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Time-resolved observation of molecular pseudorotation in Na3
Volume 2 13, number 5,6
CHEMICAL PHYSICS LETTERS
I5 October 1993
Time-resolved observation of molecular pseudorotation in Na3 K. Kobe, H. Kiihling, S. Rutz, E. Schreiber, J.P. Wolf, L. Wijste Institutftir Experimentalphysik, Freie UniversitiitBerlin, Arnimallee 14, D-14195 Berlin, Germany
M. Broyer and Ph. Dugourd Laboratoire de Spectromhrie Ionique et Molhlaire (ussocie au CNRS No. 171). Universitt!Lyon I, B&iment 205.43 Boulevard du I1 Novembre 1918..69622 Vilieurbanne Cedex, France Received 22 July 1993; in final form 19 August 1993
The temporal behaviour of the pseudorotating B state of Nas was investigated in a two-photon-ionization (TPI) experiment, employing picosecond laser pulses and a variable delay between the excitation and ionization step. The results exhibit the pseudorotational motion as a temporal sequence. The detailed analysis of the vibronic function time evolution afftrms a pseudo-dahnTeller (PJT) model for the interpretation of the B state spectroscopic data.
Metal clusters of different sizes exhibit distinctive features, which range from purely molecular behaviour in very small particles to solid-like properties in large aggregates. The size-dependent phenomena can be related to surface-volume ratios, structural arrangements and electron-electron interactions inside the cluster. The pronounced dynamic properties of metal clusters, however, are mainly due to vibronically coupled internal degrees of freedom, which result in efficient energy transfer channels. Since the quantity of coupled vibrations increases drastically with the number of participating atoms, an identification of individual energetic pathways inside the “vibronic soup” of the cluster becomes extremely difficult, unless simple systems are chosen. The sodium trimer is a simple system which is a well-known metal cluster. In the equilibrium geometry of the ground state Na, adopts - due to JahnTeller distortion - a well-localized obtuse-angled triangular shape [ 1,2]. TPI spectra of the electronically excited B state, however, revealed pseudorotation features [ 3-51. Under the assumption of vibronic coupling (E@e) inside the doubly degenerate excited ‘E’ electronic state, the spectra could be reproduced with a quadratic Jahn-Teller model [ 41. Ab initio calculations performed later pointed 554
out the existence of a non-degenerate electronic state of 2A{ symmetry in the dose vicinity of the 2E’ state [ 61. Another interpretation assuming vibronic coupling of type (E +A) @e between the non-degenerate 2A’,state and the doubly degenerate excited ‘E’ state provided an equally well-matching reproduction of the experimental data. However, while the first interpretation was based on the assumption of fractional quantization and a quadratic Jahn-Teller model, the second interpretation was based on integer J values and a pseudo-Jahn-Teller model. No final conclusion can be drawn, unless further experimental information is made available. Two possible approaches can be followed to solve the problem: The first one was carried out by Ernst and co-workers [ 7 ] who investigated the Na3 B-X system at rotational resolution and found their results in favour of the pseudo-Jahn-Teller effect interpretation. Our approach was to use time-resolved experiments which have recently been demonstrated as being efficient at studying the dynamics of molecules and clusters [ 8131. We measured the temporal evolution of the TPI of the B state of sodium trimers by use of a tunable dye laser (rhodamine 6G) synchronously pumped by the green line of a mode-locked Ar+ laser. The repetition rate of the laser pulses being continuously controlled
0009-2614/93/S 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 2 13, number 5,6
CHEMICAL PHYSICS LETTERS
by means of a fast avalanche diode ( tti,= 25 ps) and a sampling oscilloscope (20 GHz) was 82.5 MHz. The dye laser provided nearly tranform-limited (single-sided exponential) pulses of 1.25 ps (fwhm ) duration as estimated from the measured autocorrelation. Within the tuning range of the dye laser (600633 nm) the bandwidth was approximately 32 cm-’ and we reached a pulse energy of 2 n.J. To measure the temporal evolution of the B state, we applied a pump and probe technique. The beam of the dye laser
15 October 1993
is divided into two parts (fig. 1). A first (pump) photon was used to excite the Naj clusters. A second (probe) photon of the same wavelength, being optically delayed in time, ionized the excited clusters, The polarization vectors of both photons were parallel. The temporal delay was performed with a dcmotor-driven linear translation stage controlled by an optical encoder. Hence, the temporal resolution of the apparatus (fig. 1) was - using deconvolution and least-squares tit technique - about 0.1 ps.
