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Fluorescence lifetime of the 1A2 state of rotationally cooled SO2 in a seeded supersonic jet
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
1 August 1981
FLUORESCENCE LIFETIME OF THE 1A2 STATE OF ROTATIONALLY COOLED SO 2 IN A SEEDED SUPERSONIC JET * Hajime WATANABE, Yoshihiko HYODO, Soji TSUCHIYA Department of Pure and Applied Science, College of GeneralEducation, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
and Seiichiro KODA Department of Reaction Chemistry, Faculty of Engineering, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan Received 30 March 1981; in final form 18 April 1981
SO2, rotationally cooled by nozzle expansion, is excited in its first allowed absorption band, i.e. the "E" band, by a laser pulse. The time-resolved fluorescence shows a bi-exponential decay; the shorter lifetime (~5/~s) is found for spectral peaks attributed to the 1A~ state, the longer one (~26 #s) for peaks of strongly coupled states.
1. Introduction
Electronically excited SO 2 exhibits anomalous lifetime behavior, which has been discussed in terms of the vibronic coupling of the A(1A2) state with the B'(1B1) state that also couples with the X (1A 1) state by the Renner-Teller interaction. Spin-orbit interaction of 1A2 with the 3B2 and 3B 1 states may also be expected. These coupling mechanisms were discussed first by Brand et al. [1] based on spectroscopic analyses. Regarding the anomalous lifetime behavior of the fluorescence a large number of studies have been carried out. Recently, it was reported by Brus and McDonald [2] and Su et al. [3] that the fluorescence decay was bi-exponential; the long-lived component of the decay was attributed tentatively to the 1B1 state and the short-lived one to the 1A2 in spite of the fact that the band origin of the 1B1 state estimated from the above kinetic approach was in disagreement with that determined spectroscopically by Hamada and Merer [4]. More recently, Holtermann et al. [5] * This research has been supported in part by a Grant-in-Aid from the Ministry of Education (No. 522011).
found a single exponential decay with a collisionfree lifetime of 13/as of the fluorescence from some selected vibronic levels. In order to discuss these differences of the experimental results, it is desirable to prepare SO 2 in a well-defined spectroscopic state as Holtermann et al. have intended. Thus, we propose here the lifetime measurement of excited SO 2 molecules in a supersonic nozzle beam, because vib-rotation. ally cooled molecules are obtained under essentially collision-free condition. Trials in this context were already presented for several molecules including NO 2 [6]. In this letter, we describe the results of lifetime measurements of rotationally cooled SO 2 excited to its first absorption region, particularly Clements' " E " band [7]. The resulting fluorescence decayed bi-exponentially with a short lifetime of ~5 #s. This value may be assigned as that of the initially prepared pure 1A2 state.
2. Experimental A supersonic nozzle jet was produced in the vacuum chamber of a stainless steel tube of 15 cm in
0 0 0 9 - 2 6 1 4 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company
439
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
diameter and 90 cm in length, which was separated into two parts; the first one was a skimmer chamber and the other was for measurement of the fluorescence excitation spectra having two Brewster windows to introduce the laser beam and a lens system collecting the laser-induced fluorescence light. The main chamber was evacuated by a 6" diffusion pump backed by a mechanical booster pump (70 m 3 h - l ) . The laser beam crossed the jet at a distance of 5 mm from the nozzle, and both the laser beam and the optical axis of the fluorescence detection system were placed normal to the axis of the supersonic jet. The exciting laser was a frequency-doubled dye laser (Molectron DL14) with a line width of 0.5 cm -1 and a pulse width of 4 ns. The fluorescence excitation spectra were obtained by a boxcar integrator with a gate time of 1-2/as after the laser pulse. For the lifetime measurements, SO 2 was excited by laser light of a given wavelength, and the resulting fluorescence emitted in the direction o f the nozzle axis detected by a photomultiplier through a lens and an ultraviolet absorbing filter to remove scattered light at