906
J. Phys. Chem. 1983, 87,906-908
Quantum Beats in the Fluorescence of Jet-Cooled SO,(i ‘A,) under a Weak Magnetic Fleld Hajlme Watanabe, Sol1 Tsuchlya, Department of Pure and Applied Sciences, college of General Educatlon, Unlverslty of Tokyo, Komba, Meguro-ku, Tokyo 153, Japan
and Seilchlro Koda” h p a r t m n t of Reaction Chemistry, Faculty of Englnwring, Unlverslty of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan (Recehd: December 1, 1982; I n Flnal Form: January 25, 1983)
The fluorescence from SOz(AlAz) in a single ro-vibronic level, which is formed through the ‘Ro(0)transition of the “E”band absorption of jet-cooled SOz, shows a beating decay under an applied weak magnetic field. The polarization of the beating fluorescence and its frequency as a function of the magnetic field strength can be analyzed on the basis of the theory of time-dependent level crossing spectroscopy. It was shown that this particular rotational level of the upper electronic state (lA2) possesses an anomalously high magnetic moment kJ= 0.14) through intramolecular couplings among the relevant electronic states.
In our r e c p t fluorescence decay measurements of jetcooled S02(AlA2), it was demonstrated that SO2 in each single ro-vibronic level exhibits biexponential decay with a short lifetime of 3-5 m and a long one of 15-30 ps.l This observation suggests the conclusion that the initially prepared lA2 state by laser irradiation couples with a small number of other levels having a small oscillator strength. The electronic structure of SO2 is very complicated even in the A state region.2 The lA2state may couple with the highly vibrationally excited ground electronic state. The X state is the Renner-Teller pair of the ‘B1 state which lies near the lA2state, and incomplete annihilation of the orbital angular momentum is expected. Furthermore, the lA2 state may couple with some triplet states through a spin-orbit interaction. Thus, it is quite probable that the SOz molecule in some rotational level of the upper electronic state possesses a sizable permanent magnetic moment. This implies that the fluorescence decay may be affected by an applied magnetic field, and that a beating fluorescence decay may occur. The investigation of the quantum beating phenomenon should afford valuable information on the intramolecular coupling mechanism. Thus, a number of papers have been published which report the successful observation of the beating fluorescence of intermediate case molecules such as dicarbonyl c o m p ~ u n d s , ~diazabenzene,68 -~ and SOz(C 1B2).g Of these studies, the magnetic field effects have been investigated by three gr0ups,4,~~~ and the discussions have been made mostly in terms of the magnetic perturbation of the states which couple with the S1state. In the excitation of a large molecule like diazabenzene, however, due to the very small rotational spacings, it is difficult to (1) Watanabe, H.; Hyodo, Y.; Tsuchiya, S.; Koda, S. J. Phys. Chem. 1982,86,685. Watanabe, H.; Tsuchiya, S.;Koda, S. Ibid. 1982,86,4274. (2) Brand, J. C. D.; Hardwick, J. L.; Humphrey, D. R.; Hamada, Y.; Merer, A. J. Can. J.Phys. 1976,54, 186. (3) Chaiken, J.; Gurnick, M.; McDonald, J. D. J . Chem. Phys. 1981, 74, 106. (4) Hsnke, W. E.; Selzle, H. L.; Hays, T. R.; Lin, S. H.; Schlag, E. W. Chem. Phys. Lett. 1981, 77, 448. (5) Chaiken, J.; McDonald, J. D. J. Chem. Phys. 1982, 77, 669. (6) Okajima, S.; Saigusa, H.; Lim, E. C. J. Chem. Phys. 1982, 76,2096. (7) van der Meer, B. J.; Jonkman, H. Th.; ter Horst, G . M.; Kommandeur, J. J. Chem. Phys. 1982, 76, 2099. (8) Felker, P. M.; Lambert, Wm. R.; Zewail, A. H. Chem. Phys. Lett. 1982, 89, 309. (9) Scharfin, W.; Ivanco, M.; Wallace, S. C. J. Chem. Phys. 1982, 76, 2095.
