5459
J. Phys. Chem. 1984,88, 5459-5465
FEATURE ARTICLE Energy Redistribution in Isolated Molecules and the Question of Mode-Selective Laser Chemistry Revisited Nicolaas Bloembergenf and Ahmed H. Zewail*s Arthur Amos Noyes Laboratory of Chemical Physics' and Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91 I25 (Received: April 26, 1984)
New experiments on the dynamics of collisionless energy redistribution in molecules indicate possibilities for laser-selective chemistry with (sub)picosecond pulses.
The excitation of molecules by electromagnetic radiation constitutes the broad field of molecular spectroscopy. The myriad of discrete spectral lines attest to the existence of sharply defined, discrete rotational, vibrational, and electronic excitation. During the past few decades molecules have been produced with large amounts of vibrational energy, either close to or above the dissociation limit, by monochromatic laser pulses in the absence of collisions. Previously, dissociation was usually achieved by thermal heating. With lasers, however, high vibrational states are reached either by absorption of many infrared photons or one or more photons in the visible or near ultraviolet or by a combination of these radiations. Such high collisionless excitation has been the subject of numerous experimental and theoretical studies, which have been reviewed in several recent publications (for reviews see, e.g., ref 1-5). The problem is complex because the large anharmonic coupling and the very high density of vibrational energy states lead to broad response functions. These are usually described in a statistical manner, because individual discrete energy levels cannot be resolved. In the presence of collisions an ergodic distribution on the energy shell is quickly established, but different viewpoints persist about the appropriate description of the highly excited vibrational state in the absence of collisions. Collisonless intramolecular vibrational-energy redistribution (IVR) is expected to proceed on a (very) short time scale. Because of this belief, several years ago it was proposed2 that ultrashort laser pulses (picosecond or shorter) be used for laser-selective chemistry, provided the reaction rates are on a short time scale. At that time, however, no information about the dynamics of IVR in real time was available. In view of recent developments made by using picosecond pulses and molecular beams to study isolated molecules,6 it is important to focus on the central problems and questions involved in the following: (a) the preparation of a molecular state by ultrashort pulses; (b) the coherence properties of the system; and (c) the (re)distribution of energy among the different degrees of freedom in the isolated, highly excited molecules. It is the purpose of this article to critically examine the different parameters that enter into the description of laser energization of molecules, IVR, and the inseparability of lightmolecule dynamics. We will also present some new and relevant experiments that are important to this problem. It is not our intention here to review all work in this field. 'Contribution No. 7017. *Sherman Fairchild Distinguished Scholar at the California Institute of Technology. Permanent address: Pierce Hall, Harvard University, Cambridge, MA 02138. 8 Camille & Henry Dreyfus Foundation Teacher-Scholar.
IVR and Chemical Reactivity A major motivation for many of the studies was the goal of mode-selective chemistry. Could molecules be prepared in a state of high vibrational energy by absorption of monochromatic laser radiation which would be markedly different from the ergodic ensemble which results if the same energy is imparted by heating, i.e., by collisions with a thermal bath? Consider, for example, the molecule CF3Br. It can absorb energy at a frequency v corresponding to the C-Br vibration. If irradiated with an intense infrared laser pulse near v the C-Br vibration is highly excited and dissociation occurs. CF,Br
-
CF3
+ Br
If irradiated with a laser pulse near the frequency v', the C-F bond is highly excited, and one might expect the dissociation products CF2Br and F. This does not occur. At a high level of excitation, the anharmonic coupling between the normal modes is so strong that the energy is redistributed among all normal modes. The dissociation reaction proceeds in a roughly similar manner as for a thermally excited unimolecular reaction. This description in terms of normal modes of vibrations permits a good grasp on the spectral density of the (mu1ti)photon transition matrix elements responsible for the excitation. Subsequently the energy is transferred to other normal modes by the strong anharmonicity in the highly excited state. Alternatively, one may use the molecular eigenstates (ME), which are superpositions of normal mode states. The excitation spectrum of the ME is, however, less obvious. There also remains the question of the percentages of each normal mode character in the ME states that are reached by the absorption of one or many photons. Thus, the question of which state one excites is important to selectivity and chemical reactivity. This point will be addressed further.