Mode Locked Argon-Ion-Laser
Chopper
Autocorrelator \h
\
_A A
rc
r
..N
;‘.
Lens
,;:,
Molecular Beam
Computer
4
Quadrupole-MassSpectrometer
Lock-In 4
Fig. 1. Experimental apparatus for the transient TPI of the B state.
555
Volume 213, number 5,6
CHEMICAL PHYSICS LETTERS
The sodium clusters were produced by coexpansion of sodium vapour of moderate particle pressure ( 100 mbar) together with about 5-7 bar argon as in inert carrier gas through a small cylindrical nozzle of nearly 70 pm diameter. This expansion system provided rotational and vibrational trimer temperatures of about 10 and 50 K, respectively. The arrangement, however, allows to raise the stagnation pressure up to 30 bar, so that extremely cold clusters can be produced. The photoionized Na, clusters were detected by a quadrupole mass spectrometer with 1 amu resolution. A lock-in technique was attempted to discriminate the TPI signal due to one single laser pulse. In fig. 2a, the spectral dependence of the TPI signal of the B state measured with this apparatus is shown. Due to the rather broad bandwith of the ultrashort pulses of the dye laser, as well as the small difference in energy of neighbouring vibrational-rotational states, the tine structure, as seen in the highly resolved (one-colour TPI ) spectra of Delacretaz (ref. [ 141, tip. 2b), smeared out to a certain extent. For example, the intense peaks observed in the picosecond spectrum, at the beginning of each vibronic sequence correspond to three vibronic levels, j= l/2, j= 3/2- and j=3/2+ in the Delacretaz et al. labell-
15 October 1993
ing [ 41. The small intensity of the first peak at 625 nm in the picosecond spectrum is due to threshold effects in the ionization process: a photon of same energy is used for the ionization and excitation, the total energy of the two photons at 625 nm is therefore very close to the threshold and the ionization is not very efficient. A typical result of time-resolved TPI measurements on the B state is presented in fig. 3. The temporal evolution in fig. 3a corresponds to the resonant intense peak at 620 nm. A clear beat structure, symmetrical to the time delay At=O, is observed. The period of these oscillations amounts approximately to 2.9 ps cf= 330 GHz). The oscillation decays with a time constant of about 4 ps. Contrary to this, no significant structure of oscillation is found for transient non-resonant TPI (fig. 3b). To check the time response function of our experiment, we perform three-photon ionization of Naz, known to be a very short process [ 10,111 in comparison to the pulse width of the exciting laser. The result, shown in fig. 3c, leads to a pulse width of about 1.25 ps in agreement with the measured autocorrelation. In order to interpret these results, we have to calculate the temporal evolution of the excited vibronic
t H
610
615
620
625
X/nm + Fig. 2. Vibronic pseudorotation sequence appearing in the B stat6 of NaJ. The u values (OJ, 2, 3) represent the vibrational distortion amplitudes; (a) spectrum measured after ps excitation; (b) highly resolved spectra [ 141.
556
-20
-10
0 At/ps
10
20
--)
Fig. 3. Time-resolved TPI-signal of the B state of Na, (excitation wavelength 619.7 nm); (a) resonant excitation; (b) non-resonant excitation; (c) system response to the exciting laser pulse.
