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IR spectroscopy and dynamics of a strongly vibrationally excited polyatomic molecule: CF3I
Volume 146, number 1,2
CHEMICAL PHYSICS LETTERS
29 April 1988
IR SPECTROSCOPY AND DYNAMICS OF A STRONGLY VIBRATIONALLY EXCITED POLYATOMIC MOLECULE: CFJ O.V. BOYARKIN, S.I. IONOV and V.N. BAGRATASHVILI Laboratory of Luser Chemistry, Research Centre for Laser Technology ojthe Academy ofSciences of the USSR, Troitzk, Moscow Region 142092, USSR Received 28 January 1988
The photodissociation technique was used to measure the linear IR absorption spectrum (v, and vq modes) of rotationally jetcooled CF,I molecules with vibrational energy EG Drc 19000 cm-‘, where D is the dissociation threshold. The dissociation yield of CF,I in the molecular beam was determined by resonant multiphoton ionization of atoms. A narrow resonance with a halfwidth g< 3 cm-’ was observed for the first time in the IR spectrum of a highly excited molecule. The Y, band revealed Fermiresonance structure, which provides evidence for the presence of beats accompanying the intramolecular vibrational relaxation. Analysis of the vq band shape showed that intramolecular broadening of the IR spectrum of a highly excited molecule can be related not only to energy and phase relaxation processes but also to intramolecular inhomogeneous broadening.
1. Introduction Linear IR absorption spectra of polyatomic molecules having vibrational energies of the order of the dissociation threshold are of considerable interest. These spectra have considerable practical value, in particular for the development of laser chemical technology based on IR multiphoton excitation effects (e.g. laser separation of isotopes, laser-radical synthesis, etc.) [ 11. The IR spectroscopy of highly excited molecules is also of fundamental significance. In recent years, various multidimensional dynamical systems possessing weak non-linearity have been extensively studied [ 2,3 1. A polyatomic molecule provides an example of such a system. Of particular interest are molecules with a sufficiently high level of vibrational excitation to induce IVR via intermode anharmonicity [ 1,4-6 1. However, the IR spectroscopy of highly excited molecules is not studied at present for practical reasons. The major difficulty that impedes experimental investigation is inhomogeneous broadening of the spectrum of an ensemble of highly excited molecules. The problem of vibrational inhomogeneous broadening can be solved by creating a mono-ener106
getic ensemble of molecules, for example, through non-radiative transitions [ 71, The other way to suppress vibrational inhomogeneous broadening is to use photodissociation techniques for measuring the IR absorption spectra [8-l 11. These methods allow the investigation of molecules within a narrow energy interval just below or just above the dissociation threshold. In this work, the CFJ molecule has been studied using photodissociation techniques [ 10,121 based on the measurement of small increments in the dissociation yield during the action of a probing IR pulse on the preexcited molecule. The dissociation yields were measured by the method of resonance photoionization of atoms. The CF31 molecule was chosen for our study because experimental evidence exists that small polyatomic molecules (&F&l [ 13 1, CFJ [ 9 ] ) may have the Fermi-resonance structure of linear absorption spectra even at a high level of vibrational excitation. Moreover, the Fermi-resonance structure has been clearly observed in the spectrum of high overtones of the C-H vibration in some molecules [ 14,151. In the present work, we have directly observed such a structure in the linear IR absorption spectrum cor-
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responding to the dipole-active vl mode of the CF31 molecule with vibrational energy Ex 19000 cm- I.
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tion technique has been described in detail elsewhere [ 171. The sequence of laser pulses is shown in fig. 1.
2. Experiment 3. Results The experimental apparatus used in this work is similar to that described elsewhere [ 11,16 1. Two IR beams produced by TEA CO2 lasers propagate in the opposite direction to a pulsed molecular beam (fig. 1). The cross section of the laser beams (0.8 X 0.8 cm’) exceeded the molecular beam diameter (x 0.1 cm). The first IR pulse (w, = 1076 cm-‘, G1~0.53 J/cm2, z= 1.5 ys) produced the preliminary excitation via IR-multiphoton absorption. This resulted in the dissociation of ~5% of molecules excited above the dissociation threshold. The second IR pulse served as a probe for the spectral measurements. The frequency of this radiation was varied within the range 1087.9 to 876.5 cm- ’ ( "CO2 and 13C02 laser generation). The maximum fluence was 1 J/cm’, the laser pulse duration 1.5 j.ls. The total dissociation yield in our experiments was measured by the photoionization method. For this purpose, the second harmonic of a dye laser cf= 15 cm, EUv% 100 @, 7%8 ns, AOZ 1 cm- ’) was focused on the central part of the molecular beam and tuned to the two-photon resonance (5p ‘P3,26p 4P3,Z) of the three-photon ionization of iodine atoms, one of the initial products. The photoioniza-
Fig. 2 presents characteristic curves of the dissociation yield of CF31 versus the fluence of the probing IR field. It can be seen that at low Q2 the experimental points give a good straight-line fit. As can be easily shown, the slope -dp/d@$ of the line is proportional to the absorption cross section of molecules with energy ExDx19000 cm-’ [18], where D is the dissociation threshold. Indeed, for a weak probing IR field S@,, the small increment in the dissociation yield, is 6/3=&&6cP,, where a& is the cross section for the IR upward transitions of molecules with vibrational energy D- fiw,< E< D, andf, is the fraction of such molecules. This relation is valid for small molecules (e.g. CF,I), for which
0
0
WI
0.4
0.05
0.6
0.1
0.15
uv w2
x
!
0
0.2
5
15
0
I
0.05
0.1
t* /Us
Fig. 1. (a) Mutual orientation of molecular and laser beams in the experiment; o, = 1076 cm-‘; 9, =0.5 J/cm*; w2= 1088-876 cm-‘; 1.,=2982.3 A. (b) Sequence of the laser pulses.