the position which faced the nozzle at a distance of 35 cm. It was unnecessary to make a geometrical correction of the fluorescence detection efficiency due to movement of the emitting molecules in the jet [6], since the excited SO 2 has a relatively short lifetime. In most of the experiments, a simple nozzle jet was employed without a skimmer since the fluorescence spectrum and its decay were common in measurements with and without a skimmer. The sample gases of SO 2 (Matheson, research grade) which was seeded in AR (99.999% pure) were expanded through the nozzle of 85/am in diameter resulting in a rotational temperature of SO 2 in the range of 1 0 - 3 K when the source pressure was 3 0 0 - 5 0 0 Tort with the background pressure less than 5 X 10 - 4 Torr. 3. Results and discussion Fig. 1 shows the integrated fluorescence excitation spectrum of the " E " band. The fluorescence signal in the wavelength range longer than 330 nm was sampled during 1-2/as after the laser pulse. Also shown in fig. 1 is the spectrum simulated on the basis of the spectroscopic constants given by Hamada and Merer [4] and the computation program developed by Nakagawa 440
1 August 1981 rg0(J)
rRl(J )
I [I II
rR2(J )
02 6 31 ITrl~ r
PP1(J)
131 -TT-I PRI(J ) 4 3 2 64 2
(2)
I-[7 ~ 234 65
Pp2,j )
t C4)
l l All ,
: ii!i ii :}04.15
304.20
aoz,.25 a o 4 . a o
wavelength
ao4.as
/ nm
Fig. 1. Fluorescence excitation spectrum of SO2 Lq the "E" band region. The solid fine shows the observed spectrum obtained on laser excitation of the nozzle-expanded S02/Ar mix-
ture with a source pressure of 300 Tort and a nozzle diameter of 85 tam. The broken line shows the calculated spectrum with a rotational temperature of 10 K.
[8]. In this spectrum, the individual rotational lines, which are denoted in the upper part of fig. 1, are convoluted with a gaussian function of 0.005 nm fwhm, which is the line shape of the exciting laser pulse. Due to the relatively wide spectral width of the exciting laser, each rotational line could not be resolved. The observed sub-structures in the " E " band are numbered as specified in fig. 1. The observed and calculated spectra are essentially in agreement with each other assuming the rotational temperature to be 10 K. However, it should be noted that the calculation gives a single sharp peak in the vicinity of 304.23 nm while the observed spectrum shows a rather broad complex structure, and that some continuous background fluorescence appears in the range 304.2-304.4 nm which is not predicted by the calculations. The fluorescence decay is confirmed to be the same in observations both in the nozzle jet and in the more collimated beam with a skimmer. Moreover, the decay is independent of the seeding fraction of SO 2 in the range 1 - 5 % as well as of the distance between the nozzle and the laser beam which has been varied from 2
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
(a) c-
io . c-
E- band peak(4)
q, . ~'~,~'"%
101 r-
®
8
100
0
'
2'0 ' time / ,us
20
'
102 Io r ®
To., 101
6'0
(b) peak(6)
'%
Rb
r-
100 '
2JO time
'
4'0
i
6'0
/ `us
Fig. 2. Semilogarithmic plots of the fluorescence decays. •: observed intensity, o: observed one from which the longlived component is subtracted. (a): peak (4), (b): peak (6). to 10 mm. Thus, it is concluded that the excited SO 2 in the jet fluoresces under collisionless conditions. In fig. 2, two examples of logarithmic plots of the fluorescence are shown as a function of time after the laser pulse. It is seen clearly that the fluorescence decays bi-exponentially according to the equation I ( t ) = I 0 exp(-t/~-S) +/0L exp(--t/rL) , where/0 and T are the fluorescence intensity at t = 0 and the lifetime, respectively, and the subscripts S and L correspond to components having short and long lifetimes, respectively. It is found from figs. 2a and 2b that though the determined values of ~-S and "/'L are almost the same for the fluorescence of both peaks (4) and (6), the ratio 10/1°L is quite different; the value of 4.5 for the fluorescence at peak (4) is contrasted with 1.1 for the one at peak (6). The observed data summarized in table 1 indicate that the four pe~ks ( 1 ) - ( 4 ) have almost the same short and long lifetimes with the short-lived component being more significant by a factor of 4 - 5 than the long-lived, while for peaks
1 August 1981