volume 2 13,number 5,6
CHEMICALPHYSICSLETTERS
eigenfunctions using two hypotheses for the B state: The quadratic-Jahn-Teller (QJT) effect used by Delacr&az et al. [ 4 ] and the pseudo-Jahn-Teller (PJT) effect proposed by Meiswinkel and Kijppel [ 15,16 1. In the case of the QJT effect, we have the coupling scheme E@e, where E is the 3 2E’ twofold degenerate electronic state and e the degenerate vibration. In the case of the PJT effect, we have the coupling scheme (E+A)@e, where E is the 3 *E twofold degenerate electronic state, A is the 2 ‘A; electronic state and e again the degenerate vibration. In fig. 3a, three vibronic levels are simultaneously excited: v= 1, j= l/2, j= 3/2-, j= 3 / 2+ in the QJT model, V= I, j= 0, j= 1, j= 2 in the PJT model. The eigenfunction at the time t=O may be expressed as
Iv(t=O)>=
c Gin> ’ n
(1)
In) is the vibronic eigenfunction of the various pumped levels. In ( 1) the number of terms is larger than three because some levels are degenerate. C,, may be calculated from the matrix element of the electric dipole between the ground state and the state I n). The vibronic eigenfunction 1n) may be calculated in the two models described above. The time evolution is given by
Iv(t))=
C CneiE(n)f’*[n). 78
15October 1993
triangle geometry. The eventual time oscillation of the photoionization cross section results from the geometrical change of the B state as a function of time and the geometry of Na3+remaining as an equilateral triangle. Therefore we consider that the FranckCondon factors between the excited levels of the B state (eq. (2)) and the vibrational level v+=O of the Na: ground state are a good representation of the phenomena involved in the photoionization process. To determine the C, coefficients in eq. (2), we use Franck-Condon factors between the Na, ground state and the B state. The phase between the C, coefficient is not known and this means that we are only able to calculate the oscillation frequency and not the oscillation phase. Figs. 4a and 4b, respectively, show the temporal evolution of F,,, in the QJT model and the PJT model. Since we do not know the relative intensity of the ionization process from the tl and Ed electronic states, respectively, we have calculated F,, in two cases: a)
(2)
E(n) is the energy of various vibronic levels. E(n)
takes three values E,, E,, E3 given from the spectroscopic results: &-El=5 cm-’ and &-E,=18.5 cm-‘. The time evolution leads to an oscillation of w(t) between the two electronic eigenfunctions 1cl) and 1c2) of respective symmetry B2 and A1 in CZV.This oscillating behaviour may lead to an oscillation of the Franck-Condon factors between the excited B state and the vibrational levels of the Na: ground states. In fact, a great number of vibrational levels of the Na$ ground state are involved in the photoionization process. It is difficult to take into account all these vibrational levels because the Na: ground state is not sufficiently known [ 171 to realize all these calculations. We have therefore performed a model calculation and have calculated only the Franck-Condon factor F,,, between the excited state (eq. (2))
and the v+ =O vibrational level of Na: . The main property of the Na: ground state is its equilateral
L 0
I
0
I
1
I
I
2
4
6 t/ps -
8
10
I
I
I
I
I
2
4
6 t/ps -
8
10
Fig. 4. Temporalevolution of the Franck-Condon factorF,+ betweenthe excitedstate (eq. (2)) and the v+ -0 vibrational level of Na: in the case of (a) the quadraticJahn-Teller model; (b) the pseudo-Jahn-Tellermodel; (-) intensity 1 for electronic state t , and 0 for t2, (. -. ) intensity 0 for t, and 1 for ~2.
557
Volume 2 13, number 56
CHEMICAL PHYSICS LETTERS
(i) intensity 1 for eI and 0 for e2 (solid line): (ii) intensity 0 for cl and 1 for e2 (dashed line). In fig. 4 we do not obtain any oscillating behaviour in the case of the QJT model. By contrast, we obtain an oscillation of about 2.5 ps for the PJT model in reasonable agreement with the experimental results (2.9 ps). The oscillation frequency corresponds roughly to oZ3= E3 - E2 = 400 GHz. This frequency is easy to understand: in the PJT model, the level u= 1, j= 0 of E, energy has very low intensity because the Franck-Condon factor between this level and the Na, ground state is close to zero. Our timeresolved experiment is therefore in favour of the pseudo-Jahn-Teller effect in the Naj B state. If we compare the experiment (fig. 3 ) and our calculations (fig. 4) two points remain to be discussed. In the experiment, the oscillation decays with a time constant of about 4 ps. This effect is probably due to the rotational structure: (i) From one rotational level of the ground state, three rotational levels are pumped in the B state. This means that the initial eigenfunction w( t = 0) is more complicated than in our calculations. (ii) Due to strong Coriolis coupling, the vibronic energy varies significantly with the rotational quantum number and the experimental signal corresponds to an incoherent superposition of all the rotational levels. The time decay associated with this phenomenon may be estimated from the rotational contour of the various vibronic bands and this estimation is in reasonable agreement with the experimental decay. In conclusion, we have observed the time evolution of the Na3 B state pseudorotational motion and our experimental results are in favour of the pseudoJahn-Teller model for the interpretation of the Na3 B state.
