J. Phys. Chem. 1994, 98, 1394-1397
1394
A Model for the Temperature Dependence of the Near UV Absorption Spectra of Organic Peroxy Radicals Jeffrey A. Joens Department of Chemistry, Florida International University, Miami, Florida 331 99 Received: June 16, 1993; In Final Form: October 28, 1993”
A Gaussian approximation, based on the sum rules that apply for allowed electronic transitions, is used to model room-temperature and high-temperature absorption data for three organic peroxy radicals. For HO2, the absorption spectra calculated from the model are in good agreement with available experimental data for temperatures in the range 300-1 100 K. For CH302 and CzH502, there is again good agreement between the experimental and calculated spectra at room temperature. A satisfactory fit to the high-temperature data for these two species can also be achieved if the integrated band strength of the experimental data is increased by 10-1 5%, suggesting a systematic error in the normalization procedure used in finding the experimental cross sections. The use of the fitting parameters obtained from the sum rule model to obtain information about the excited electronic state potential of RO2 radicals and limitations of the present model are also discussed.
Introduction
spectrum is given by the equation20s21
Organic peroxy radicals (RO2) are important reaction intermediates in the oxidation of hydrocarbons both in the atmosphere and in combustion. In several studies of the kinetics of organic peroxy radical reactions, time-resolved UV absorption spectroscopy has been used to monitor radical concentration.I-l4 Because of this, there is great interest in determining accurate absorption cross sections for organic peroxy radicals over a wide range of temperatures. There have been numerous studies of the room-temperature absorption spectra of organic peroxy radicals, as summarized in two recent reviews.15J6 For HO2, CH302, and C2H5O2, the consistency of recent spectral measurements has meant that accurate room-temperature absorption cross sections are available for these species. In addition, a few measurements of the absorption spectra of these three radicals have been carried out at high temperature. The purpose of the present paper is to develop a model for the temperature dependence of the near UV absorption spectra of RO2 radicals. The model will be used to fit room-temperature data for organic peroxy radical spectra and to predict changes in the spectra with temperature.
Calculation of UV Absorption Spectra The near UV room-temperature absorption spectra of RO2 radicals are approximately Gaussian in shape. This suggests that a Gaussian model for the temperaturedependence of these spectra be used. One model that is often used is the Sulzer-Wieland equation,17developed from a quasidiatomic or separable harmonic oscillator model for the molecular absorption spectrum in which the upper electronic state in the active vibrational mode of the molecule is approximated by a linear repulsive potential. However, it has been shown that the Sulzer-Wieland equation, both in its original formI7 and as modified by Troe and co-workers,18 incorrectly accounts for the frequency dependence of the absorption spectrum and the changes in mean frequency and width of the absorption spectrum with temperature.19-20 An improved Gaussian model for the temperature dependence of a continuous electronic absorption spectrum, the sum rule model, was recently developed.20 In this model, the absorption ~~~~~~
@
Abstract published in Aduance ACS Abstracts, January 1 , 1994.
where
u2(T) = (w;/S)[(l
+ r ) ’ / ( l - r)’] +
and r = exp(-hcw,/kT) (4) The above equations involve four parameters: we, the vibrational frequency of the active mode in the lower electronic state that is primarily responsible for determining theshape of the absorption spectrum; IO,the integrated band strength of the spectrum; and VOand 8, the parameters describing the upper electronic state, which is approximated by a linear repulsive potential. Note that we, VO, and 8 have units of reciprocal centimeters and IOhas units of cm2 molecule-I. While the above model has assumed that there is only one active vibrational mode in the molecule, eqs 1-4 can easily be extended to cases where two or more active vibrational modes are present. For both HO2 22-24 and CH302,25molecular orbital calculations indicate that the 0-0stretching mode is dissociative and therefore primarily responsible for determining the shape and temperature dependence of the near UV absorption spectrum. For HO2, experimental s t ~ d i e s ~show ~ , ~ ’that the major products of the photodissociation reaction are 0 + OH, as expected for breaking of the 0-0 bond. For