(5) and (6) the long-lived component contributes nearly to the same extent to the total fluorescence as the short-lived component. This different behavior of the fluorescence of peaks (5) and (6) may be connected with the fact that the observed excitation spectrum in the vicinity of these peaks disagrees with the one calculated based on the spectroscopic constants determined for the 1A2 state. Thus, it is concluded that the fluorescence of peak (6) and its vicinity originates from states different from 1A2 while the other peaks must be assigned to fluorescence from the pure 1A2 state. This conclusion is evidenced by a further experimental fact that only the long-lived component is found for all peaks in the " D " band which disagrees with the calculated spectrum based on Hamada and Merer's molecular constants. In spite of the fact found by Holtermann et al. [9] that the cross sections for rotational transitions of SO 2 (1A2) in collisions with ground-state SO 2 are very large, excited SO 2 molecules in the present nozzle jet must be free from transitions induced by collisions owing to the very low translational temperature and the small concentration of the seeded SO 2 in the jet. In addition, the contribution of SO 2 dimers or "SO 2carrier gas" van der Waals molecules to the observed spectrum can be disregarded. Thus, the two fluorescence lifetimes determined in this experiment should be discussed in terms of intramolecular photophysics of an isolated SO 2 molecule. The longer lifetime may be attributed to the S component in the previous study [2,3], while the L component may not be observed in this study since the emitting species having a very long Table 1 Observed lifetimes of SO2 excited in the "E" band a) Absorption b) peak number
Laser r S (~s) wavelengttt (rim)
rL(#S)
~S/~L
(1) (2) (3) (4) (5) (6)
304.17 s 304.189 304.202 304.210 304.230 304.23s
27 26.8 24.3 25.5 16.8 15.8
4 5.1 4.1 4.1 1.2 1.1
5 5.2 5.0 4.5 4.3 3.7
a) The probable error is ±5% except for peak (1), whose error is around -+10%. b) See fig. 1. 441
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
lifetime in the jet cross over the detectable area of the fluorescence. The short-lived component found here which has not been detected in the former experiments [2,3,5] is designated as the VS component. The radiative lifetime of the 1A2 state was estimated to be ~-O.6/2s by Strickler and Howell [10] on the basis of the integrated absorption coefficient. This value was revised to ~3/~s b y Holtermann et al. [5] by taking into account an absorption overlap of the transitions to the 1A2 and 1B1 states. The latter value is in good agreement with the present VS lifetime. As an answer to the question why the previous researchers have missed the VS component, it is possible that the VS component becomes appreciable only in a limited number o f lower rotational levels which are attained in absorption of less perturbed bands such as the " E " band at a very low rotational temperature. In the previous experiments, the fluorescence decays have been observed at room temperature. Thus, the initial states whose rotational levels are relatively high would be strongly coupled among the 1A2 and 1B1 states due to efficient internal conversion. In addition to this, it is probable that a collision-induced internal conversion results in minor contribution o f the non-perturbed 1A2 state even under a pressure of SO 2 as low as 0.1 mTorr.
442
1 August 1981
In conclusion, the radiative lifetime of the pure 1A2 state is determined to be ~ 5 las and those o f states coupled with the 1B 1 state would be 1 6 - 2 7 tas. The latter value has been believed as that of the 1 A2 state in previous studies.
References [1] J.C.D. Brand, J.L. Hardwick, D.R. Humphrey, Y. Hamada and A.J. Meter, Can. J. Phys. 54 (1976) 186. [2] L.E. Brus and J.R. McDonald, J. Chem. Phys. 61 (1974) 97. [3] F. Su, J.W. Bottenheim, H.W. Sidebottom, J.G. Calvert and E.K. Damon, Intern. J. Chem. Kinetics 10 (1978) 125. [4] Y. Hamada and A.J. Meter, Can. J. Phys. 53 (1975) 2555. [5 ] D.L. Holtermann, E.K.C. Lee and R. Nanes, Chem. Phys. Letters 75 (1980) 91. [6] C.H. Chen, S.D. Kramer, D.W. Clark and M.G. Payne, Chem. Phys. Letters 65 (1979) 419. [7] J.H. Clements, Phys. Rev. 47 (1935) 224. [8 ] T. Nakagawa, Library Program Y4DB16, Computer Center, University of Tokyo. [9] D.L. Holtermann, E.K.C. Lee and R. Nanes, Chem. Phys. Letters 75 (1980) 249. [10] S.J. Strickler and D.E. Howell, J. Chem. Phys. 49 (1968) 1947.