select a single ro-vibronic level for discussion of the magnetic field effect on a single level in the S1manifold. This latter effect would be the main target of the present study. In this Letter, we will report our recent observation of a clear beating fluorescence decay of S02(A‘A2) excited by the ‘%(O) transition of the “E” band under a relatively weak magnetic field, which seems to be the first example of a kind of time-resolved level crossing spectroscopy applied to triatomic molecules.’O The nozzle jet apparatus has been described in a previous paper.l Briefly, SO2 in Ar less than 1% in concentration was expanded through a nozzle of 50 gm diameter. The excitation laser, which was a frequency-doubled dye laser (Molectron DL 14p) having a line width of 0.02 cm-’ with an intracavity etalon and was polarized almost linearly in the vertical direction, was focused on the jet at the distance of 0.7-0.9 cm from the nozzle exit along the normal direction. The internal wall of the nozzle chamber was covered with a p-metal plate of 0.5 mm thickness so as to keep the residual magnetic field less than 20 mG at the jet portion. A magnetic field with a strength of up to 2 G was applied by use of electric coils placed inside the chamber, in the two directions illustrated in Figure 1. The field strength was calibrated at atmospheric pressure by a flux gate magnetometer (HP, 428B) as a function of current through the coil. Fluorescence of wavelength longer than 330 nm, emitted in a direction parallel or normal to the nozzle axis, was detected either with or without a polarizer, at the distance of 35 cm from the nozzle exit. The direction of the polarizer is specified in Figure 1 as P1-P4. The signal from the photomultiplier was treated first by a preamplifier and fed into an averager via a transient digitizer (Iwasaki, SM1300 + DM701). The time resolution of the system was 0.3 ws. We have already reported in a previous paper1 that the fluorescence from the (J’&’,K;) = (l,l,O) level to which SO2 is excited by the rRo(0) transition of the ”E” band decays with a beating oscillation to some extent. However, this beating must be attributed to the residual magnetic field in the previous chamber which was not covered by a p-metal plate, since the beating almost disappears at the zero magnetic field in the present apparatus. In Figure (IO) Very recently, Professor Zare of Stanford communicated to us observation of Zeeman quantum beats in N02(A2Bz).Brucat, P. J.; Zare, R. N. J . Chem. Phys. 1983, 78, 100.
0022-3854/83/2087-0906$0 1.50/0 0 1983 American Chemical Society
The Journal of Physical Chemistty, Vol. 87, No. 6, 1983 907
Letters
(a)
8 G3po‘arizer
H,
I
0.88
Gauss
P.M
p3
‘4
Afluorescence
laser polarization Figure 1. Geometrical arrangement of the observation system of the laser-induced fluorescence of jet-cooled SOz with application of the magnetic field Hand with the polarizer P for detection of the fiuores-
@ I u
time I (b)
H,
JJS
= 1.30 Gauss
t i m e I ,us
Figure 2. The observed fluorescence decay of SO@ ’Az) excited by the ‘R,(O) transition of the “E” band under the magnetic field H,. The fluorescence emltted in the direction parallel to the bt axis is observed without a polarizer.
Figure 3. The observed fluorescence decay of SO$A ’A2) excited by the ‘R,(O) transition of the “E” band. (a) A magnetic field parallel to the laser Is applied, and the fluorescence emitted in the direction parallel to the jet axis is detected wlthout a polarizer (l), with a vertical polarizer (2), and with a horizontal polarizer (3). (b) A magnetic field parallel to the jet axis is applied and the fluorescence emitted in the vertical directlon Is detected without a polarizer (4), with a vertical polarizer (5), and with a horizontal polarizer (6).
2 are shown the fluorescence decays under a variety of magnetic field strengths, where the field direction was selected parallel to the laser (H,in Figure 1) and the fluorescence was observed in a direction parallel to the nozzle axis without a polarizer. At zero magnetic field, the fluorescence decays in a biexponential way as has been found for other revibronic levels. However, if the strength of the field is increased, the beating appears and its frequency increases. Figure 3a shows that the beating becomes more significant relative to the exponential decay when a linear polarizer is inserted in the vertical direction (PI), and the beating disappears when the polarizer is rotated to the horizontal direction (P2).Quite similar phenomenon was found when the fluorescence was observed in a direction normal to both the laser and the nozzle axis, keeping the magnetic field parallel to the laser.
Through the polarizer in the direction normal to the magnetic field (P3),the beating appears, while through the polarizer in the direction parallel to the field (P4),it disappears. In this case, the observed beating oscillation through the P, polarizer has a phase difference of 180’ from the previous one observed through the PI polarizer. In Figure 3b are shown the beating fluorescence data obtained in a magnetic field in the direction normal to the When the fluorescenceis observed in a direction laser (HJ. parallel to both the jet axis and the magnetic field, it is shown in Figure 3b that the beating appears through the polarizers either parallel (P,) or normal (P2) to the polarization of the laser. However, the beating oscillations in two cases are different in their phase by exactly 180°, so that the beating disappears if the fluorescence is observed with no polarizer. In Table I, the phase of the
time I u s
908
The Journal of Physical Chemistry, Vol. 87, No. 6, 1983
Letters
TABLE I : Characterization of the Phase of a Beating Oscillation as a Function of the Directions of the Magnetic Field, the Observed Fluorescence, and the Polarizer (See Figure 1) magnetic field
H, H2
a
P,
P,
a
oc
+
-d
o
-
-
0
P,
P,
+b t
+
o
+
Beating starts at the a Observed without a polarizer. maximum intensity. N o beating. Beating starts at the minimum intensity.