PROBE FLUENCE
, J/cm2
Fig. 2. Characteristic curves of the dissociation yield versus the fluence of the probing IR field: A= 15%.
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the unimolecular decay rate k (E> D) is sufficiently large in comparison with the reciprocal time of the experiment [ 19 1. Fig. 3 shows the spectral dependence of the linear increment of the dissociation yield -@/d&, which represents (within an accuracy of up to the factor fb) the linear absorption spectrum c$ (0) of CFJ molecules with energy Ex 19000 cm-‘. The mutual disposition of the three sharp peaks in the experimental spectrum of CFJ near the dissociation threshold (w=975, 1035, 1047 cm-l) agrees to a good accuracy with the mutual disposition of the harmonic frequency UT( 1075 cm- ’) and the nearest Fermi resonances @+v$ (1028 cm-‘) and 2v$’ (1081 cm-‘) [20] (see also fig. 3b). The peaks ijz+ F3,2?1 and 2P5 of highly excited CF31 molecules were shifted by ~40 cm-’ to the red from the harmonic frequencies due to anharmonicity. The absorption band in the range o> 1070 cm-’ is quite naturally attributed to the IR active mode v4 of a highly excited molecule ( V$= 1187 cm-‘).
Fig. 3. (a) Spectral dependence of the small increments in the dissociation yield during the action of the probing pulse on the preliminary excited molecules. The solid line for wz 1070 cm-’ shows the band calculated for CFJ with EsD within the intramolecular broadening model (see text). (b) Mutual disposition of the IR active frequency V, and the anharmonically coupled vibrations 2~3and u2+v3. In a highly excited molecule the Fermi resonances 2v, and v2+u3 interact with other states of the molecule.
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It should be noted that the halfwidth of the narrowest peak in the experimental spectrum, 2v5, is yc 3 cm-‘, which is the sharpest resonance observed so far in the IR spectra of highly excited molecules. Recently sharp resonances have been observed in overtone spectra ofjet-cooled benzene [ 2 11. The presence of narrow resonances in the spectrum allows, in principle, highly selective excitation of the strongly vibrationally excited molecules, which might be of importance for the future development of laserchemical technology. It is known that narrow resonances in the spectrum correspond to long-lived nonstationary states (e.g. rivR> lo-‘* s for 2~~). The presence of such states may serve as a general basis for mode-selective laser chemistry.
4. Fermi-resonancestructureof the vI band and intramolecularvibrational relaxation of highly excited CFJ molecules Recently, the experimental, non-structurized homogeneously broadened Lorentzian absorption spectrum corresponding to the IR active mode v21 was reported for the (CF,)$I molecule with vibrational energy Eu35000 cm-’ [ 11,161. What is the reason for the difference between our experimental spectrum of the (small) highly excited CFJ molecule (fig. 3a) and the spectrum of the (large) ( CF3)&I molecule? To answer this question, let us consider qualitatively the mechanism of formation of the IR absorption band of a highly excited polyatomic molecule. The anharmonic interaction of the IR active mode v, with the close-lying combined vibrations v,_+Vjresults in the latter acquiring dipole activity and becoming noticeable in the absorption spectrum. These Fermi resonances, in their turn, interact with other states of the molecule, and so on [ 1] (see fig. 3b). If the anharmonic interaction is sufficiently strong, the absorption bands corresponding to the individual Fermi resonances overlap to form a single smooth band with a maximum at the frequency of the IR active mode vP The necessary condition for such overlapping in the case of anharmanic interaction of the lowest (third) order can be written as [22] 2y,pp w 1 .
(1)
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In this case, a Lorentzian IR band is predicted, with half-width yPdetermined from the relation [ 221 yP%‘Icx:p;cJn’(nS l)‘-1 )
(2)
where x3 and n are the characteristic values of the anharmonicity constant and the occupation number of the molecular modes, respectively, I=0 for the Fermi resonances of the type v, x vi- Vjand I= 1 for up= vi+ vj. Condition ( 1) is well satisfied for large molecules (CF,),CI having a high density of Fermi resonances fl% 0.3 cm (y=9 cm-‘), and homogeneous Iorentzian IR bands have been observed for these highly excited molecules [ 11,161. For the vI mode of the CFJ molecule pp x 0.03 cm (see rig. 3b). Assuming that x36&=8.2 cm-’ [ 201 (which is the largest known value for the thirdorder constant of this molecule), we obtain yI G 30 cm-’ and 2y,py ~2. Thus condition (1) is not satisfied for the CFJ molecule. The experimental data presented in fig. 3 show that in this case the anharmonic interaction is insufficient to provide overlapping of the bands corresponding to separate Fermi resonances. It is well known that the linear absorption spectrum of any system is related to its dynamical properties [23]. Let us consider the structure of the absorption band vl of highly excited CF,I from the viewpoint of IVR processes. Let a single vibrational quantum be added to the v, mode of the preliminary highly excited molecule. (This can be done using an ultra-short coherent IR pulse whose spectrum covers the whole v, band, including v”,+ %;,Zl and 25,. ) The presence of structure in the IR absorption band shows that the evolution of such a non-stationary state has the character of beats. The excess vibrational energy introduced by the IR pulse to the vi mode will oscillate between the states cZt &, v”,and 2c5 with frequencies determined by the distances between the corresponding peaks in the spectrum. The lower limit of the decay time of these oscillations can be estimated using the peak widths. Similar quantum beats accompanying the IVR process have been observed on a real time scale for electronically excited anthracene [ 61. Our spectroscopic experiment shows directly that the IVR process occurs through Fermi resonances. This conclusion agrees with experimental data on high overtone spectroscopy of the C-H chromophore [ 14,15 1.