CHEMICAL PHYSICS LETTERS
1 August 1981
FLUORESCENCE LIFETIME OF THE 1A2 STATE OF ROTATIONALLY COOLED SO 2 IN A SEEDED SUPERSONIC JET * Hajime WATANABE, Yoshihiko HYODO, Soji TSUCHIYA Department of Pure and Applied Science, College of GeneralEducation, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
and Seiichiro KODA Department of Reaction Chemistry, Faculty of Engineering, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan Received 30 March 1981; in final form 18 April 1981
SO2, rotationally cooled by nozzle expansion, is excited in its first allowed absorption band, i.e. the "E" band, by a laser pulse. The time-resolved fluorescence shows a bi-exponential decay; the shorter lifetime (~5/~s) is found for spectral peaks attributed to the 1A~ state, the longer one (~26 #s) for peaks of strongly coupled states.
1. Introduction
Electronically excited SO 2 exhibits anomalous lifetime behavior, which has been discussed in terms of the vibronic coupling of the A(1A2) state with the B'(1B1) state that also couples with the X (1A 1) state by the Renner-Teller interaction. Spin-orbit interaction of 1A2 with the 3B2 and 3B 1 states may also be expected. These coupling mechanisms were discussed first by Brand et al. [1] based on spectroscopic analyses. Regarding the anomalous lifetime behavior of the fluorescence a large number of studies have been carried out. Recently, it was reported by Brus and McDonald [2] and Su et al. [3] that the fluorescence decay was bi-exponential; the long-lived component of the decay was attributed tentatively to the 1B1 state and the short-lived one to the 1A2 in spite of the fact that the band origin of the 1B1 state estimated from the above kinetic approach was in disagreement with that determined spectroscopically by Hamada and Merer [4]. More recently, Holtermann et al. [5] * This research has been supported in part by a Grant-in-Aid from the Ministry of Education (No. 522011).
found a single exponential decay with a collisionfree lifetime of 13/as of the fluorescence from some selected vibronic levels. In order to discuss these differences of the experimental results, it is desirable to prepare SO 2 in a well-defined spectroscopic state as Holtermann et al. have intended. Thus, we propose here the lifetime measurement of excited SO 2 molecules in a supersonic nozzle beam, because vib-rotation. ally cooled molecules are obtained under essentially collision-free condition. Trials in this context were already presented for several molecules including NO 2 [6]. In this letter, we describe the results of lifetime measurements of rotationally cooled SO 2 excited to its first absorption region, particularly Clements' " E " band [7]. The resulting fluorescence decayed bi-exponentially with a short lifetime of ~5 #s. This value may be assigned as that of the initially prepared pure 1A2 state.
2. Experimental A supersonic nozzle jet was produced in the vacuum chamber of a stainless steel tube of 15 cm in
0 0 0 9 - 2 6 1 4 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company
439
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
diameter and 90 cm in length, which was separated into two parts; the first one was a skimmer chamber and the other was for measurement of the fluorescence excitation spectra having two Brewster windows to introduce the laser beam and a lens system collecting the laser-induced fluorescence light. The main chamber was evacuated by a 6" diffusion pump backed by a mechanical booster pump (70 m 3 h - l ) . The laser beam crossed the jet at a distance of 5 mm from the nozzle, and both the laser beam and the optical axis of the fluorescence detection system were placed normal to the axis of the supersonic jet. The exciting laser was a frequency-doubled dye laser (Molectron DL14) with a line width of 0.5 cm -1 and a pulse width of 4 ns. The fluorescence excitation spectra were obtained by a boxcar integrator with a gate time of 1-2/as after the laser pulse. For the lifetime measurements, SO 2 was excited by laser light of a given wavelength, and the resulting fluorescence emitted in the direction o f the nozzle axis detected by a photomultiplier through a lens and an ultraviolet absorbing filter to remove scattered light at the position which faced the nozzle at a distance of 35 cm. It was unnecessary to make a geometrical correction