CH302, photodissociation at 248 nm appears to form CH3 + 02as the major initial products28 (9(CH3 + 02) = 0.74 f 0.13; 9 ( C H 3 0 + 0) = 0.26 f 0.13), suggesting that the dynamics of the photodissociation process on the upper electronic state potential are complicated. However, this does not exclude having the 0-0stretching mode as the active mode in CH3O2, as the absorption spectrum acts only as a probe of the Franck-Condon region of the upper electronic state and not of the entire upper state potential surface. For CH3O2 and C ~ H J O ~ , it is therefore assumed that the 0-0stretching mode is the active vibrational mode. By identifying theactivevibrational mode in theorganic peroxy radical as the 0-0stretching mode, three parameters are left to be determined in eqs 1-4, IO, VO,and 8. The general procedure
0022-365419412098-1394$04.50/0 0 1994 American Chemical Society
Absorption Spectra of Organic Peroxy Radicals
The Journal of Physical Chemistry, Vol. 98, No. 5, 1994 1395
TABLE 1: Fitting Parameters Used in the Gaussian Representation of the Absorption Spectra of RO, Radicals. molecule 1018 10 ( c d molecule-') w,b (cm-I) VO(cm-1) 6 (cm-1) 48000 5800 0.889 1097 H02 1112 42080 5955 CHa0z 1.185 1112 41880 5320 CzHsOz 1.055 0 Calculated using the procedure given in the text. Values for we are taken from Table 111.27 and 111.28 of ref 15. 200
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Wavelength (nm)
Figure 2. Experimental and calculated high-temperature spectra of HOz: (-) calculated spectra at T = 577 K (top), T = 677,777 and 1100 K (bottom); experimentaldata at (0) T = 577 K,(0) T = 677 K,(A) T = 777 K, and (0) T = 1100 K. The experimentalcross sections have been normalized to give a best fit to the calculated spectra, as discussed
in the text.
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Wavelength (nm)
Figure 1. Experimental and calculated spectra of H02 at T = 300 K:
calculated from parameters in Table 1, (0)ref 32, (0) ref 33, and (A)ref 30. Experimentalcross sections have been normalized to a cross section of 3.47 x 10-18 cm2 molecule-1 at h = 220 nm. (-)
used to obtain these parameters is as follows. The experimental data for the room-temperature absorption cross sections of a particular radical are fit to eq 1, with the quality of the fit measured in terms of the relative rms error. A best fit to the data is obtained by varying IO,p, and u in eq 1 until the minimum in the relative rms error is found. Equations 2 and 3 are then used to find Vo and j3 from p and u. Once this has been done, eqs 1 4 can be used to find the absorption spectrum as a function of temperature. In cases where sufficient temperature-dependent cross section data are availabile, l o , VO,and j3 are found by minimizing the relative rms error using experimental data a t all temperatures. The details of the fitting of the absorption spectra of various organic peroxy radicals are given below. Note that absorption cross sections are given in units of cm2 molecule-', base e. HO2. There have been several measurements of the roomtemperature absorption spectrum of the hydroperoxyl radi ~ a l . l J - 5 Critical . ~ ~ ~ ~reviews of these measurements were recently presented.15J6 While there is significant variation in the absolute intensity of the near UV absorption spectrum of HOz obtained in various experiments, a majority of the results give a value for the absorption cross section at 220 nm in the range 3.4-3.5 X 10-l8 cm2molecule-l. Lightfoot and co-workers'5 have therefore suggested that absorption spectra from different laboratories be scaled to a cross section of 3.47 X 10-18 cm2 molecule-1 at 220 nm. When this is done, there is in general good agreement among cross section data from different experiments. There have been two measurements of the absorption spectrum of hydroperoxyl radical at elevated temperatures. First, in a shock tube experiment, Troe has reported absorption cross sections for H02 at wavelengths between 210-250 nm and a temperature of 1100 K.34,3s More recently, Lightfoot and Jemi-Alade have measured the relative absorption spectrum of HO2 a t 298, 577, 677, and 777 K.32 Using the parameters obtained by fitting the room-temperature data of Lightfoot and Jemi-Alade as a starting point, a best fit to all of their experimental data wascarriedout.36 The parameters corresponding to the best fit to the data are given in Table 1. It is interesting to note that the parameters obtained by fitting all of the data differ only slightly from those found using only the room-temperature data. In Figure 1, the calculated roomtemperature absorption spectrum is compared to the three most recent room temperature measurements of the experimental cross sections. In Figure 2, the absorption spectra calculated using eqs
