Resonances in the photodissociation of isotopic molecular oxygen—II. The second and third bands

J. Quant. Specfrosc. Radial. Transfer Vol. 40, No. 4, pp. 469-411, 1988

Printed in Great Britain. All rights reserved

0022~4073/88$3.00+ 0.00 Copyright 0 1988Pergamon Press plc

RESONANCES IN THE PHOTODISSOCIATION ISOTOPIC MOLECULAR OXYGEN-II. THE SECOND AND THIRD BANDS

OF

B. R. LEWIS, S. T. GIBSON, M. EMAMI,~ and J. H. CARVER Research School of Physical Sciences, The Australian National University, Canberra, Australia 2600 (Received 13 April 1988)

Abstract-We present detailed photoabsorption cross-section measurements for the (14) and (2-O) bands of the E3C;-X3X:, transition of molecular oxygen. The isotopic molecules 1602, 160180 and “Oz were studied at 79 and 295 K, with an instrumental resolution of 0.06 A FWHM. We find that the bands are further examples of Beutler-Fano resonances in molecular photodissociation.

INTRODUCTION The photoabsorption spectrum of 160, from 1165 to 1320 A is dominated by Tanaka’s progression I,’ consisting of strong, diffuse bands at 1244 8, (longest), 1206 A (second), and 1172 A (third). These are the (w), (14) and (24) transitions from the ground state to the mixed valenceRydberg E3Z; state (labelled B’ by some authors2s3). A weak band at 1269 A is the (O-l) band of the s3me progression. In an earlier work,4 hereafter referred to as I, we reviewed previous experimental and theoretical studies of the E3C;-X3X; transition, and presented detailed photoabsorption cross section measurements for the (CO) and (&l) bands of the molecules 160,, ‘60180 and 1802. These bands exhibit significant broadening and asymmetry, strongly dependent on isotopic mass, due to configuration interaction with the continuum of the B3&-X3X; transition. We found that an empirical band model, based on Beutler-Fano lineshapes, was capable of accurate cross section prediction out to several 8, from the band centres, including minima observed in the wings of the (0) band for all isotopes. It was clear that the longest band of 0, was a rare example of a Beutler-Fano resonance due to predissociation in photoabsorption. At large distances from the band centre, there is some evidence from I that the model cross sections deviate from the measurements due to the effects of neighbouring resonances and the energy-dependences of the Fano parameters. A more complete theoretical description is required. Potential energy curves for the E3C; and B3Z; states undergo an avoided crossing in accordance with the adiabatic non-crossing rule,5-8 and coupling of the two excited states by the radial component of the nuclear kinetic energy operator is expected to be large in the avoided-crossing region, leading to significant non-adiabatic effects on the molecular energy eigenstates and the 9 Resonances due to absorption into mixed states can be treated corresponding photoabsorption. theoretically by solving the coupled SchrGdinger equations. This method has been applied to resonances were well coupled ‘l7 states in OH by van Dishoeck et al,” who noted that individual described by Beutler-Fano profiles. Torop et al9 have developed a similar treatment which has been applied by Wang et al” to an interpretation of the temperature dependence of the O2 photoabsorption cross section in the region 130&1600 A. Wang et al,” using the diabatic form of the coupled equations given by Torop et a1,9 recently calculated photoabsorption cross sections for O2 in the region of the longest band. Using an iterative procedure, theyI found potential curves for the Rydberg and valence states which mix to form the B3C; and E3C; states, and a value of 0.469 eV for the diabatic electronic coupling constant, by fitting their calculations to the experimental cross sections of I. The anomalous isotope shift for the longest band and the observed4 variations in width and asymmetry with rotation were TPermanent address: Department of Physics, College of Arts and Science, Shiraz University, Iran.