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5. Widths of spectral bands: contribution from intramolecularinhomogeneous broadening The broadening of IR absorption bands of highly excited molecules may be due to the following: ( 1) the rotational contour, (2) vibrational inhomogeneous broadening of the spectrum of a non-monoenergetic ensemble of molecules, and (3) intramolecular broadening of the spectrum of an isolated molecule. Before turning to a discussion of the most interesting factor, the intramolecular broadening, we consider contributions from the trivial reasons ( 1) and (2). Assuming that the rotational temperature of the jet-cooled molecules T,,,,x 20 K [ 241, we obtain the width of the rotational contour &W 2J2kThcB~2 cm-l (B=0.05 cm-’ [25]). To evaluate the vibrational inhomogeneous broadening &b, note that the experimentally measured small increments of the dissociation yield are due to the absorption of radiation by molecules having vibrational energy E in the range D- Am2< E < D. From the shift of the v, band observed for the growth of E from zero to D, we obtain %i~~~jtO~[V~(D)-V~(O)]/D~2 cm-‘. A comparison of the estimated inhomogeneous broadening with the experimental spectrum reveals that all peaks, except for 2v5, exhibit greater widths. Therefore, we have obtained the practically homogeneous IR absorption spectrum of CF31 near the dissociation threshold. The major intramolecular broadening mechanisms of the IR bands of highly excited molecules are intramolecular vibrational relaxation and phase relaxation [ 26-33 1. Recently, it has been suggested that broadening of the IR spectrum of a single highly excited molecule may be due to so-called “intramolecular inhomogeneous broadening”. We shall demonstrate that this mechanism dominates in the case of the v4 band (fig. 3 ). Consider a highly excited molecule within a narrow energy interval dE around E. The interval dE contains a large number of harmonic states (n’,,...,n(). Each set of occupation numbers which satisfies the condition (3) corresponds to its own resonance frequency of the IR active vi mode 109
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involving a single molecule an inhomogeneously broadened spectrum will be obtained. In this case [341
(4) where vi are the harmonic frequencies; gk and nk are the degeneracy factor and occupation number of the kth mode, respectively, and &, are the anharmonicity constants. Note that the harmonic states are not stationary due to anharmonic interactions. The redistribution of energy between the isoenergetic harmonic states of an isolated molecule during the IVR process leads to frequency fluctuations and broadening of the absorption band up In the general case, the shape of an absorption band of an oscillator with fluctuating frequency depends on the relation between the frequency dispersion &(o-I$)2j((o)
29 April 1988
(5)
(wheref( w ) and ii, are the distribution function and the mean frequency of the oscillator) and the correlation time w ( t + z) w w ( t ) [ 34 1. The fast fluctuation case, zA*: 1, corresponds to the phase relaxation in highly excited molecules which has been treated in refs. [ 3 1,321. In this case, the homogeneous Lorentzian shape of the absorption band has been predicted. If the fluctuations are slow, 74~ 1, the absorption spectrum of the molecule changes during the characteristic time XT. Then, for the measurement time t z+ z even in a hypothetical experiment
a(o)=f(co)A.
(6)
In systems with a large number of degrees of freedom, f(w) is a Gaussian. Hence, in the case of intramolecular inhomogeneous broadening, a Gaussian shape of the spectrum of polyatomic molecules may be anticipated. Note, that such intramolecular inhomogeneity may, in principle, be overcome in photodissociation experiments of the “hole-burning” type [ 35 1. Fig. 4 shows the experimental spectrum ofthev,bandlnaversus (o-oo)2,whereoo=1090 cm- ’is the expected position of the band maximum. It should be noted that the selection of w. is arbitrary, since only a part of the v4 band has been measured in the experiment. However, this uncertainty can be eliminated by taking into account the additional condition for the relation of the integral intensities of the v4 and Y, bands: S,/S, ~0.88 [36], which is satisfied in our case. From fig. 4 it can be seen that the experimental spectrum gives a good fit to a Gaussian with a dispersion of A= 17 cm-‘. Note also that attempts to describe the experimental v4 band by a Lorentzian fail, since they give a half-width value y= 50 cm-’ leading to considerably overstated S4/S1 ratio. Note in addition that the v4band has no
d/3/d$ ,arb.un.
2-
I-
r
-1.
__ ___--900 I
.
I
950
I
01
1.
IO00
*
.,,I,,,.,
I050 LJAVENUMBER. cm-'
Fig. 4. Experimental spectrum of the v4band in coordinates rectifying the Gaussian. The calculated spectrum is a straight line having the best fit to the experimental points (A= 17 cm-‘).
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close Fermi resonances of third or even fourth order. Therefore, no structure is anticipated in this band. Fig. 4 presents the results of calculations on the v4 band performed within the intramolecular inhomogeneous broadening model. The f( w) values were calculated by determining the number of states of a molecule falling within the energy interval 18 800
(7)
For the 3, mode we obtain from eq. (6) y= 7 cm-‘, which is in good agreement with experiment. The insufficient accuracy of the measurements does not allow us to judge the exact shape of the 0, band,
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Lorentzian or Gaussian. A definite conclusion about the presence of narrowing [ 341 for the vi band can be made only on the basis of more accurate measurements of the spectral shape.
6. Conclusions The main results obtained in this work are: ( 1) The IR linear absorption spectrum of rotationally cooled CFJ near its dissociation threshold was measured by the photodissociation technique. For the first time, a narrow resonance with half-width y< 3 cm- ’has been observed in the IR spectrum of a highly excited molecule. (2) The absorption band corresponding to the v1 vibration revealed Fermi-resonance structure, showing evidence for the presence of beats during the IVR. This proves experimentally that Fermi resonances are doorway states in the redistribution of vibrational energy in an isolated molecule. (3) It is shown that the intramolecular broadening of the IR band of a highly excited molecule can be due not only to energy and phase relaxation processes, but also to intramolecular inhomogeneous broadening.