Important Parameters and Sectral Complexity The problem of coupled anharmonic oscillators is already quite complex as the computer calculations on the simple two-mode (1) Bloembergen, N.; Yablonovitch, E. Phys. Today 1978, 32, 23. (2) Zewail, A. H. Phys. Today 1980, 33, 27. (3) Fuss, W.; Kompa, K. L. Prog. Quantum. Electron. 1981, 7, 117. (4) Letokhov, V. S.'Nonlinear Laser Chemistry, Chemical Physics 22"; Springer-Verlag: Heidelberg, West Germany, 1983. (5) King, D. S. In "Dynamics of Excited States"; Lawley, K. P., Ed.; Wiley: New York, 1982. (6) Zewail, A. H. Faraday Discuss. Chem. SOC.1983, 75, 315, and references therein.
0022-3654/84/2088-5459$01.50/00 1984 American Chemical Society
5460 The Journal of Physical Chemistry, Vola 88, No. 23, 1984 U
At
TABLE I: Important Parameters for Selective-Mode Excitation and
U'
k-4
-
Zewail and Bloembergen
TIME
Figure 1. A simple schematic for a classical picture for energy redistribution between normal modes in a highly excited vibrational eigenstate. Henon-Heiles model demonstrate.' It appears that rather abrupt transitions from quasi-periodic to quasi-chaotic motions in phase space occur when the energy increases. Even the electronic motion in the simple system of a hydrogen atom can become chaotic if the energy spacing between the Rydberg levels becomes comparable to the quadratic Zeeman effect on the orbitals.8 A simple schematic for a classical picture of the situation is shown in Figure 1 for two modes (or the two bonds) of frequency Y and u'. At a certain time interval the motion appears to be quasi-periodic with a frequency u, then there are rather abrupt irregular transition to a quasi-periodic motion a t u', etc. This corresponds to the transfer and randomization of energy between the normal modes by the anharmonicity. The time intervals at which the transitions occur are determined by the nature of the anharmonic coupling, Vah, and the quantum mechanical energy mismatch, A, between the normal mode states, which are in Fermi resonance. Theoretical calculations usually assume that somehow we start the experiment by having the energy in one mode ( u or u'). In reality this creation of specific mode excitation depends upon a number of important parameters, which we introduce here and discuss later. The time of excitation is one of these parameters that plays a significant role. The pulse width, t , of the laser source is the excitation time or the time during which the ME's can be excited. As discussed later for the problem of two coupled modes, when the laser frequency width (which is related to the pulse width) spans the eigenstates' energy spread, then some specific mode can be excited. If the time of excitation is short compared to the two characteristic times r5A-l and h I/anh-', it appears appropriate to say that one normal mode is first excited and then the energy is transferred back and forth between modes. If only two energy eigenstates are involved, the oscillation (or resonance) between the modes would occur at a frequency, (2/h)[(A2/4) Van>]1/2. If the time of excitation is longer, it may be preferable to say that a M E superposition mode is excited. The above description does not require the laser to be intense; the intensity of the laser simply determines the number of excited molecules while the pulse duration and shape determine the nature of the states excited. For a narrow-band intense laser excitation a measure for the time of excitation is the inverse Rabi frequency wR-l. Here wR = h-'lgI1El for a one photon transition with dipole matrix element Ipl and IEI is the electric field amplitude. For a where AE multiphoton transition one has wR = h-lJgJ"JEJ"hE1-n, is the energy mismatch in virtual intermediate states and n is the number of photons. Again, if wR-l is short compared to h Vanh-l, then the laser can excite the ME's in phase and specific mode excitation may be a ~ h i e v e d . ~ In reality, the energy levels are never infinitely sharp even for an isolated molecule. The natural lifetime for spontaneous