470

B. R. LEWIS et al

predicted correctly by the coupled-equations model. The complex variations in linewidth and line profile for each isotopic form of the molecule were reproduced correctly by calculations with a single set of potentials, and a single coupling constant, changing only the reduced mass of the molecule. The coupled-equations model, however, underestimates the cross section in the region of the minimum near 1247 A for ‘*O,, and it was in just this region that our empirical band model4 failed to fit the experimental cross sections at 79 and 295 K with a single set of parameters. Similar conclusions were reached in both papers,4,‘2 namely that a weak, underlying continuum due to another state contributes to the cross section near 1247 A. It is clear that the experimental cross sections of I, together with widths and asymmetries obtained from our empirical band modeL4 provide significant data against which the coupledequations calculations may be tested. It is also seen from the work of Wang et alI2 that almost all of the observed absorption in the region of the longest band may be attributed to transitions into the coupled ‘C; states. The sensitivity of the calculations to the precise form of the potential curves and strength of the coupling is such that it is unlikely that realistic cross sections can be produced by ab initio calculations without reference to experimental data.‘* In this work we extend the cross section measurements of I to the (l-0) and (24) bands and examine whether an empirical band model, based on Beutler-Fano lineshapes, is consistent with the measurements. Comparison between the experimental cross sections and the results of coupled-equations calculations will enable the refinement of the potential energy curves of Wang et al’* to higher energies. The most comprehensive previous cross section measurements for the (1-O) and (2-O) bands of 1602 are those of Ogawa and Ogawa,‘) but they are of insufficient detail for an accurate determination of the theoretical parameters.14 Cross sections for ‘60’80 and l8O2 have not been measured previously.

EXPERIMENTAL

METHOD

The apparatus and experimental technique were discussed in detail in I. Briefly, background radiation from a pulsed discharge in argon was dispersed by a 2.2 m scanning monochromator’5 operating in the first order with a FWHM resolution of -0.06 A. Radiation was detected photoelectrically before entering and after leaving the 10 cm, controlled-temperature absorption cell. We studied three gas samples, 99.8% 160, 53% “0, 99% “0, with cell temperatures of 295 and 79 K, and with wavelength increments of XL-160 mA, depending on the scale of the structure in the cross section. Cell pressures were in the range 0.04-30 torr. Statistical errors in the resultant photoabsorption cross sections were normally <2%, with an extra -2% uncertainty due to uncertainties in cell length, pressure and temperature. Additional uncertainties arose in the case of the 79 K measurements because of increased temperature measurement error and increased empty-cell transmission drifts. Cross sections for ‘60’80 were deduced from measured total cross sections of the 53% I80 sample by performing a weighted subtraction using the known isotopic enrichments and the previously-measured cross sections for the nearly pure 1602 and ‘“02 samples. This procedure increased the relative uncertainty in the ‘60’80 cross section, dramatically in some wavelength regions.

EMPIRICAL

MODEL

Most of the E3&-X3X; bands are diffuse, but, remarkably, the occurrence4.‘6,‘7 of rotational and fine structure in the longest band of 1802 enables the development of an empirical band model from which it is possible to obtain some information on the behaviour of linewidths and asymmetries, even for the diffuse bands. The details of the empirical band model were discussed in I. Band origins for V’ = 1,2 were obtained by fitting the model absorption spectrum to our measurements. Rotational constants B’ were obtained from preliminary calculations of Wang,‘” normalized to the measurements of Ogawa ” for the longest band of 1802. Centrifugal distortion constants D’ were calculated from the rotational constants for l8O2 and an approximate value for o1CI with appropriate isotope correction.” The splitting constants 2 and p were taken as the values

Photodissociation

of isotopic

molecular

oxygen--II

471

measured by Ogawa” for U’ = 0, 180, for all bands of all isotopic molecules. Ground state spectroscopic constants and Honl-London factors for the 3E--3EP transition were given in I. For the reasons discussed previously,4 each rotational line was described by a FanozO lineshape, given by F(C) = (q + E)/(l + 6%

(1)

where t = (v - v,)/T,

(2)

q is an asymmetry parameter, r the HWHM linewidth, and v, the wavenumber of the line centre. The linewidth was taken to vary systematically with rotation4 according to the relation

T(Y) = r, + TJJ’(J’ + 1);

(3)

contrary to I, q was taken to be independent of rotation, since the extreme broadness of the (1-O) and (2-O) bands made it impossible to determine any variation. The model band profile was built up by adding the Fano profiles of individual lines at the positions and with the relative strengths determined by the technique described above and in I. Oscillator strengths, linewidths and asymmetry parameters were determined by least-squares fitting the model cross section, after convolution in transmission with a Gaussian instrument function, to the experimental measurements. RESULTS

