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Electronic transition-moment variation in the A1π-X1Σ system of the GeO molecule
1. Quant. Spt~h~sc. Rodlol. Transfer. Vol. 16. pp. 461-469
Pergamon Press 1976 Prinled in Great Britain
ELECTRONIC TRANSITION-MOMENT VARIATION IN THE A’r-X’C SYSTEM OF THE GeO MOLECULE M. L. P. RAO,D. V. K. RAOand P. T. RAO Spectroscopy Laboratories, Andhra University, Waltair, India (Received 25 August 1975) Abstract-The spectrum of GeO was excited in a carbon arc and the relative band intensities were measured by using photographic photometry and were then interpreted in terms of Franck-Condon factors. It was found that the electronic transition moment varies as Re(r) = constant x (1- 0.476r - 0.061r’), where 1.62s r, A s 1.82. Using this relation, smoothed band strengths, band-oscillator strengths and Einstein coefficients of the bands were calculated using expressions given by Penner. The effective vibrational temperature is estimated to be 1090K. The average life times of the u’ = 0 and 1 vibrational levels have also been estimated. INTRODUCTION RECENTLY, the
A ‘r--X’Ii
system of GeO was studied under high resolution by MURTHY et al.“’ in a high-frequency discharge and the rotational constants for the upper (A ‘a) and lower (X’S) states were reported. However, no mention was made of intensity measurements of the bands. Since this particular system of GeO consists of well separated bands throughout the violet region of the spectrum, it is well suited for application of photographic methods. The relative intensities of the bands excited in a carbon are have been measured using photographic photometry. The variation of electronic transition moment with internuclear separation was determined and the Einstein coefficients and related important parameters were also obtained from measured intensities. METHOD OF COMPUTATION
The intensity of a (u’, v”) transition in emission is’*’ 1“I,“*= N,, hcvA,,,.v,
(1)
where v is the frequency of transition, N,, is the population in the excited state and A,,. ullis the Einstein coefficient which is given by the expression (2)
Here R, is the electronic transition moment, which is assumed to be independent of internuclear distance, and qU.,UI1 is the Franck-Condon factor. It follows from eqns (1) and (2) that (3) where K’ is an appropriate constant. Equation (3) can also be written as
where P,s,,m is the band strength for the (u’, v”) transition. For the proper evaluation of Franck-Condon factors, the vibrational wave functions are required for the upper and lower states. We have used the method of FRASER and JARMAIN”) with r,-shift correction. This method involves the use of the Morse potential function’4’whose validity has been tested by SAVITHRYet al. for the A ‘T and X’Z states of GeO. 467
M. L. P. RAO,D. V. K. RAO and
468
P. T. RAO
It is apparent from eqn (3) that (I,,,,../q,,.,,,
v-y = (KN”~)l’*Re (I;.,. cl.
Thus, a plot of (I,~.,,/q,..,,,Ye)“* as a function of r,,.,,, defines the dependence of R.(r) on r for the bands of each progression. To eliminate the population factor N,., the curves thus obtained for each progression are resealed according to the procedure described by TURNERand NICHOLLS.‘@ A single smooth curve showing the variation of R,(r) with r has been obtained for the entire system. This curve allows us to find the smoothed band strengths (I’,,.,.,) for all of the bands within the range of definition of R.(r). From these band strengths, oscillator strengths (_fu,,Oz.) and Einstein coefficients (A,,.,,,) have been calculated by using the relation [PENNER”)]
fu,.“.,= A,,,.-=
0.0304 x lo4 P”,. 0” g,A,,,,.,, ’
(5)
0.667 x lo6 f”,.“,, A~
D, LI ”
6)
,