beating fluorescence is characterized in relation to the directions of the applied magnetic field, the fluorescence observation, and the polarizer. Here, the notation + and - means that the fluorescence starts at the maximum and minimum intensity, respectively. The above observations could be understood on the basis of the theory of zero-field level crossing spectroscopy (HanlB effect). In the classical framework of the theory," the electron in the molecule begins to oscillate at the moment of excitation in a direction parallel to the polarization vector of the laser light. At zero magnetic field, the fluorescence light is also linearly polarized in the same direction. However, if a magnetic field is applied, the oscillating electron is perturbed by a Lorentz force, and thus, it precesses about the field direction with Larmor angular frequency. Therefore, if the fluorescence is observed through a polarizer whose direction is perpendicular to the applied magnetic field, the damped modulation of the fluorescence intensity at twice the Larmor frequency must be observed in a time-resolved experiment. This description is realized exactly in the present experiment, i.e., when the magnetic field is applied in a direction parallel to the laser beam, the beating is found only in the fluorescence observed through the P1and P3polarizers and not through the P2and P,. The phase difference between two beating oscillations observed through the PI and P3 polarizers is also understandable, since the polarization of the fluorescence must be in a direction parallel to that of the incident laser light a t the initial stage; with the P1 polarizer the fluorescence starts from its maximum intensity, while with P3 it starts from a minimum value. According to the classical model for the perpendicular type transition of a symmetric top molecule,12the following equations are derived to describe the time-evolved fluorescence intensity under a magnetic field of H (= H1): Il(t) 0~ S t [ 7 + cos (2wLt)]
(1)
12(t)0: 6 C r t
(2)
where Il and Iz are the fluorescence intensities observed with the P1and P2polarizers, respectively, I' is the natural decay width, and q is the larmor angular frequency, which is defined by use of molecular Land6 g factor (gL)and the Zeeman effect constant b,H (= 9.2732 X erg/Bohr magneton-(;) as W L = gJbmH/ h (3) Figure 4 shows the observed beat frequency, which may be interpreted as q / ~ as a,function of the field strength. A good linear relationship is found as expected from eq 3, though the beat frequency a t zero field seems to have a small finite value. This might be attributed to a zerofield splitting or to an inhomogeneous residual magnetic
&
O O
1.0
field strength
2.0
I
Gauss
Flgure 4. The observed relation between the beat frequency and the applied magnetic field strength.
field. From the slope of the linear line in Figure 4,it is concluded that gJ = 0.14. With this value the observed fluorescence decays may be reproduced by eq 1 with the assumption that r-' = 8.0 f 1.0 ,us. The Zeeman quantum beat is well-known for an atomic system" and has been found by Wallenstein et al.13 in the fluorescence from individual rotational levels of the B 3&,+ state of I2'I2 as the first example for diatomic molecules. The present quantum beat is caused by quantum mechanical interference between the possible routes to yield an emission via different Zeeman substates and differs from the high field level crossing induced by the applied magnetic field., This differs also from the quantum beat caused by the interference between the primary BornOppenheimer state and the background states such as recent observations for intermediate case molecules.8 On the basis of the present g value of 0.14, it may be stated that the initially prepared state of SO2 excited by laser irradiation, which possesses a radiative lifetime of ca. 5 ps, is not a pure 'A, state but one coupled with other electronic states. The 'A, state borrows oscillator strength from the near-lying 'B, state which correlates with the '$ state in a linear conformation. The Renner-Teller mechanism and/or the spin-orbit coupling must be responsible for the present sizable magnetic moment, though at present it may not be determined which mechanism is predominant. Our observation of oscillating decay is yet limited to *R,(O) excitation. We believe that this is not the exceptional case. By applying a stronger magnetic field, we may observe beating fluorescence decays from higher rotational levels which should possess smaller g values. A systematic study of the individual g values may be worthwhile t o reveal the complicated coupling mechanism of SOz. Acknowledgment. This work was supported by a Grant-in-Aid from the Ministry of Education (No. 56222004). Registry No. SOz, 7446-09-5.
(11) Corney, A. 'Atomic and Laser Spectroscopy"; Clarendon Press: Oxford, 1979; p 473. (12) Zare, R. N. J. Chem. Phys. 1966,45,4510.
(13) Wallenstein, R.;Paisner, J. A.; Schawlow, A. L. Phys. Reu. Lett. 1974,32, 1333.