Acknowledgement The authors would like to thank M.V. Kuz’min and A.A. Stuchebryukhov for fruitful discussions, and N.G. Petrovskaya for help in preparing the manuscript.
References [ 11 V.N. Bagratashviii, VS. Letokhov, A.A. Makarov and E.A. Ryabov, Multiple photon infrared photophysics and photochemistry (Gordon and Breach, New Yorl, 1985). [2] B.V. Chirikov, Phys. Rept. 52 (1979) 263. [3] G.M. Zaslavskii, Stochasticity of dynamical systems (Nauka, Moscow, 1984) [inRussian]. [ 41 V.E. Bondybey, Ann. Rev. Chem. 35 ( 1984) 59 1. [ 51 N. Blombergen and A.H. Zewail, J. Phys. Chem. 88 ( 1984) 5459. [6] P.M.Felker and A.H. Zewail, J. Chem. Phys. 82 (1985) 2961,2994.
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(71 A.V. Evseev, V.M. Krivtzun, Yu.A. Kuritzin, A.A. Makarov, A.A. Puretzkii, E.A. Ryabov, E.P. Snegirev and V.V. Tyakbt, Zh. Eksp. Teor. Fiz. 87 (1984) 11;Chem. Phys. 106 (1986) 131. [ 8 ] M.J. Coggiola, P.C. Cosby and J.R. Peterson, J. Chem. Phys. 72 (1980) 6507. [9] V.N. Bagratashvili, S.I. Ionov, M.V. Kuzmin, V.S. Letokhov, G.V. Mishokov and A.A. Stuchebrukhov, in: Recent advances in molecular reactor dynamics (CNRS, Paris, 1986) p. 425. [lo] S.I. Ionov, Spectrochim. Acta 143 (1987) 167. [ 111V.N. Bagratashvilli, S.I. Ionov, V.S. Letokbov, V.N. Lokhman, G.N. Makarov and A.A Stuchebrukhov, Zh. Eksp. Teor. Fiz. 93 (1987) 1188. [ 121 S.I. Ionov and V.N. Bagratashvili, Chem. Phys. Letters, to be published. 113 E. Borsella, R. Fantoni, A. Giardini-Guidoni, D.R. Adams and C.D. Cantrell, Chem. Phys. Letters 101 (1983) 86. [14 H.R. Dilbal and M. Quack, J. Chem. Phys. 81 ( 1984) 3779. 115 J.E. Baggott, M.C. Chuang, R.N. Zare, H.R. Dilbal and M. Quack, J. Chem. Phys. 82 ( 1985) 1186. 116‘I V.N. Bagratashvili, S.I. Ionov, V.S. Letokbov, V.N. Lokbman, G.N. Makarov and A.A. Stuchebrukhov, Pis’ma vZhETF 44 (1986) 450; JETP Letters 44 (1986) 580. 1171V.N. Bagratashvilli, S.I. Ionov, M.V. Kuz’min and V.S. Letokhov, Zh. Eksp. Teor. Fiz. 91 ( 1986) 766; Sov. Phys. JETP 64 (1986) 453. [18 V.N. Kondrat’ev, ed., Chemical bond tisions. Ionization potentials and electron affinities (Nauka, Moscow, 1974). [ 191Aa. F. Sudbo, P.A. Schulz, E.R. Grant, Y.A. Shen and Y.T. Lee, J. Chem. Phys. 70 (1979) 912. [ 201 W. Fuss, Spectrochim. Acta A 38 (1982) 829. [ 211 R.N. Page, Y.R. Shen and Y.T. Lee, Phys. Rev. Letters 59 (1987) 1293.
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[ 221 V.N. Bagratashvili, M.V. Kuz’min, V.S. Lctokhov and A.A. Stuchebrukhov, Chem. Phys. 97 (1985) 13. [23] L.D. Landau and E.M. Lifshitz, Theoretical physics, Vol. 5. Statistical physics (Nauka, Moscow, 1976) [in Russian]. [24] D.H. Levy, L. Wbartov and R.E. Smalley, in: Chemical and biochemical applications of lasers, Vol. 2 (Academic Press, New York, 1977) p. 1. [25] H. Burger, K. Burczyk, H. Hollenstein and M. Quack, Mol. Phys. 55 (1985) 255. [26] B. Carmeli and A. Nitzan, J. Chem. Phys. 73 (1980) 2054, 2070. [27] J. Stone, E. Thiele and M.F. Goodman, J. Chem. Phys. 75 (1981) 1712. [28] A.A. Makarov and V.V. Tyakht, Zh. Eksp. Teor. Fiz. 83 (1982) 502. [29] S. Mukamel and R. Islampour. Chem. Phys. Letters 108 (1984) 161. [ 301 A.A. Stuchebrukhov, M.V. Kuz’min, V.N. Bagratashvili and V.S. Letokhov, Chem. Phys. 107 (1986) 429. [ 3 1 ] A.A. Stuchebrukhov, Zh. Eksp. Teor. Fiz. 9 1 ( 1986) 2014. [32] M.V. Kuz’min, VS. Letokhov and A.A. Stuchebrukhov, Comments At. Mol. Pbys. 20 ( 1987) 127, 139, and references therein. [33] A.A. Makarov and V.V. Tyakht, Zh. Eksp. Teor. Fiz. 93 (1987) 1188. [ 341 R. Cubo, in: Fluctuations, relaxation and resonance in magnetic systems, ed. D. ter Haar (Oliver and Boyd, Edinburgh, 1962) p. 23. [35] V.S. Letokhov and V.P. Chebotayev, Nonlinear laser spectroscopy (Springer, Berlin 1977). [ 361 M.O. Bulanin, L.A. Shigula, T.D. Kolomiitseva and D.H. Schepkin, Opt. i Spectroskopiya 56 (1984) 663.