where g,, is the electronic degeneracy of the upper state as given by WENTINK and ISAACSON.“’ Here we follow the method of taking into account the state degeneracies that was employed by NICHOLLS.@’ EXPERIMENTALPROCEDURE The A ‘T-X18 system of GeO obtained in an arc contains a number of bands which are free from overlap and are suitable for intensity measurements. The densitometric curve was recorded on a microphotometer. The relative intensities have been measured and have been scaled to 100 in Table 1; they are in reasonably good agreement with the calculated values of q,,.,.*. RESULTS The heights of the vibrational levels have been computed from the relation
A plot of log C I/v4 as a function of G’(u’) for u’ = 0, 1,2,3 and 4 yields a straight line from the Table 1. Designations of vibrational transitions, wavelengths at the band head, relative intensities (scaled to 100). Franck-Condon factors, band strengths, Einstein coefficients and f-numbers for the GeO A ‘n-X’2 transition P, ..4a.‘e’) x 10’
0.0 011 0,2 073 0,4 OS 190 131 1,2 1.4 1s 290 2,l 2,3 294 390 3,2 3.3
2695.3 2730.2 2804.2 2882.0 2963.4 3084.4 2614.6 2683.3 2574.8 2907.7 2989.7 2575.0 2638.1 2779.9 2855.5 2531.2 2662.5 2732.2
76 87 81 84 79 56 85 100 78 68 84 88 86 75 78 87 80 82
0.0541 0.1598 0.2353 0.2288 0.1614 0.0928 0.1464 0.1922 0.0669 0.0700 0.1526 0.2085 0.0730 0.1096 0.0815 0.2077 0.0987 0.0545
4.80 5.22 5.02 5.29 6.09 4.84 1.95 2.53 2.20 2.37 3.29 2.47 2.66 2.88 3.33 2.89 3.27 3.68
A,..Js -‘) x 10 A
x 10J
2.52 2.60 2.30 2.24 2.49 1.73 1.10 1.33 1.06 0.98 1.25 1.47 I .47 1.35 1.45 1.81 1.76 1.83
2.74 2.91 2.12 2.79 3.12 2.41 1.13 I .43 1.21 1.24 1.67 1.53 1.46 1.57 I .77 1.74 1.87 2.05
L
.Y-
Electronic transition-moment variation of the GeO molecule
469
slope of which the vibrational temperature has been found to be as 1090K, which is smaller than the value reported by DUBO and RAI”” for the corresponding D-X system of the isoelectronic SnC molecule. The average life times of the first two vibrational levels of the upper electronic state are calculated [BENNETI. and DALBY”“] to be 1.7 and 17.5 psec. respectively. Using the measured intensities, the computed Franck-Condon factors and r-centroids taken from SAVITHRY et uI.,‘~’ we have studied the variation of electronic transition moment with internuclear separation. The equation R, (I) = constant (1 - 0.476 r - 0.061 r2) for 1.62s r, A s 1.82 represents the variation adequately. Using this variation of R.(r) with r, smoothed band strengths, band oscillator strengths and the Einstein coefficients have been calculated from eqn (6). The results are shown in Table 1 together with measured intensities, Franck-Condon factors, and wavelengths at the band heads. Acknowledgements-The authors are indebted to Dr. Y. PRABHAKARA REDDY for assistance in obtaining the microphotometer record and to the authorities of the Computer Centre where some of the calculations were done. One of the authors (M.L.P.) wishes to thank C.S.I.R., New Delhi, for financial assistance. REFERENCES 1. A. A. N. MURTHY, D. V. K. RAOand P. T. RAO,Proc. R.I.A. 73A, 213(1973). 2. G. HERZBERO, Spectra of Diatomic Molecules. Nostrand, New York (1950). 3. P. A. FRASER and W. R. JARMAIN, Proc. Phys. Sot. A66, 1153(1953). 4. P. M. MORSE,Phys. Rev. 34, 57 (1927). 5. T. SAVITHRY, D. V. K. RAOand P. T. RAO,Nucl. Sci. 43, 329(1974). 6. R. G. TURNER and R. W. NICHOLLS, Can J. Phys. 32, 468 (1954). 7. S. S. PENNER, Quantitative Spectroscopy and Gas Emissitivities. Addison-Wesley, Reading, Mass. (1959). 8. T. WENTINK and L. ~ACSON, 1.them. Phys. 46, 603 (1967). 9. R. W. NICHOLLS, Ann. Geophys. 20, 144(1964). 10. P. S. DUBEand D. K. RAI,J. Phys. B4, 579 (1971). 11. R. G. BENNETT and E. W. DALBY, J. them. Phys. 32, llll(1960).