1 - 4 and the parameters listed in Table 1 are compared to the experimental absorption cross sections found by Lightfoot and Jemi-Alade32 and by Troe.34 The high-temperature relative absorption spectra of Lightfoot and Jemi-Alade and the shock tube data of Troe have been scaled to give the best agreement between the experimental and calculated spectra at each temperature. In all cases, the agreement between the experimental and calculated absorption spectra is within the uncertainty in the experimental results. CH302 and C2HsO2. The room-temperature near UV absorption spectrum of methylperoxy radical has been measured by several 1~12*30-32~37-43 While numerous discrepencies exist among early results for both the shape and intensity of the spectrum, recent results have been in good agreement. In their review of R02 chemistry, Lightfoot and co-workers15 have given a recommended set of absorption cross section values for CH3O2, found by normalizing and then averaging the cross sections reported by Jenkin and c o - ~ o r k e r s ,Moortgat, ~ Veyret, and Lesclaux,", Simon, Schneider, and Moortgat," Dagaut and Kuryl0,4~Jenkin and COX,^^ and Lightfoot and Jemi-Alade.32 Several measurements have also been made of the near UV absorption spectrum of ethylperoxy r a d i ~ a l . ' ~ J ~Recent ,4~~ measurements are in good agreement for the shape of the spectrum but show some scatter in absolute intensity. Lightfoot and cow o r k e r ~have ' ~ recommended that the diode array data of Bauer, Crowley, and Moortgat13 be used for the room-temperature spectrum. Recent room-temperature cross sections reported by Fenter and co-workers14 are in good agreement with the shape of the spectrum given by Bauer, Crowley, and Moortgat but are approximately 10% higher in intensity. Equation 1 was used to fit therecommended room-temperature absorption cross sections given by Lightfoot and co-workers for C H ~ O Zand , the data of Bauer, Crowley, and Moortgat for C2H502. The parameters corresponding to the best agreement between the experimental and calculated spectra are given in Table 1. The calculated room-temperature spectra, and those of recent experimental results, are given in Figures 3 and 4. There is only one report of a measurement of the complete absorption spectrum of methylperoxy radical at elevated temperature, that of Lightfoot and J e r ~ i - A l a d e .In ~ ~their experiment, relative absorption cross sections for CH3O2 were measured a t 662 K. The relative cross sections were converted to absolute cross sections by comparison of the CH3O2 spectrum to that of ozone a t the same temperature, taken from the shock tube data of Astholz, Croce, and Troe.49 In one addition experiment, Sander and Watson6 found no substantial change in the cross section for CH3O2 a t 250 nm over the temperature range 248-417 K. The parameters given in Table 1 have been used to calculate the absorption spectrum for CH3O2 at 662 K. In Figure 5, the results are compared to the experimental data of Lightfoot and
Joens
1396 The Journal of Physical Chemistry, Vol. 98, No. 5, 1994
0 r
X
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Wavelength (nm)
Figure 3. Experimental and calculated spectra of CH3O2 at T = 300 K: (-) calculated from parameters in Table 1, ( 0 )ref 15 (recommended values), (0),ref 32, ( 0 )ref 12, and (A) ref 11. Data from ref 12 have cm2 molecule-I at A been normalized to a cross section of 4.58 X
= 240 nm.
radical at high temperature is that of Fenter and co-workers at 600 K.I4 In Figure 5, the calculated absorption spectrum of CzHs02 at 600 K, found using the parameters given in Table 1, is compared to the experimental cross sections. As in the case of the methylperoxy radical spectrum, the agreement between the experimental and calculated spectra for CzHsOz is better if the integrated band strength of the experimental cross sections is increased. A 10%increase in band strength for the experimental spectrum gives the best agreement between the experimental and calculated results. Since the experimental cross sections were found relative to the methylperoxy radical spectrum at the same temperature, a rescaling of the CH3O2 spectrum, as suggested above, would also accounted for the observed intensity difference between the experimental and calculated spectra of C2H5O2 at 600 K.
Discussion
X
200
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Wavelength (nm)
Figure 4. Experimental and calculated spectra of C2H~02at T = 300 K: (-) calculatedfrom parameters in Table 1, ( 0 )ref 13 (recommended values from ref 15), (0)ref 14, and (box) ref 49. Data from ref 14 have cm2molecule-’ at X been normalized to a cross section of 4.36 X
= 240 nm.