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IR SPECTROSCOPY AND DYNAMICS OF A STRONGLY VIBRATIONALLY EXCITED POLYATOMIC MOLECULE: CFJ O.V. BOYARKIN, S.I. IONOV and V.N. BAGRATASHVILI Laboratory of Luser Chemistry, Research Centre for Laser Technology ojthe Academy ofSciences of the USSR, Troitzk, Moscow Region 142092, USSR Received 28 January 1988
The photodissociation technique was used to measure the linear IR absorption spectrum (v, and vq modes) of rotationally jetcooled CF,I molecules with vibrational energy EG Drc 19000 cm-‘, where D is the dissociation threshold. The dissociation yield of CF,I in the molecular beam was determined by resonant multiphoton ionization of atoms. A narrow resonance with a halfwidth g< 3 cm-’ was observed for the first time in the IR spectrum of a highly excited molecule. The Y, band revealed Fermiresonance structure, which provides evidence for the presence of beats accompanying the intramolecular vibrational relaxation. Analysis of the vq band shape showed that intramolecular broadening of the IR spectrum of a highly excited molecule can be related not only to energy and phase relaxation processes but also to intramolecular inhomogeneous broadening.
1. Introduction Linear IR absorption spectra of polyatomic molecules having vibrational energies of the order of the dissociation threshold are of considerable interest. These spectra have considerable practical value, in particular for the development of laser chemical technology based on IR multiphoton excitation effects (e.g. laser separation of isotopes, laser-radical synthesis, etc.) [ 11. The IR spectroscopy of highly excited molecules is also of fundamental significance. In recent years, various multidimensional dynamical systems possessing weak non-linearity have been extensively studied [ 2,3 1. A polyatomic molecule provides an example of such a system. Of particular interest are molecules with a sufficiently high level of vibrational excitation to induce IVR via intermode anharmonicity [ 1,4-6 1. However, the IR spectroscopy of highly excited molecules is not studied at present for practical reasons. The major difficulty that impedes experimental investigation is inhomogeneous broadening of the spectrum of an ensemble of highly excited molecules. The problem of vibrational inhomogeneous broadening can be solved by creating a mono-ener106
getic ensemble of molecules, for example, through non-radiative transitions [ 71, The other way to suppress vibrational inhomogeneous broadening is to use photodissociation techniques for measuring the IR absorption spectra [8-l 11. These methods allow the investigation of molecules within a narrow energy interval just below or just above the dissociation threshold. In this work, the CFJ molecule has been studied using photodissociation techniques [ 10,121 based on the measurement of small increments in the dissociation yield during the action of a probing IR pulse on the preexcited molecule. The dissociation yields were measured by the method of resonance photoionization of atoms. The CF31 molecule was chosen for our study because experimental evidence exists that small polyatomic molecules (&F&l [ 13 1, CFJ [ 9 ] ) may have the Fermi-resonance structure of linear absorption spectra even at a high level of vibrational excitation. Moreover, the Fermi-resonance structure has been clearly observed in the spectrum of high overtones of the C-H vibration in some molecules [ 14,151. In the present work, we have directly observed such a structure in the linear IR absorption spectrum cor-
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responding to the dipole-active vl mode of the CF31 molecule with vibrational energy Ex 19000 cm- I.
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tion technique has been described in detail elsewhere [ 171. The sequence of laser pulses is shown in fig. 1.
2. Experiment 3. Results The experimental apparatus used in this work is similar to that described elsewhere [ 11,16 1. Two IR beams produced by TEA CO2 lasers propagate in the opposite direction to a pulsed molecular beam (fig. 1). The cross section of the laser beams (0.8 X 0.8 cm’) exceeded the molecular beam diameter (x 0.1 cm). The first IR pulse (w, = 1076 cm-‘, G1~0.53 J/cm2, z= 1.5 ys) produced the preliminary excitation via IR-multiphoton absorption. This resulted in the dissociation of ~5% of molecules excited above the dissociation threshold. The second IR pulse served as a probe for the spectral measurements. The frequency of this radiation was varied within the range 1087.9 to 876.5 cm- ’ ( "CO2 and 13C02 laser generation). The maximum fluence was 1 J/cm’, the laser pulse duration 1.5 j.ls. The total dissociation yield in our experiments was measured by the photoionization method. For this purpose, the second harmonic of a dye laser cf= 15 cm, EUv% 100 @, 7%8 ns, AOZ 1 cm- ’) was focused on the central part of the molecular beam and tuned to the two-photon resonance (5p ‘P3,26p 4P3,Z) of the three-photon ionization of iodine atoms, one of the initial products. The photoioniza-
Fig. 2 presents characteristic curves of the dissociation yield of CF31 versus the fluence of the probing IR field. It can be seen that at low Q2 the experimental points give a good straight-line fit. As can be easily shown, the slope -dp/d@$ of the line is proportional to the absorption cross section of molecules with energy ExDx19000 cm-’ [18], where D is the dissociation threshold. Indeed, for a weak probing IR field S@,, the small increment in the dissociation yield, is 6/3=&&6cP,, where a& is the cross section for the IR upward transitions of molecules with vibrational energy D- fiw,< E< D, andf, is the fraction of such molecules. This relation is valid for small molecules (e.g. CF,I), for which
0
0
WI
0.4
0.05
0.6
0.1
0.15
uv w2
x
!
0
0.2
5
15
0
I
0.05
0.1
t* /Us
Fig. 1. (a) Mutual orientation of molecular and laser beams in the experiment; o, = 1076 cm-‘; 9, =0.5 J/cm*; w2= 1088-876 cm-‘; 1.,=2982.3 A. (b) Sequence of the laser pulses.