Pergamon Press 1976 Prinled in Great Britain
ELECTRONIC TRANSITION-MOMENT VARIATION IN THE A’r-X’C SYSTEM OF THE GeO MOLECULE M. L. P. RAO,D. V. K. RAOand P. T. RAO Spectroscopy Laboratories, Andhra University, Waltair, India (Received 25 August 1975) Abstract-The spectrum of GeO was excited in a carbon arc and the relative band intensities were measured by using photographic photometry and were then interpreted in terms of Franck-Condon factors. It was found that the electronic transition moment varies as Re(r) = constant x (1- 0.476r - 0.061r’), where 1.62s r, A s 1.82. Using this relation, smoothed band strengths, band-oscillator strengths and Einstein coefficients of the bands were calculated using expressions given by Penner. The effective vibrational temperature is estimated to be 1090K. The average life times of the u’ = 0 and 1 vibrational levels have also been estimated. INTRODUCTION RECENTLY, the
A ‘r--X’Ii
system of GeO was studied under high resolution by MURTHY et al.“’ in a high-frequency discharge and the rotational constants for the upper (A ‘a) and lower (X’S) states were reported. However, no mention was made of intensity measurements of the bands. Since this particular system of GeO consists of well separated bands throughout the violet region of the spectrum, it is well suited for application of photographic methods. The relative intensities of the bands excited in a carbon are have been measured using photographic photometry. The variation of electronic transition moment with internuclear separation was determined and the Einstein coefficients and related important parameters were also obtained from measured intensities. METHOD OF COMPUTATION
The intensity of a (u’, v”) transition in emission is’*’ 1“I,“*= N,, hcvA,,,.v,
(1)
where v is the frequency of transition, N,, is the population in the excited state and A,,. ullis the Einstein coefficient which is given by the expression (2)
Here R, is the electronic transition moment, which is assumed to be independent of internuclear distance, and qU.,UI1 is the Franck-Condon factor. It follows from eqns (1) and (2) that (3) where K’ is an appropriate constant. Equation (3) can also be written as
where P,s,,m is the band strength for the (u’, v”) transition. For the proper evaluation of Franck-Condon factors, the vibrational wave functions are required for the upper and lower states. We have used the method of FRASER and JARMAIN”) with r,-shift correction. This method involves the use of the Morse potential function’4’whose validity has been tested by SAVITHRYet al. for the A ‘T and X’Z states of GeO. 467
M. L. P. RAO,D. V. K. RAO and
468
P. T. RAO
It is apparent from eqn (3) that (I,,,,../q,,.,,,
v-y = (KN”~)l’*Re (I;.,. cl.
Thus, a plot of (I,~.,,/q,..,,,Ye)“* as a function of r,,.,,, defines the dependence of R.(r) on r for the bands of each progression. To eliminate the population factor N,., the curves thus obtained for each progression are resealed according to the procedure described by TURNERand NICHOLLS.‘@ A single smooth curve showing the variation of R,(r) with r has been obtained for the entire system. This curve allows us to find the smoothed band strengths (I’,,.,.,) for all of the bands within the range of definition of R.(r). From these band strengths, oscillator strengths (_fu,,Oz.) and Einstein coefficients (A,,.,,,) have been calculated by using the relation [PENNER”)]
fu,.“.,= A,,,.-=
0.0304 x lo4 P”,. 0” g,A,,,,.,, ’
(5)
0.667 x lo6 f”,.“,, A~
D, LI ”
6)
,