of the fluorescence detection efficiency due to movement of the emitting molecules in the jet [6], since the excited SO 2 has a relatively short lifetime. In most of the experiments, a simple nozzle jet was employed without a skimmer since the fluorescence spectrum and its decay were common in measurements with and without a skimmer. The sample gases of SO 2 (Matheson, research grade) which was seeded in AR (99.999% pure) were expanded through the nozzle of 85/am in diameter resulting in a rotational temperature of SO 2 in the range of 1 0 - 3 K when the source pressure was 3 0 0 - 5 0 0 Tort with the background pressure less than 5 X 10 - 4 Torr. 3. Results and discussion Fig. 1 shows the integrated fluorescence excitation spectrum of the " E " band. The fluorescence signal in the wavelength range longer than 330 nm was sampled during 1-2/as after the laser pulse. Also shown in fig. 1 is the spectrum simulated on the basis of the spectroscopic constants given by Hamada and Merer [4] and the computation program developed by Nakagawa 440
1 August 1981 rg0(J)
rRl(J )
I [I II
rR2(J )
02 6 31 ITrl~ r
PP1(J)
131 -TT-I PRI(J ) 4 3 2 64 2
(2)
I-[7 ~ 234 65
Pp2,j )
t C4)
l l All ,
: ii!i ii :}04.15
304.20
aoz,.25 a o 4 . a o
wavelength
ao4.as
/ nm
Fig. 1. Fluorescence excitation spectrum of SO2 Lq the "E" band region. The solid fine shows the observed spectrum obtained on laser excitation of the nozzle-expanded S02/Ar mix-
ture with a source pressure of 300 Tort and a nozzle diameter of 85 tam. The broken line shows the calculated spectrum with a rotational temperature of 10 K.
[8]. In this spectrum, the individual rotational lines, which are denoted in the upper part of fig. 1, are convoluted with a gaussian function of 0.005 nm fwhm, which is the line shape of the exciting laser pulse. Due to the relatively wide spectral width of the exciting laser, each rotational line could not be resolved. The observed sub-structures in the " E " band are numbered as specified in fig. 1. The observed and calculated spectra are essentially in agreement with each other assuming the rotational temperature to be 10 K. However, it should be noted that the calculation gives a single sharp peak in the vicinity of 304.23 nm while the observed spectrum shows a rather broad complex structure, and that some continuous background fluorescence appears in the range 304.2-304.4 nm which is not predicted by the calculations. The fluorescence decay is confirmed to be the same in observations both in the nozzle jet and in the more collimated beam with a skimmer. Moreover, the decay is independent of the seeding fraction of SO 2 in the range 1 - 5 % as well as of the distance between the nozzle and the laser beam which has been varied from 2
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
(a) c-
io . c-
E- band peak(4)
q, . ~'~,~'"%
101 r-
®
8
100
0
'
2'0 ' time / ,us
20
'
102 Io r ®
To., 101
6'0
(b) peak(6)
'%
Rb
r-
100 '
2JO time
'
4'0
i
6'0
/ `us
Fig. 2. Semilogarithmic plots of the fluorescence decays. •: observed intensity, o: observed one from which the longlived component is subtracted. (a): peak (4), (b): peak (6). to 10 mm. Thus, it is concluded that the excited SO 2 in the jet fluoresces under collisionless conditions. In fig. 2, two examples of logarithmic plots of the fluorescence are shown as a function of time after the laser pulse. It is seen clearly that the fluorescence decays bi-exponentially according to the equation I ( t ) = I 0 exp(-t/~-S) +/0L exp(--t/rL) , where/0 and T are the fluorescence intensity at t = 0 and the lifetime, respectively, and the subscripts S and L correspond to components having short and long lifetimes, respectively. It is found from figs. 2a and 2b that though the determined values of ~-S and "/'L are almost the same for the fluorescence of both peaks (4) and (6), the ratio 10/1°L is quite different; the value of 4.5 for the fluorescence at peak (4) is contrasted with 1.1 for the one at peak (6). The observed data summarized in table 1 indicate that the four pe~ks ( 1 ) - ( 4 ) have almost the same short and long lifetimes with the short-lived component being more significant by a factor of 4 - 5 than the long-lived, while for peaks
1 August 1981