558
15 October 1993
This work has been financially supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 337 (TP AS).
References
[ 1 ] J.L. Martins, R. CarandJ. Buttet, J. Chem. Phys. 78 (1983) 5646. [2] M. Broyer, G. Delacretaz, P. Labastie, J.P. Wolf and L. Wbste, J. Phys. Chem. 91 (1987) 2626. [ 3 ] G. Delacretaz and L. Waste, Surface Sci. 156 ( 1985) 770. [4] G. Delacretaz, E.R. Grant, R.L. Whetten, L. Wiiste and J. W. Zwanziger, Phys. Rev. Letters 56 ( 1986) 2598. [5] M. Broyer, G. Delacrttaz, P. Labastie, R.L. Wbetten, J.P. Wolf and L. Wiiste, Z. Physik D 131 ( 1986) 131. [ 61F. Cocchini, Th.H. Upton and W. Andreoni, J. Chem. Phys. 88 (1988) 6068. [ 7 ] S.Rakowsky, W.E. Ernst and R.F.W. Herrmann, Z. Physik D26 (1983) 273. [ 8 ] D. Ray, N.E. Levinger, J.M. Popanikolas and WC. Lineberger, J. Chem. Phys 91 (1989) 6533. [ 9 ] M. Dantus, M.H.M. Jansen and A.H. Zewail, Chem. Phys. Letters 181 (1991) 281. [ 10] T. Baumert, M. Grosser, R. Thalweiser and G. Gerber, Phys. Rev. Letters 67 ( 1991) 3753. [ 111T. Baumert, C. Rottgermann, C. Rothenfusser, R. Thalweiser, V. Weiss and G. Gerber, Phys. Rev. Letters 69 (1992) 1512. [ 121E. Schreiber, H. Kiihling, K. Kobe, S. Rutz and L. W&e, Ber. Bunsenges. Physik Chem. 96 (1992) 1301. [ 13] S. Rutz, K. Kobe, H. Kiihling, E. Schreiber and L. Wiiste, Z. Physik D 26 (1993) 276. [ 141G. Delacrttaz, Thesis, Lausanne (1985). [ 15] R. Meiswinkel and H. Kiippcl, Chem. Phys. 144 ( 1990) 117. [ 16] R. Meiswinkel and H. Koppel, Z. Physik D 19 ( 1991) 63. [ 17] .I. Gaus, K. Kobe, V. Bona%-Koutecky, H. Kiihling, J. Manz, B. Reischl, S. Rutz, E. Schreiber and L. Wiiste, J. Phys. Chem., to be published.
CHEMICAL PHYSICS LETTERS
I5 October 1993
Time-resolved observation of molecular pseudorotation in Na3 K. Kobe, H. Kiihling, S. Rutz, E. Schreiber, J.P. Wolf, L. Wijste Institutftir Experimentalphysik, Freie UniversitiitBerlin, Arnimallee 14, D-14195 Berlin, Germany
M. Broyer and Ph. Dugourd Laboratoire de Spectromhrie Ionique et Molhlaire (ussocie au CNRS No. 171). Universitt!Lyon I, B&iment 205.43 Boulevard du I1 Novembre 1918..69622 Vilieurbanne Cedex, France Received 22 July 1993; in final form 19 August 1993
The temporal behaviour of the pseudorotating B state of Nas was investigated in a two-photon-ionization (TPI) experiment, employing picosecond laser pulses and a variable delay between the excitation and ionization step. The results exhibit the pseudorotational motion as a temporal sequence. The detailed analysis of the vibronic function time evolution afftrms a pseudo-dahnTeller (PJT) model for the interpretation of the B state spectroscopic data.