AND

DISCUSSION

In Fig. 1, we present measured photoabsorption cross sections for the (2-O) band of the isotopic molecules I60 23 ‘60’80 and ‘*O, at 295 K, together with model cross sections. The measurements of Ogawa and Ogawa I3 for 1602 agree well with ours except near the band centre where theyI significantly underestimate the true cross section. It is not possible to construct a 3Z;-3X; band model which is consistent with the band profile of Ogawa and 0gawa.13 The (24) band is diffuse for all molecules, but a double head, corresponding to the P and R branches, can be seen in the case of “0,. The width of the band increases significantly from ‘*02 to 1602, but there is a strong asymmetry of the same sign for all molecules, the long wavelength wing being stronger. The isotopic shift, based on peak positions, is significantly smaller from 1602 to ‘60’80 than from ‘60’80 to ‘*Oz. Similar conclusions can be drawn from the cross sections measured at 79 K which are given in Fig. 2. At the lower temperature, the band widths become smaller and the peak cross sections larger 5 = Ogawa 4

(2-O)

Band,

and Ogawa

295K

3

1180

1175

Wavelength

1185

l/i)

Fig. I. Measured photoabsorption cross sections for the third bands of ‘60,. ‘60% and ‘80, at room temperature, together with the measurements of Ogawa and Ogawa’) for ‘60,. and model cross sections (lines) generated with the parameters given in the text.

B. R. LEWIS et al

472

5-

(2-O)

Band,

79K

‘802

4-

160’80

1165

1170

1175

Wavelength

1180

1185

(A)

Fig. 2. Measured photoabsorption cross sections for the third bands of ‘60,, “%I’*0 and “0, liquid-nitrogen temperature, together with model cross sections (lines) generated with the parameters Fig. 1.

at of

due to restriction of the rotational structure of the band. This effect is largest for “02 which has the narrowest (2-O) band, and the double head is no longer in evidence at 79 K. Superimposed on the (2-O) band of the E3C;-X’C; transition are weak structures due to the (54) band of the forbidden transition c(‘C,+-X3C;, and, in the case of 160,, the (5-O) band of the forbidden transition /?‘X:-X’XC,. These forbidden bands also become more localized and more prominent at the lower temperature, but they are not of concern to us in this work. Regions where the forbidden bands occur were excluded from the empirical band model fitting procedure. The solid curves given in Figs. 1 and 2 are model fits to the experimental cross sections based on the following parameters: for 160,, v,,= 85,245.8 cm-‘, ,f= 8.3 x 10P4, r = 121 cm-‘, q = 7.5; for ‘60’80, v,, = 85,141.7 cm-‘, f = 6.6 x 10m4,r = 68 cm-‘, q = 4.6; for ‘*O,, v,,= 84,983.9 cm-‘, TJ = 2.6 x 10m4cm I, q = 7.4. The good agreement observed between f =6.3 x 10-4,r,=26cm-‘,

1165

1175

1170

Wavelength

1180

(A)

taken at 295 and 79 K, in the region of the Fig. 3. Measured photoabsorption cross sections, short-wavelength wings of the third bands of “0, and ‘60’80, together with model cross sections (lines) generated with the parameters of Fig. 1.

