratospheric Modeling,
Evaluation Number 11.
JP952692X