Metal clusters of different sizes exhibit distinctive features, which range from purely molecular behaviour in very small particles to solid-like properties in large aggregates. The size-dependent phenomena can be related to surface-volume ratios, structural arrangements and electron-electron interactions inside the cluster. The pronounced dynamic properties of metal clusters, however, are mainly due to vibronically coupled internal degrees of freedom, which result in efficient energy transfer channels. Since the quantity of coupled vibrations increases drastically with the number of participating atoms, an identification of individual energetic pathways inside the “vibronic soup” of the cluster becomes extremely difficult, unless simple systems are chosen. The sodium trimer is a simple system which is a well-known metal cluster. In the equilibrium geometry of the ground state Na, adopts - due to JahnTeller distortion - a well-localized obtuse-angled triangular shape [ 1,2]. TPI spectra of the electronically excited B state, however, revealed pseudorotation features [ 3-51. Under the assumption of vibronic coupling (E@e) inside the doubly degenerate excited ‘E’ electronic state, the spectra could be reproduced with a quadratic Jahn-Teller model [ 41. Ab initio calculations performed later pointed 554
out the existence of a non-degenerate electronic state of 2A{ symmetry in the dose vicinity of the 2E’ state [ 61. Another interpretation assuming vibronic coupling of type (E +A) @e between the non-degenerate 2A’,state and the doubly degenerate excited ‘E’ state provided an equally well-matching reproduction of the experimental data. However, while the first interpretation was based on the assumption of fractional quantization and a quadratic Jahn-Teller model, the second interpretation was based on integer J values and a pseudo-Jahn-Teller model. No final conclusion can be drawn, unless further experimental information is made available. Two possible approaches can be followed to solve the problem: The first one was carried out by Ernst and co-workers [ 7 ] who investigated the Na3 B-X system at rotational resolution and found their results in favour of the pseudo-Jahn-Teller effect interpretation. Our approach was to use time-resolved experiments which have recently been demonstrated as being efficient at studying the dynamics of molecules and clusters [ 8131. We measured the temporal evolution of the TPI of the B state of sodium trimers by use of a tunable dye laser (rhodamine 6G) synchronously pumped by the green line of a mode-locked Ar+ laser. The repetition rate of the laser pulses being continuously controlled
0009-2614/93/S 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 2 13, number 5,6
CHEMICAL PHYSICS LETTERS
by means of a fast avalanche diode ( tti,= 25 ps) and a sampling oscilloscope (20 GHz) was 82.5 MHz. The dye laser provided nearly tranform-limited (single-sided exponential) pulses of 1.25 ps (fwhm ) duration as estimated from the measured autocorrelation. Within the tuning range of the dye laser (600633 nm) the bandwidth was approximately 32 cm-’ and we reached a pulse energy of 2 n.J. To measure the temporal evolution of the B state, we applied a pump and probe technique. The beam of the dye laser
15 October 1993
is divided into two parts (fig. 1). A first (pump) photon was used to excite the Naj clusters. A second (probe) photon of the same wavelength, being optically delayed in time, ionized the excited clusters, The polarization vectors of both photons were parallel. The temporal delay was performed with a dcmotor-driven linear translation stage controlled by an optical encoder. Hence, the temporal resolution of the apparatus (fig. 1) was - using deconvolution and least-squares tit technique - about 0.1 ps.
Mode Locked Argon-Ion-Laser
Chopper
Autocorrelator \h
\
_A A
rc
r
..N
;‘.
Lens
,;:,
Molecular Beam
Computer
4
Quadrupole-MassSpectrometer
Lock-In 4
Fig. 1. Experimental apparatus for the transient TPI of the B state.