PROBE FLUENCE
, J/cm2
Fig. 2. Characteristic curves of the dissociation yield versus the fluence of the probing IR field: A= 15%.
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the unimolecular decay rate k (E> D) is sufficiently large in comparison with the reciprocal time of the experiment [ 19 1. Fig. 3 shows the spectral dependence of the linear increment of the dissociation yield -@/d&, which represents (within an accuracy of up to the factor fb) the linear absorption spectrum c$ (0) of CFJ molecules with energy Ex 19000 cm-‘. The mutual disposition of the three sharp peaks in the experimental spectrum of CFJ near the dissociation threshold (w=975, 1035, 1047 cm-l) agrees to a good accuracy with the mutual disposition of the harmonic frequency UT( 1075 cm- ’) and the nearest Fermi resonances @+v$ (1028 cm-‘) and 2v$’ (1081 cm-‘) [20] (see also fig. 3b). The peaks ijz+ F3,2?1 and 2P5 of highly excited CF31 molecules were shifted by ~40 cm-’ to the red from the harmonic frequencies due to anharmonicity. The absorption band in the range o> 1070 cm-’ is quite naturally attributed to the IR active mode v4 of a highly excited molecule ( V$= 1187 cm-‘).
Fig. 3. (a) Spectral dependence of the small increments in the dissociation yield during the action of the probing pulse on the preliminary excited molecules. The solid line for wz 1070 cm-’ shows the band calculated for CFJ with EsD within the intramolecular broadening model (see text). (b) Mutual disposition of the IR active frequency V, and the anharmonically coupled vibrations 2~3and u2+v3. In a highly excited molecule the Fermi resonances 2v, and v2+u3 interact with other states of the molecule.
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It should be noted that the halfwidth of the narrowest peak in the experimental spectrum, 2v5, is yc 3 cm-‘, which is the sharpest resonance observed so far in the IR spectra of highly excited molecules. Recently sharp resonances have been observed in overtone spectra ofjet-cooled benzene [ 2 11. The presence of narrow resonances in the spectrum allows, in principle, highly selective excitation of the strongly vibrationally excited molecules, which might be of importance for the future development of laserchemical technology. It is known that narrow resonances in the spectrum correspond to long-lived nonstationary states (e.g. rivR> lo-‘* s for 2~~). The presence of such states may serve as a general basis for mode-selective laser chemistry.
4. Fermi-resonancestructureof the vI band and intramolecularvibrational relaxation of highly excited CFJ molecules Recently, the experimental, non-structurized homogeneously broadened Lorentzian absorption spectrum corresponding to the IR active mode v21 was reported for the (CF,)$I molecule with vibrational energy Eu35000 cm-’ [ 11,161. What is the reason for the difference between our experimental spectrum of the (small) highly excited CFJ molecule (fig. 3a) and the spectrum of the (large) ( CF3)&I molecule? To answer this question, let us consider qualitatively the mechanism of formation of the IR absorption band of a highly excited polyatomic molecule. The anharmonic interaction of the IR active mode v, with the close-lying combined vibrations v,_+Vjresults in the latter acquiring dipole activity and becoming noticeable in the absorption spectrum. These Fermi resonances, in their turn, interact with other states of the molecule, and so on [ 1] (see fig. 3b). If the anharmonic interaction is sufficiently strong, the absorption bands corresponding to the individual Fermi resonances overlap to form a single smooth band with a maximum at the frequency of the IR active mode vP The necessary condition for such overlapping in the case of anharmanic interaction of the lowest (third) order can be written as [22] 2y,pp w 1 .
(1)
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In this case, a Lorentzian IR band is predicted, with half-width yPdetermined from the relation [ 221 yP%‘Icx:p;cJn’(nS l)‘-1 )
(2)
where x3 and n are the characteristic values of the anharmonicity constant and the occupation number of the molecular modes, respectively, I=0 for the Fermi resonances of the type v, x vi- Vjand I= 1 for up= vi+ vj. Condition ( 1) is well satisfied for large molecules (CF,),CI having a high density of Fermi resonances fl% 0.3 cm (y=9 cm-‘), and homogeneous Iorentzian IR bands have been observed for these highly excited molecules [ 11,161. For the vI mode of the CFJ molecule pp x 0.03 cm (see rig. 3b). Assuming that x36&=8.2 cm-’ [ 201 (which is the largest known value for the thirdorder constant of this molecule), we obtain yI G 30 cm-’ and 2y,py ~2. Thus condition (1) is not satisfied for the CFJ molecule. The experimental data presented in fig. 3 show that in this case the anharmonic interaction is insufficient to provide overlapping of the bands corresponding to separate Fermi resonances. It is well known that the linear absorption spectrum of any system is related to its dynamical properties [23]. Let us consider the structure of the absorption band vl of highly excited CF,I from the viewpoint of IVR processes. Let a single vibrational quantum be added to the v, mode of the preliminary highly excited molecule. (This can be done using an ultra-short coherent IR pulse whose spectrum covers the whole v, band, including v”,+ %;,Zl and 25,. ) The presence of structure in the IR absorption band shows that the evolution of such a non-stationary state has the character of beats. The excess vibrational energy introduced by the IR pulse to the vi mode will oscillate between the states cZt &, v”,and 2c5 with frequencies determined by the distances between the corresponding peaks in the spectrum. The lower limit of the decay time of these oscillations can be estimated using the peak widths. Similar quantum beats accompanying the IVR process have been observed on a real time scale for electronically excited anthracene [ 61. Our spectroscopic experiment shows directly that the IVR process occurs through Fermi resonances. This conclusion agrees with experimental data on high overtone spectroscopy of the C-H chromophore [ 14,15 1.