+
(7) Several groups have contributed to the theoretical studies of mode coupling in isolated systems. The work of the groups of R. Marcus, S.Rice, W. Reinhardt, E. Heller, P. Brumer, M. Shapiro, I. Percival, J. Delos, J. Jortner, D. Noid, M. Kosyzkowski, M. Berry, M. Tabor, J. Ford, and others can be found in the review article: Noid, D.W.; Koszykowski, M. L.; Marcus, R. A. Annu. Rev. Phys. Chem. 1981,32, 267. More recent work by the H. Taylor group can be found in: Hose, G.; Taylor, H. S.Chem. Phys. 1984, 84, 375. Hose, G.; Taylor, H. S.; Bai, Y . J. Chem. Phys., in press. (8) Reinhardt, W. P.; Farrelly, D. J. Phys. (Orsuy, Fr.) 1982, 43, C2-29. ( 9 ) This is analogous to the situation in magnetic resonance where a short and intense pulse can induce free induction decay. In this case the power broadening during the pulse is sufficient to drive states in phase in the rotating frame of reference.
Relaxation molecular mode frequency angular frequency energy mismatch between modes anharmonic coupling matrix element spontaneous emission decay time energy relaxation time (homogeneous) pure dephasing time (homogeneous) total dephasing time (homogeneous) total dephasing time (inhomogeneous) inhomogeneous width (or distribution) density of molecular states
v fJJ
(4 (4
A Vanh TSP
T, TZ' T, Tz*
Awinh P(W), P(E)
laser (source) pulse width coherence time coherence width pulse shape interaction Rabi frequency flip angle emission decay, r8,,must be introduced. In addition, the incident laser radiation is not exactly monochromatic or perfectly coherent. The pulse has a finite duration t, (which must be smaller than the time between collisions in a gaseous sample or the transit time of interaction in a beam experiment) and finite coherence time t,. Consequently, the frequency spectrum of the laser may not be Fourier transform limited; that is, AoL Irpl. In most practical cases of highly excited polyatomic molecules the situation is much more complicated, because the average energy spacing between vibrational states becomes quite smaIl at high excitation. It is given by the inverse of the density of states, which we denote as p ( E ) = h-'p(w). There are usually many excited states lying within energy interval nh(w - AWL)and nh(w A q ) above the initial state. Furthermore, there is a distribution over initial states in a gaseous sample at temperature T . This distribution will be more important for higher temperatures, heavier molecules, and lower frequencies of the softest modes. Often only a selected subset of initial states can take part in the excitation process. The remaining fraction q cannot reach a highly excited state and is said to be "bottlenecked." The averaging over all initially occupied rotational and vibrational states and the summation over all final states usually lead to a broad inhomogeneous distribution Acoin,, of spectrally unresolved resonances, if the excitation is high. The following array of pertinent frequencies in collisionless laser excitation of molecules can now be introduced: AWL,wR, Vanh/h, p-'(w), AWinh, and r,p-'. Table I summarizes these and other important dynamical parameters.
+
Molecular Size Effects The role of the vibrational density of states is illustrated by the remarkable difference in the multiphoton infrared dissociation process with the size of the molecule. In a diatomic molecule there is only one vibrational degree of freedom, leading to a discrete set of energy levels below the dissociation limit. Due to the anharmonicity, one can have at most one (multiphoton) resonance to a bound excited state le), for which lwcg- nwLl C AWL,rSp-l. Dissociation would consequently require a very high order multiphoton process nhwL > Edisst. The required intensities for observable dissociationloexceed lOI3 W/cm2. At these field strengths ionization and gas electric breakdown of the gas would occur first. In molecules like SF6,or more massive ones, provided Va, is large enough, the conditions p-' C AWL or AWLC p-l