555
Volume 213, number 5,6
CHEMICAL PHYSICS LETTERS
The sodium clusters were produced by coexpansion of sodium vapour of moderate particle pressure ( 100 mbar) together with about 5-7 bar argon as in inert carrier gas through a small cylindrical nozzle of nearly 70 pm diameter. This expansion system provided rotational and vibrational trimer temperatures of about 10 and 50 K, respectively. The arrangement, however, allows to raise the stagnation pressure up to 30 bar, so that extremely cold clusters can be produced. The photoionized Na, clusters were detected by a quadrupole mass spectrometer with 1 amu resolution. A lock-in technique was attempted to discriminate the TPI signal due to one single laser pulse. In fig. 2a, the spectral dependence of the TPI signal of the B state measured with this apparatus is shown. Due to the rather broad bandwith of the ultrashort pulses of the dye laser, as well as the small difference in energy of neighbouring vibrational-rotational states, the tine structure, as seen in the highly resolved (one-colour TPI ) spectra of Delacretaz (ref. [ 141, tip. 2b), smeared out to a certain extent. For example, the intense peaks observed in the picosecond spectrum, at the beginning of each vibronic sequence correspond to three vibronic levels, j= l/2, j= 3/2- and j=3/2+ in the Delacretaz et al. labell-
15 October 1993
ing [ 41. The small intensity of the first peak at 625 nm in the picosecond spectrum is due to threshold effects in the ionization process: a photon of same energy is used for the ionization and excitation, the total energy of the two photons at 625 nm is therefore very close to the threshold and the ionization is not very efficient. A typical result of time-resolved TPI measurements on the B state is presented in fig. 3. The temporal evolution in fig. 3a corresponds to the resonant intense peak at 620 nm. A clear beat structure, symmetrical to the time delay At=O, is observed. The period of these oscillations amounts approximately to 2.9 ps cf= 330 GHz). The oscillation decays with a time constant of about 4 ps. Contrary to this, no significant structure of oscillation is found for transient non-resonant TPI (fig. 3b). To check the time response function of our experiment, we perform three-photon ionization of Naz, known to be a very short process [ 10,111 in comparison to the pulse width of the exciting laser. The result, shown in fig. 3c, leads to a pulse width of about 1.25 ps in agreement with the measured autocorrelation. In order to interpret these results, we have to calculate the temporal evolution of the excited vibronic
t H
610
615
620
625
X/nm + Fig. 2. Vibronic pseudorotation sequence appearing in the B stat6 of NaJ. The u values (OJ, 2, 3) represent the vibrational distortion amplitudes; (a) spectrum measured after ps excitation; (b) highly resolved spectra [ 141.
556
-20
-10
0 At/ps
10
20
--)
Fig. 3. Time-resolved TPI-signal of the B state of Na, (excitation wavelength 619.7 nm); (a) resonant excitation; (b) non-resonant excitation; (c) system response to the exciting laser pulse.
volume 2 13,number 5,6
CHEMICALPHYSICSLETTERS
eigenfunctions using two hypotheses for the B state: The quadratic-Jahn-Teller (QJT) effect used by Delacr&az et al. [ 4 ] and the pseudo-Jahn-Teller (PJT) effect proposed by Meiswinkel and Kijppel [ 15,16 1. In the case of the QJT effect, we have the coupling scheme E@e, where E is the 3 2E’ twofold degenerate electronic state and e the degenerate vibration. In the case of the PJT effect, we have the coupling scheme (E+A)@e, where E is the 3 *E twofold degenerate electronic state, A is the 2 ‘A; electronic state and e again the degenerate vibration. In fig. 3a, three vibronic levels are simultaneously excited: v= 1, j= l/2, j= 3/2-, j= 3 / 2+ in the QJT model, V= I, j= 0, j= 1, j= 2 in the PJT model. The eigenfunction at the time t=O may be expressed as
Iv(t=O)>=
c Gin> ’ n
(1)
In) is the vibronic eigenfunction of the various pumped levels. In ( 1) the number of terms is larger than three because some levels are degenerate. C,, may be calculated from the matrix element of the electric dipole between the ground state and the state I n). The vibronic eigenfunction 1n) may be calculated in the two models described above. The time evolution is given by
Iv(t))=
C CneiE(n)f’*[n). 78
15October 1993