200
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Wavelength (nm)
Figure 5. Experimental and calculated spectra of CH302 and C2H502 at high temperature: CH302 spectrum at T = 662 K (-) calculated from parametersin Table 1;(0)experimental data fromref 32, normalized against ozone data of ref 50; ( 0 )experimental data from ref 32, normalized
to give the best agreement between the calculated and experimentalspectra C2H~02at T = 600 K (- - -) calculated from parameters in Table 1; (0) experimentaldata from ref 14, normalized against CH302 data from ref 32; (H) experimental data from ref 14, normalized to give the best agreement between the calculated and experimental spectra. Jemi-Alade. If the absolute cross section values reported by Lightfoot and Jemi-Alade are used, there is a significant difference between the intensity of the calculated spectrum and the experimental spectrum. However, if the integrated band strength of the experimental spectrum is increased by 15% to give a best fit of the experimental to the calculated spectrum, much better agreement is found. Such a change in band strength is within the uncertainty in the high temperature absorption cross section values of ozone used by Lightfoot and Jemi-Alade to normalize their 662K data for CH3Oz and is consistent with the observation that the integrated band strength reported for ozone is systematically low at elevated temperatures.50 The only absorption spectrum reported for the ethylperoxy
The sum rule method for finding a Gaussian representation for a continuous electronic absorption spectrum provides a means for modeling the near UV absorption spectra of organic peroxy radicals at both room temperature and elevated temperatures. The spectra calculated by this method are in good agreement with the available experimental data for HOz, CH3O2, and CzH502, as shown above. The method therefore provides a simple and useful approach for modeling the absorption spectra of R02 radicals. The fitting parameters obtained from the analysis of experimental data for RO2 spectra provide information on the excited electronic state potential in the Frarrck-Condon region of the dissociative vibrational mode of the molecule. For CH3O2 and C ~ H s 0 2the “H3C-O” and “0-0”stretching vibrations are actually mixtures of these two local mode vibrations, making a comparison between the results found from fitting of the experimental spectrum and those obtained from molecular orbital calculations difficult to carry out. For HOz, however, it is possible to compare information obtained from the analysis of absorption data to results found from molecular orbital calculations. If HO2 is treated as a quasidiatomic molecule, then 8, the slope of the excited electronic state potential in the direction of the 0-0 stretching vibration, is related to the change in the 0-0bond length by the relationship51
Using the information given in Table 1 for HOz and prd = 1.37 X g for the reduced mass of HO-0 gives dV’/droo = 9.5 X lo5cm-* nm-I. The corresponding value for dV’/aroo, based on molecular orbital calculations, is 9.3 X lo5 cm-I nm-I from Langhoff and Jaffe,23sz and 8.3 X lo5cm-’ nm-I from Vasquez, Peyerimhoff, and Buenker.24.53 The agreement between the molecular orbital results and those found from fitting the experimental absorption spectrum of H02 is excellent and suggests that the fitting parameters obtained from the analysis of absorption data can be used to provide useful information on the excited electronic state potential for other ROz radicals. At high temperatures, deviations from a simple Gaussianshaped spectrum are expected to occur. These deviations can be accounted for by using higher spectral moments to find modified Gaussian representations for the absorption spectrum. Coalson and KarplusS4 have derived a general expression for the third moment of an absorption spectrum and shown how this can be used in a cumulant expansion for the absorption spectrum. Joens2I has pointed out that this procedure gives nonphysical absorption coefficients a t high temperatures for model systems and has presented a procedure based on information theory that uses the third and fourth moments of the spectrum to account for deviations from a pure Gaussian shape. In both of these procedures, the modified Gaussian representations for the absorption spectrum do not require additional fitting parameters to be used.
Absorption Spectra of Organic Peroxy Radicals A detailed comparison of the Gaussian approximation to exact absorption spectra for the linear repulsive model has been presented by Joens.2' Differences between the calculated and exact spectra for the model system become significant (>10%) for values of r > 0.2, which for R02 radicals corresponds to temperature greater than 1000 K. This gives an upper limit on the temperature at which the Gaussian approximation is expected to apply. At higher temperatures, the expressions for the third and fourth spectral moments found by Joens for the linear repulsive model potential can be used to find a modified Gaussian approximation to the absorption spectrum using information theory. The spectra calculated by this procedure are in good agreement with the exact results for the linear repulsive model for values of r < 0.35,21corresponding to temperatures up to 1500 K for RO2 radicals. The information theory approach is therefore recommended for modeling high-temperature data for R02 absorption spectra.
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