where g,, is the electronic degeneracy of the upper state as given by WENTINK and ISAACSON.“’ Here we follow the method of taking into account the state degeneracies that was employed by NICHOLLS.@’ EXPERIMENTALPROCEDURE The A ‘T-X18 system of GeO obtained in an arc contains a number of bands which are free from overlap and are suitable for intensity measurements. The densitometric curve was recorded on a microphotometer. The relative intensities have been measured and have been scaled to 100 in Table 1; they are in reasonably good agreement with the calculated values of q,,.,.*. RESULTS The heights of the vibrational levels have been computed from the relation
A plot of log C I/v4 as a function of G’(u’) for u’ = 0, 1,2,3 and 4 yields a straight line from the Table 1. Designations of vibrational transitions, wavelengths at the band head, relative intensities (scaled to 100). Franck-Condon factors, band strengths, Einstein coefficients and f-numbers for the GeO A ‘n-X’2 transition P, ..4a.‘e’) x 10’
0.0 011 0,2 073 0,4 OS 190 131 1,2 1.4 1s 290 2,l 2,3 294 390 3,2 3.3
2695.3 2730.2 2804.2 2882.0 2963.4 3084.4 2614.6 2683.3 2574.8 2907.7 2989.7 2575.0 2638.1 2779.9 2855.5 2531.2 2662.5 2732.2
76 87 81 84 79 56 85 100 78 68 84 88 86 75 78 87 80 82
0.0541 0.1598 0.2353 0.2288 0.1614 0.0928 0.1464 0.1922 0.0669 0.0700 0.1526 0.2085 0.0730 0.1096 0.0815 0.2077 0.0987 0.0545
4.80 5.22 5.02 5.29 6.09 4.84 1.95 2.53 2.20 2.37 3.29 2.47 2.66 2.88 3.33 2.89 3.27 3.68
A,..Js -‘) x 10 A
x 10J
2.52 2.60 2.30 2.24 2.49 1.73 1.10 1.33 1.06 0.98 1.25 1.47 I .47 1.35 1.45 1.81 1.76 1.83
2.74 2.91 2.12 2.79 3.12 2.41 1.13 I .43 1.21 1.24 1.67 1.53 1.46 1.57 I .77 1.74 1.87 2.05
L
.Y-
Electronic transition-moment variation of the GeO molecule
469
slope of which the vibrational temperature has been found to be as 1090K, which is smaller than the value reported by DUBO and RAI”” for the corresponding D-X system of the isoelectronic SnC molecule. The average life times of the first two vibrational levels of the upper electronic state are calculated [BENNETI. and DALBY”“] to be 1.7 and 17.5 psec. respectively. Using the measured intensities, the computed Franck-Condon factors and r-centroids taken from SAVITHRY et uI.,‘~’ we have studied the variation of electronic transition moment with internuclear separation. The equation R, (I) = constant (1 - 0.476 r - 0.061 r2) for 1.62s r, A s 1.82 represents the variation adequately. Using this variation of R.(r) with r, smoothed band strengths, band oscillator strengths and the Einstein coefficients have been calculated from eqn (6). The results are shown in Table 1 together with measured intensities, Franck-Condon factors, and wavelengths at the band heads. Acknowledgements-The authors are indebted to Dr. Y. PRABHAKARA REDDY for assistance in obtaining the microphotometer record and to the authorities of the Computer Centre where some of the calculations were done. One of the authors (M.L.P.) wishes to thank C.S.I.R., New Delhi, for financial assistance. REFERENCES 1. A. A. N. MURTHY, D. V. K. RAOand P. T. RAO,Proc. R.I.A. 73A, 213(1973). 2. G. HERZBERO, Spectra of Diatomic Molecules. Nostrand, New York (1950). 3. P. A. FRASER and W. R. JARMAIN, Proc. Phys. Sot. A66, 1153(1953). 4. P. M. MORSE,Phys. Rev. 34, 57 (1927). 5. T. SAVITHRY, D. V. K. RAOand P. T. RAO,Nucl. Sci. 43, 329(1974). 6. R. G. TURNER and R. W. NICHOLLS, Can J. Phys. 32, 468 (1954). 7. S. S. PENNER, Quantitative Spectroscopy and Gas Emissitivities. Addison-Wesley, Reading, Mass. (1959). 8. T. WENTINK and L. ~ACSON, 1.them. Phys. 46, 603 (1967). 9. R. W. NICHOLLS, Ann. Geophys. 20, 144(1964). 10. P. S. DUBEand D. K. RAI,J. Phys. B4, 579 (1971). 11. R. G. BENNETT and E. W. DALBY, J. them. Phys. 32, llll(1960).