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5. Widths of spectral bands: contribution from intramolecularinhomogeneous broadening The broadening of IR absorption bands of highly excited molecules may be due to the following: ( 1) the rotational contour, (2) vibrational inhomogeneous broadening of the spectrum of a non-monoenergetic ensemble of molecules, and (3) intramolecular broadening of the spectrum of an isolated molecule. Before turning to a discussion of the most interesting factor, the intramolecular broadening, we consider contributions from the trivial reasons ( 1) and (2). Assuming that the rotational temperature of the jet-cooled molecules T,,,,x 20 K [ 241, we obtain the width of the rotational contour &W 2J2kThcB~2 cm-l (B=0.05 cm-’ [25]). To evaluate the vibrational inhomogeneous broadening &b, note that the experimentally measured small increments of the dissociation yield are due to the absorption of radiation by molecules having vibrational energy E in the range D- Am2< E < D. From the shift of the v, band observed for the growth of E from zero to D, we obtain %i~~~jtO~[V~(D)-V~(O)]/D~2 cm-‘. A comparison of the estimated inhomogeneous broadening with the experimental spectrum reveals that all peaks, except for 2v5, exhibit greater widths. Therefore, we have obtained the practically homogeneous IR absorption spectrum of CF31 near the dissociation threshold. The major intramolecular broadening mechanisms of the IR bands of highly excited molecules are intramolecular vibrational relaxation and phase relaxation [ 26-33 1. Recently, it has been suggested that broadening of the IR spectrum of a single highly excited molecule may be due to so-called “intramolecular inhomogeneous broadening”. We shall demonstrate that this mechanism dominates in the case of the v4 band (fig. 3 ). Consider a highly excited molecule within a narrow energy interval dE around E. The interval dE contains a large number of harmonic states (n’,,...,n(). Each set of occupation numbers which satisfies the condition (3) corresponds to its own resonance frequency of the IR active vi mode 109
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involving a single molecule an inhomogeneously broadened spectrum will be obtained. In this case [341
(4) where vi are the harmonic frequencies; gk and nk are the degeneracy factor and occupation number of the kth mode, respectively, and &, are the anharmonicity constants. Note that the harmonic states are not stationary due to anharmonic interactions. The redistribution of energy between the isoenergetic harmonic states of an isolated molecule during the IVR process leads to frequency fluctuations and broadening of the absorption band up In the general case, the shape of an absorption band of an oscillator with fluctuating frequency depends on the relation between the frequency dispersion &(o-I$)2j((o)
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(5)
(wheref( w ) and ii, are the distribution function and the mean frequency of the oscillator) and the correlation time w ( t + z) w w ( t ) [ 34 1. The fast fluctuation case, zA*: 1, corresponds to the phase relaxation in highly excited molecules which has been treated in refs. [ 3 1,321. In this case, the homogeneous Lorentzian shape of the absorption band has been predicted. If the fluctuations are slow, 74~ 1, the absorption spectrum of the molecule changes during the characteristic time XT. Then, for the measurement time t z+ z even in a hypothetical experiment
a(o)=f(co)A.
(6)
In systems with a large number of degrees of freedom, f(w) is a Gaussian. Hence, in the case of intramolecular inhomogeneous broadening, a Gaussian shape of the spectrum of polyatomic molecules may be anticipated. Note, that such intramolecular inhomogeneity may, in principle, be overcome in photodissociation experiments of the “hole-burning” type [ 35 1. Fig. 4 shows the experimental spectrum ofthev,bandlnaversus (o-oo)2,whereoo=1090 cm- ’is the expected position of the band maximum. It should be noted that the selection of w. is arbitrary, since only a part of the v4 band has been measured in the experiment. However, this uncertainty can be eliminated by taking into account the additional condition for the relation of the integral intensities of the v4 and Y, bands: S,/S, ~0.88 [36], which is satisfied in our case. From fig. 4 it can be seen that the experimental spectrum gives a good fit to a Gaussian with a dispersion of A= 17 cm-‘. Note also that attempts to describe the experimental v4 band by a Lorentzian fail, since they give a half-width value y= 50 cm-’ leading to considerably overstated S4/S1 ratio. Note in addition that the v4band has no
d/3/d$ ,arb.un.
2-
I-
r
-1.
__ ___--900 I
.
I
950
I
01
1.
IO00
*
.,,I,,,.,
I050 LJAVENUMBER. cm-'
Fig. 4. Experimental spectrum of the v4band in coordinates rectifying the Gaussian. The calculated spectrum is a straight line having the best fit to the experimental points (A= 17 cm-‘).
110
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close Fermi resonances of third or even fourth order. Therefore, no structure is anticipated in this band. Fig. 4 presents the results of calculations on the v4 band performed within the intramolecular inhomogeneous broadening model. The f( w) values were calculated by determining the number of states of a molecule falling within the energy interval 18 800
(7)
For the 3, mode we obtain from eq. (6) y= 7 cm-‘, which is in good agreement with experiment. The insufficient accuracy of the measurements does not allow us to judge the exact shape of the 0, band,
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Lorentzian or Gaussian. A definite conclusion about the presence of narrowing [ 341 for the vi band can be made only on the basis of more accurate measurements of the spectral shape.
6. Conclusions The main results obtained in this work are: ( 1) The IR linear absorption spectrum of rotationally cooled CFJ near its dissociation threshold was measured by the photodissociation technique. For the first time, a narrow resonance with half-width y< 3 cm- ’has been observed in the IR spectrum of a highly excited molecule. (2) The absorption band corresponding to the v1 vibration revealed Fermi-resonance structure, showing evidence for the presence of beats during the IVR. This proves experimentally that Fermi resonances are doorway states in the redistribution of vibrational energy in an isolated molecule. (3) It is shown that the intramolecular broadening of the IR band of a highly excited molecule can be due not only to energy and phase relaxation processes, but also to intramolecular inhomogeneous broadening.