Photodissociation

of isotopic molecular oxygen-II

413

the measured cross sections at both temperatures and model cross sections calculated with a single set of parameters supports the validity of the 3Z;-3ZZ; band model. The narrowest linewidths for the (2-O) band are five times larger than the broadest linewidths measured in I for the longest band. This greater diffuseness makes it extremely difficult to detect any systematic variation in r or q with rotation. Nevertheless, as implied by the parameters listed previously, it appears that linewidths in the (2-O) band of 1802 increase slightly with rotation. In Fig. 3, we present experimental cross sections in the region of the short wavelength wing of the (24) bands of ‘*02 and ‘60’80 at 79 and 295 K, together with model cross sections based on the parameters given previously. Deep cross section minima are observed near 1174 A for ‘*02 and near 1170 A for ‘60’80, despite decreased accuracy for the latter molecule. The increased cross section near 1165 A is due to the (CM) band of a Rydberg transition ‘flU--X3Z; which is not heavily predissociated. The good agreement between the measured cross sections in this region, at both temperatures and model calculations based on fits performed over the band centres, is a conclusive vindication of the empirical band model. As in the case of the longest band presented in I, we have unambiguous Fano minima associated with the (220) bands of ‘*02 and ‘60’s0. The third band is thus another example of a Beutler-Fano resonance in molecular photodissociation. It is impossible to detect the minimum for the (2-O) band of 1602, since, from Eqs. (1) and (2) and the model values of q and r given previously for this molecule, the minimum would be expected to occur near the centre of the strong 3LZ,,-X3X; transition mentioned earlier. In Figs. 4 and 5, we present measured photoabsorption cross sections for the (la) band of the isotopic molecules ‘60’80 and 180, at 295 and 79 K, together with model cross sections. There is little isotopic or temperature dependence of the band widths or asymmetries, and, together with the (2-O) band of 1602, these are the broadest of the bands studied here or in I. For both molecules, the bands appear nearly symmetric. The only irregularities visible in Figs. 4 and 5 are due to the (4-O) bands of the forbidden transitions c(‘XJ - X3X; and /I’X: - X3X;. We have not presented cross sections for the (14) band of 1602because strong interference from the (4-O)B'C: - X3X:, band makes the measured cross sections useless for the fitting of either the empirical band model or the coupled-equations calculations. The interference will be discussed in detail elsewhere.2’ The solid curves given in Figs. 4 and 5 are model fits to the experimental cross sections based on the following parameters: for ‘*02, v0 = 82,786.l cm-‘,f = 7.9 x 10m3,r = 109 cm-‘, q = - 140; for ‘60’80, v0 = 82858.7 cm-‘, f = 8.0 x 10m3, r = 106 cm-‘, q = 60. The forbidden bands have been excluded from the fit. Due to the extreme broadness of the (la)) band, it is not possible to determine the dependence on rotation of any parameter, and the values of q are very uncertain

(1-O) Band, 295K t

1205 Wavelength

1210 (A)

Fig. 4. Measured photoabsorption cross sections for the second bands of ‘80, and ‘60’*0 at room temperature, together with model cross sections (lines) generated with the parameters given in the text.

B. R. LEWIS et al

(1-O) Band, 79K

1195

1200

1205

Wavelength Fig. 5. Measured temperature,

1210

1215

1220

(A)

photoabsorption cross sections for the second bands of “0, and W’*O at liquid-nitrogen together with model cross sections (lines) generated with the parameters of Fig. 4.

because of interference from the forbidden bands, possible energy dependence of the Fano parameters, and interaction with adjacent E3Z;-X3C; resonances. No Fano minima are visible for the (1-O) band for reasons similar to those mentioned previously for the (2&O)band of 160,. The product 1q 1r is much larger for the (la) band than for any other band studied here or in I. For these reasons, the good agreement between the model and our experimental cross sections for the (1-O) band is not, in itself, a verification of the lineshape used in our empirical model. For example, a Lorentzian shape may fit nearly as well, but, when taken together with the results for the (&O)4 and (2-O) bands, it is seen that a model based on Fano lineshapes is the only one capable of fitting all bands. In Tables 1 and 2, we have summarized the spectroscopic constants, oscillator strengths, widths, and asymmetries obtained from our measurements of cross sections for the (l&O) and (24) bands of the isotopic molecules 1602, ‘60’80 and “Oz. Using the tabulated parameters together with our model, it is possible to generate accurately the (l&O) and (220) cross sections to a distance of several A from the band centres, with the exception of the regions where the forbidden bands occur. It is necessary to discuss the meaning of the oscillator strengths presented in Tables 1 and 2. Because of the intimate mixing of the B3Z; and E3C; states and consequent spreading of the strength of the bound state into the underlying continuum, the concept of a bound state oscillator strength is difficult to define and the total (bound + continuum) ‘CL oscillator strength becomes wavelength interval dependent. The oscillator strengths mentioned previously in this paper and in I are bound state oscillator strengths of the fit, calculated effectively by integrating the fitted Fano lineshape fess the continuum contribution. In the case of the longest band4 q is relatively large (continuum small), r is small, and the model is a good fit to the observed cross section out to a large number of halfwidths from the band centre. As a result, the oscillator strength of the fit is nearly equal to that obtained by integrating the experimental cross section. This result does not obtain for the (la) and (220) bands. In the case of the (2-O) bands of the 180, and ‘60’80, there is an extended continuum component of the cross section which may include contributions from adjacent resonances, and thus the integrated oscillator strength exceeds the fitted bound oscillator strength. For the remaining broad bands, the (2-O) for 1602 and the (l&O) for “0, and ‘60’80, the fitted cross section significantly overestimates the actual cross section in the more distant wings, and the continuum components are less prominent. For this reason the oscillator strength obtained by integrating the cross section is less than the fitted oscillator strength. Both estimates are given in Tables 1 and 2. The only previous measurement of oscillator strength for the (la) and (24) bands is from the electron energy-loss measurements of Huebner et al,” who obtained the values 8.04 x 1O-3 and

