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 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
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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.
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