Acknowledgement The authors would like to thank M.V. Kuz’min and A.A. Stuchebryukhov for fruitful discussions, and N.G. Petrovskaya for help in preparing the manuscript.
References [ 11 V.N. Bagratashviii, VS. Letokhov, A.A. Makarov and E.A. Ryabov, Multiple photon infrared photophysics and photochemistry (Gordon and Breach, New Yorl, 1985). [2] B.V. Chirikov, Phys. Rept. 52 (1979) 263. [3] G.M. Zaslavskii, Stochasticity of dynamical systems (Nauka, Moscow, 1984) [inRussian]. [ 41 V.E. Bondybey, Ann. Rev. Chem. 35 ( 1984) 59 1. [ 51 N. Blombergen and A.H. Zewail, J. Phys. Chem. 88 ( 1984) 5459. [6] P.M.Felker and A.H. Zewail, J. Chem. Phys. 82 (1985) 2961,2994.
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(71 A.V. Evseev, V.M. Krivtzun, Yu.A. Kuritzin, A.A. Makarov, A.A. Puretzkii, E.A. Ryabov, E.P. Snegirev and V.V. Tyakbt, Zh. Eksp. Teor. Fiz. 87 (1984) 11;Chem. Phys. 106 (1986) 131. [ 8 ] M.J. Coggiola, P.C. Cosby and J.R. Peterson, J. Chem. Phys. 72 (1980) 6507. [9] V.N. Bagratashvili, S.I. Ionov, M.V. Kuzmin, V.S. Letokhov, G.V. Mishokov and A.A. Stuchebrukhov, in: Recent advances in molecular reactor dynamics (CNRS, Paris, 1986) p. 425. [lo] S.I. Ionov, Spectrochim. Acta 143 (1987) 167. [ 111V.N. Bagratashvilli, S.I. Ionov, V.S. Letokbov, V.N. Lokhman, G.N. Makarov and A.A Stuchebrukhov, Zh. Eksp. Teor. Fiz. 93 (1987) 1188. [ 121 S.I. Ionov and V.N. Bagratashvili, Chem. Phys. Letters, to be published. 113 E. Borsella, R. Fantoni, A. Giardini-Guidoni, D.R. Adams and C.D. Cantrell, Chem. Phys. Letters 101 (1983) 86. [14 H.R. Dilbal and M. Quack, J. Chem. Phys. 81 ( 1984) 3779. 115 J.E. Baggott, M.C. Chuang, R.N. Zare, H.R. Dilbal and M. Quack, J. Chem. Phys. 82 ( 1985) 1186. 116‘I V.N. Bagratashvili, S.I. Ionov, V.S. Letokbov, V.N. Lokbman, G.N. Makarov and A.A. Stuchebrukhov, Pis’ma vZhETF 44 (1986) 450; JETP Letters 44 (1986) 580. 1171V.N. Bagratashvilli, S.I. Ionov, M.V. Kuz’min and V.S. Letokhov, Zh. Eksp. Teor. Fiz. 91 ( 1986) 766; Sov. Phys. JETP 64 (1986) 453. [18 V.N. Kondrat’ev, ed., Chemical bond tisions. Ionization potentials and electron affinities (Nauka, Moscow, 1974). [ 191Aa. F. Sudbo, P.A. Schulz, E.R. Grant, Y.A. Shen and Y.T. Lee, J. Chem. Phys. 70 (1979) 912. [ 201 W. Fuss, Spectrochim. Acta A 38 (1982) 829. [ 211 R.N. Page, Y.R. Shen and Y.T. Lee, Phys. Rev. Letters 59 (1987) 1293.
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[ 221 V.N. Bagratashvili, M.V. Kuz’min, V.S. Lctokhov and A.A. Stuchebrukhov, Chem. Phys. 97 (1985) 13. [23] L.D. Landau and E.M. Lifshitz, Theoretical physics, Vol. 5. Statistical physics (Nauka, Moscow, 1976) [in Russian]. [24] D.H. Levy, L. Wbartov and R.E. Smalley, in: Chemical and biochemical applications of lasers, Vol. 2 (Academic Press, New York, 1977) p. 1. [25] H. Burger, K. Burczyk, H. Hollenstein and M. Quack, Mol. Phys. 55 (1985) 255. [26] B. Carmeli and A. Nitzan, J. Chem. Phys. 73 (1980) 2054, 2070. [27] J. Stone, E. Thiele and M.F. Goodman, J. Chem. Phys. 75 (1981) 1712. [28] A.A. Makarov and V.V. Tyakht, Zh. Eksp. Teor. Fiz. 83 (1982) 502. [29] S. Mukamel and R. Islampour. Chem. Phys. Letters 108 (1984) 161. [ 301 A.A. Stuchebrukhov, M.V. Kuz’min, V.N. Bagratashvili and V.S. Letokhov, Chem. Phys. 107 (1986) 429. [ 3 1 ] A.A. Stuchebrukhov, Zh. Eksp. Teor. Fiz. 9 1 ( 1986) 2014. [32] M.V. Kuz’min, VS. Letokhov and A.A. Stuchebrukhov, Comments At. Mol. Pbys. 20 ( 1987) 127, 139, and references therein. [33] A.A. Makarov and V.V. Tyakht, Zh. Eksp. Teor. Fiz. 93 (1987) 1188. [ 341 R. Cubo, in: Fluctuations, relaxation and resonance in magnetic systems, ed. D. ter Haar (Oliver and Boyd, Edinburgh, 1962) p. 23. [35] V.S. Letokhov and V.P. Chebotayev, Nonlinear laser spectroscopy (Springer, Berlin 1977). [ 361 M.O. Bulanin, L.A. Shigula, T.D. Kolomiitseva and D.H. Schepkin, Opt. i Spectroskopiya 56 (1984) 663.