Photodissociation

of isotopic molecular oxygen--II

475

Table 1. A summary of the results of this work for the (2-O) band of the E’Z;-X3Z; transition. Band origins, widths, asymmetries and oscillator strengths which include error estimates have been determined by fitting an empirical model to the measured cross sections. Other spectroscopic constants for the upper level of the transition are given also. The splitting constants forall isotopic molecules weretakenasA = -3.3725~1~' and p =O.O45cm-'.I' Unitsarecm-',exceptforq and f, whicharedimensionless. 160

160180

la0

2

2

V cl

85245.af2

a5141.7f4

84983.9+2

B'

1.4271+

1.3439+

1.2702+

D'

4.5ox1o-6 *

3.76~10-~*

3.27~10-~*

121f5'

68f3 §

26.0f1.5

OS

05

(2.6f1.3)x10-4

4

7.5fl.O

4.6kO.4

7.4f0.5

fn

(8.3f0.3)x10-4

(6.6f0.3)x10-4

(6.3+0.2)x10-4

f”

7.axloq4

7.6~10-~

7.7x1o-4

ro rJ

+ Calculations la0 17 2' * Calculated ' rJ=O was

of Wang,

ia

normalized

to

B’ for

v’=O,

from B' and an approximate value for we'.

forced in the fit since this parameter could not

be determined

accurately.

' Fitted oscillator

strengths

(see text).

' Integrated oscillator strengths,h= 1166.6-1187.4; (1602), h=l170.0-1185.0i (1601'0), A=1173.6-1185.1; (l'0,).

Contributions

from forbidden

bands have

been removed.

1.47 x 10e3 for the second and third bands of 160,, respectively. The electron energy-loss oscillator strength** is only slightly larger than our integrated optical value for the second band, but, as was observed in I for the longest band, the electron energy-loss oscillator strength for the third band is nearly double our optical value. The optical oscillator strengths should be regarded as superseding the electron energy-loss values. Because of the difficulties mentioned previously, and the presence of the forbidden bands, it is difficult to determine accurately the isotopic dependence of oscillator strength for the (2-O) band, but there may be a small decrease in f with increasing isotopic mass. There is no significant isotopic dependence for the (1-O) band. CONCLUSIONS We have presented the most detailed photoabsorption cross section measurements available for the (2-O) band of the E3E:;-X3E; transition of 1602and the first such measurements for the (la)

B. R. LEWISet al

476

Table 2. A summary of the results of this work for the (14) band of the ,!?E;-X%; transition. Band origins, widths, asymmetries and oscillator strengths which include error estimates have heen determined by fitting an empirical model to the measured cross sections. Other spectroscopic constants for the upper level of the transition are given also. The splitting constants for each isotopic molecule were taken as 1 = - 3.3725 cm-’ and p = 0.045 cm-‘.” Units are cm-’ except for q and f, which are dimensionless. 160180

”

82858.724

0

2

82786.lf2

B’

1.3596

D’

2.53~10-~*

2.21

r

106+3

109f2

4

-60

--140

fB

(8.0?0.2)~10-~

(7.9+0.1)x10-3

rn

7.1x1o-3

7.ox1o-3

+ Calculations * Calculated ’ Fitted ’

180

of from

Wang, 8’

oscillator

Integrated Contributions

+

1.2848+

18

and

normalized an

strengths

oscillator from

approximate (see

strengths, forbidden

to

B’

x

for

value

lo-6*

v’=O, for

180

2’

17

we’.

text).