triangle geometry. The eventual time oscillation of the photoionization cross section results from the geometrical change of the B state as a function of time and the geometry of Na3+remaining as an equilateral triangle. Therefore we consider that the FranckCondon factors between the excited levels of the B state (eq. (2)) and the vibrational level v+=O of the Na: ground state are a good representation of the phenomena involved in the photoionization process. To determine the C, coefficients in eq. (2), we use Franck-Condon factors between the Na, ground state and the B state. The phase between the C, coefficient is not known and this means that we are only able to calculate the oscillation frequency and not the oscillation phase. Figs. 4a and 4b, respectively, show the temporal evolution of F,,, in the QJT model and the PJT model. Since we do not know the relative intensity of the ionization process from the tl and Ed electronic states, respectively, we have calculated F,, in two cases: a)
(2)
E(n) is the energy of various vibronic levels. E(n)
takes three values E,, E,, E3 given from the spectroscopic results: &-El=5 cm-’ and &-E,=18.5 cm-‘. The time evolution leads to an oscillation of w(t) between the two electronic eigenfunctions 1cl) and 1c2) of respective symmetry B2 and A1 in CZV.This oscillating behaviour may lead to an oscillation of the Franck-Condon factors between the excited B state and the vibrational levels of the Na: ground states. In fact, a great number of vibrational levels of the Na$ ground state are involved in the photoionization process. It is difficult to take into account all these vibrational levels because the Na: ground state is not sufficiently known [ 171 to realize all these calculations. We have therefore performed a model calculation and have calculated only the Franck-Condon factor F,,, between the excited state (eq. (2))
and the v+ =O vibrational level of Na: . The main property of the Na: ground state is its equilateral
L 0
I
0
I
1
I
I
2
4
6 t/ps -
8
10
I
I
I
I
I
2
4
6 t/ps -
8
10
Fig. 4. Temporalevolution of the Franck-Condon factorF,+ betweenthe excitedstate (eq. (2)) and the v+ -0 vibrational level of Na: in the case of (a) the quadraticJahn-Teller model; (b) the pseudo-Jahn-Tellermodel; (-) intensity 1 for electronic state t , and 0 for t2, (. -. ) intensity 0 for t, and 1 for ~2.
557
Volume 2 13, number 56
CHEMICAL PHYSICS LETTERS
(i) intensity 1 for eI and 0 for e2 (solid line): (ii) intensity 0 for cl and 1 for e2 (dashed line). In fig. 4 we do not obtain any oscillating behaviour in the case of the QJT model. By contrast, we obtain an oscillation of about 2.5 ps for the PJT model in reasonable agreement with the experimental results (2.9 ps). The oscillation frequency corresponds roughly to oZ3= E3 - E2 = 400 GHz. This frequency is easy to understand: in the PJT model, the level u= 1, j= 0 of E, energy has very low intensity because the Franck-Condon factor between this level and the Na, ground state is close to zero. Our timeresolved experiment is therefore in favour of the pseudo-Jahn-Teller effect in the Naj B state. If we compare the experiment (fig. 3 ) and our calculations (fig. 4) two points remain to be discussed. In the experiment, the oscillation decays with a time constant of about 4 ps. This effect is probably due to the rotational structure: (i) From one rotational level of the ground state, three rotational levels are pumped in the B state. This means that the initial eigenfunction w( t = 0) is more complicated than in our calculations. (ii) Due to strong Coriolis coupling, the vibronic energy varies significantly with the rotational quantum number and the experimental signal corresponds to an incoherent superposition of all the rotational levels. The time decay associated with this phenomenon may be estimated from the rotational contour of the various vibronic bands and this estimation is in reasonable agreement with the experimental decay. In conclusion, we have observed the time evolution of the Na3 B state pseudorotational motion and our experimental results are in favour of the pseudoJahn-Teller model for the interpretation of the Na3 B state.
558
15 October 1993
This work has been financially supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 337 (TP AS).
References
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