(5) and (6) the long-lived component contributes nearly to the same extent to the total fluorescence as the short-lived component. This different behavior of the fluorescence of peaks (5) and (6) may be connected with the fact that the observed excitation spectrum in the vicinity of these peaks disagrees with the one calculated based on the spectroscopic constants determined for the 1A2 state. Thus, it is concluded that the fluorescence of peak (6) and its vicinity originates from states different from 1A2 while the other peaks must be assigned to fluorescence from the pure 1A2 state. This conclusion is evidenced by a further experimental fact that only the long-lived component is found for all peaks in the " D " band which disagrees with the calculated spectrum based on Hamada and Merer's molecular constants. In spite of the fact found by Holtermann et al. [9] that the cross sections for rotational transitions of SO 2 (1A2) in collisions with ground-state SO 2 are very large, excited SO 2 molecules in the present nozzle jet must be free from transitions induced by collisions owing to the very low translational temperature and the small concentration of the seeded SO 2 in the jet. In addition, the contribution of SO 2 dimers or "SO 2carrier gas" van der Waals molecules to the observed spectrum can be disregarded. Thus, the two fluorescence lifetimes determined in this experiment should be discussed in terms of intramolecular photophysics of an isolated SO 2 molecule. The longer lifetime may be attributed to the S component in the previous study [2,3], while the L component may not be observed in this study since the emitting species having a very long Table 1 Observed lifetimes of SO2 excited in the "E" band a) Absorption b) peak number
Laser r S (~s) wavelengttt (rim)
rL(#S)
~S/~L
(1) (2) (3) (4) (5) (6)
304.17 s 304.189 304.202 304.210 304.230 304.23s
27 26.8 24.3 25.5 16.8 15.8
4 5.1 4.1 4.1 1.2 1.1
5 5.2 5.0 4.5 4.3 3.7
a) The probable error is ±5% except for peak (1), whose error is around -+10%. b) See fig. 1. 441
Volume 81, number 3
CHEMICAL PHYSICS LETTERS
lifetime in the jet cross over the detectable area of the fluorescence. The short-lived component found here which has not been detected in the former experiments [2,3,5] is designated as the VS component. The radiative lifetime of the 1A2 state was estimated to be ~-O.6/2s by Strickler and Howell [10] on the basis of the integrated absorption coefficient. This value was revised to ~3/~s b y Holtermann et al. [5] by taking into account an absorption overlap of the transitions to the 1A2 and 1B1 states. The latter value is in good agreement with the present VS lifetime. As an answer to the question why the previous researchers have missed the VS component, it is possible that the VS component becomes appreciable only in a limited number o f lower rotational levels which are attained in absorption of less perturbed bands such as the " E " band at a very low rotational temperature. In the previous experiments, the fluorescence decays have been observed at room temperature. Thus, the initial states whose rotational levels are relatively high would be strongly coupled among the 1A2 and 1B1 states due to efficient internal conversion. In addition to this, it is probable that a collision-induced internal conversion results in minor contribution o f the non-perturbed 1A2 state even under a pressure of SO 2 as low as 0.1 mTorr.
442
1 August 1981
In conclusion, the radiative lifetime of the pure 1A2 state is determined to be ~ 5 las and those o f states coupled with the 1B 1 state would be 1 6 - 2 7 tas. The latter value has been believed as that of the 1 A2 state in previous studies.
References [1] J.C.D. Brand, J.L. Hardwick, D.R. Humphrey, Y. Hamada and A.J. Meter, Can. J. Phys. 54 (1976) 186. [2] L.E. Brus and J.R. McDonald, J. Chem. Phys. 61 (1974) 97. [3] F. Su, J.W. Bottenheim, H.W. Sidebottom, J.G. Calvert and E.K. Damon, Intern. J. Chem. Kinetics 10 (1978) 125. [4] Y. Hamada and A.J. Meter, Can. J. Phys. 53 (1975) 2555. [5 ] D.L. Holtermann, E.K.C. Lee and R. Nanes, Chem. Phys. Letters 75 (1980) 91. [6] C.H. Chen, S.D. Kramer, D.W. Clark and M.G. Payne, Chem. Phys. Letters 65 (1979) 419. [7] J.H. Clements, Phys. Rev. 47 (1935) 224. [8 ] T. Nakagawa, Library Program Y4DB16, Computer Center, University of Tokyo. [9] D.L. Holtermann, E.K.C. Lee and R. Nanes, Chem. Phys. Letters 75 (1980) 249. [10] S.J. Strickler and D.E. Howell, J. Chem. Phys. 49 (1968) 1947.