A = 1198.1-1217.14;;. bands

have

been

removed.

and (24) bands of 1802 and ‘60’80. The broadening of the bands, caused by configuration interaction with the B3&-X3Z; continuum, is significantly greater than that observed previously4 for the longest band, and the (24) band is the most asymmetric of the bands studied here and in I. An empirical band model, based on Beutler-Fano lineshapes, is capable of accurate cross section prediction out to several A from the band centres, including minima observed in the short-wavelength wing of the (2-O) band for r802 and ‘60’s0. As we found in I, the E3E;-X3X:, transition provides a comparatively rare example of Beutler-Fano resonances due to predissociation in photoabsorption. With the aid of our empirical model, we have obtained band origins, oscillator strengths, linewidths and asymmetries which will enable the refinement of the potential curves and electronic coupling constant which may be deduced from a coupled-Schrlidinger equation treatment of the resonances.23 Our oscillator strengths, the first optical values published, are in reasonable

Photodissociation

agreement with the electron-impact the (2-O) band.

of isotopic molecular oxygen-11

477

valuesz2 for the (14) band, but are substantially smaller for

Acknowledgemenrs-The authors would like to thank C. Dedman and K. Lonsdale for valuable technical assistance. We are also grateful to A. Dalgamo, A. Blake, D. McCoy, L. Torop, and J. Wang for discussions on the theoretical aspects of resonances in molecular photodissociation. REFERENCES 1. Y. Tanaka,

.I. Chem. Phys. 20, 1728 (1952). M. Yoshimine, J. Chem. Phys. 64, 2254 (1976). D. H. Katayama, S. Ogawa, M. Ogawa, and Y. Tanaka, J. Chem. Phys. 67, 2132 (1977). B. R. Lewis, S. T. Gibson, M. Emami, and J. H. Carver, JQSRT 40, 1 (1988). R. J. Buenker and S. D. Peyerimhoff, Chem. Phys. 8, 324 (1975). R. J. Buenker and S. D. Peyerimhoff, Chem. Phys. Lett. 34, 225 (1975). R. J. Buenker and S. D. Peyerimhoff, Chem. Phys. L&t. 36, 415 (1975). M. Yoshimine, J. Chem. Phys. 64, 2254 (1976). L. Torop, D. G. McCoy, A. J. Blake, J. Wang, and T. Scholz, JQSRT 38, 9 (1987). E. F. van Dishoeck, M. C. van Hemert, A. C. Allison, and A. Dalgarno, J. Chem. Phys. 81,5709 (1984). 11. J. Wang, D. G. McCoy, A. J. Blake, and L. Torop, JQSRT 38, 19 (1987). 12. J. Wang, A. J. Blake, D. G. McCoy, and L. Torop, JQSRT 40, 501 (1988). 13. S. Ogawa and M. Ogawa, Can. J. Phys. 53, 1845 (1975). 14. R. Cimiraglia, M. Persico, and J. Tomasi, Chem. Phys. 42, 297 (1979). 15. B. R. Lewis, Appl. Opt. 22, 1546 (1983). 16. M. Ogawa, K. R. Yamawaki, A. Hashizume, and Y. Tanaka, J. Mofec. Spectrosc. 55, 425 (1975). 17. M. Ogawa, Can. J. Phys. 53, 2703 (1975). 18. J. Wang, private communication (1987). 19. G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 1. Spectra of Diatomic Molecules, Van Nostrand-Reinhold, New York, NY (1950). 20. U. Fano, Phys. Rev. 124, 1866 (1961). 21. B. R. Lewis, S. T. Gibson, and J. H. Carver, in preparation (1988). 22. R. H. Huebner, R. J. Celotta, S. R. Mielczarek, and C. E. Kuyatt, J. Chem. Phys. 63, 241 (1975). 23. J. Wang, A. J. Blake, D. G. McCoy, and L. Torop, in preparation (1988). 2. 3. 4. 5. 6. 7. 8. 9. 10.