Emission from molecules and reaction ... - ACS Publications

The Journal of

Physical Chemistry

0 Copyright, 1982, by the American Chemical Society

VOLUME 86, NUMBER 26

DECEMBER 23, 1982

FEATURE ARTICLE Emission from Molecules and Reaction Intermedlates In the Process of Falling Apart H.J. Foth, J. C. Polanyl," and H. H. Tolk Depaflment of Chemlstty, Unlwmhy of Toronto, Toronto, Canada M5S 1A 1 (Recelvsd:September 2, 1982)

This paper sweys work performed to date, in a number of laboratories,on the emhion spectra of simple unstable species having lifetimes 51 ps. Transitory diatomic and triatomic entities have been formed and observed spectroscopically in the course of (1)thermal collisions, (2) photodissociation,and (3) chemical reactions. The spectra yield a novel type of clue as to the potential functions governing the molecular dynamics. This is illustrated by new calculations which treat a simple case: photodissociation of NaI (a) under normal "free-dissociation" conditions and (b) in the laser-field-trappedcondition. In the latter case we show that there exist opportunities for a novel type of "photon-catalyzed laser".

I. Introduction The early years of spectroscopy were devoted largely to the study of emission from the sun. This led to the observation of atomic lines in both emission and absorption. In view of the enormous densities and depths of emitting and absorbing species, what was termed "collisional damping" of spectral lines had been identified by the 19th century and was interpreted, notably by Lorentz,' as being the emission or absorption spectrum of atoms undergoing a collision. Since binary collisions are effectively complete in ~ 1 0 - s, l this ~ can be regarded as the modest beginning of picosecond spectroscopy. I t was picosecond spectroscopy in which differing spectral frequencies corresponded (in general) to differing times during the collision event. Heller2 has shown in an elegant fashion how readily the one type of information transposes into the other. In this paper we shall be making the case for an extension of this poor man's picosecond spectroscopy to a variety of sub(1)H.A. Lorentz, h o c . Acad. Sci. Amsterdam, 18, 154 (1915). (2) E.J. Heller, Acc. Chem. Res., 14,368 (1981). 0022-365418212086-5027$01.25/0

picosecond events of which the most important is chemical reaction. The collisions referred to in the previous paragraph are of l-ps duration, since the collision pair is not a bound species. The present article is concerned with the spectroscopy of unbound species. For simplicity of presentation it restricts itself to emission spectroscopy. Unbound species first form and then dissociate. Since they interact with light in a similar fashion in both these phases of their existence, we have further simplified our task by centering our discussion on the spectroscopy of the second phasethe process of dissociation. There is an additional reason for selecting the dissociative half of the collision as our central topic, namely, the possibility of studying the dissociative event in isolation. This requires that the unstable species, AB*,ABC*,etc. (where A, B, C each represent an atom, and the double dagger indicates that the species have sufficient energy to dissociate) be formed in an energized state. There are many ways in which this might be done. For example, Rabinowitch? Setser? and co-workers have in the past two N

0 1982 American Chemical Society

5028

Foth et al.

The Journal of Physical Chemistry, Vol. 86, No. 26, 1982

-

decades refined a method of forming energized polyatomic FAR WINGS; A * + B molecules as the product of association reactions. Left in isolation these species fall apart. McDonald's laboratory5 \asF * has succeeded in recording the feeble infrared emission from energized molecules formed in this fashion. These experiments might appear to fall under our topic A*+B of the "emission spectra of dissociating molecules". It seems useful, however, to define our topic more narrowly. We do so in the spirit of unimolecular rate t h e ~ r y . ~ The ~~?~ molecules referred to in the preceding sentences are in A + B energized states but they will not dissociate until their energy is repartitioned so as to channel sufficient mo1 1 mentum into the form of motion that leads to bond rup'AB ture, Le., until "transition states" are formed. Thereafter, Flgure 1. Schematic diagram of the emission during the collision of dissociation takes place in approximately one vibrational an electronically excited atom with a perturber. Differing relative period. It is emission in this stage that constitutes the collision energies ET result in differing limiting emission frequencies, topic here, since the underlying motivation, as already v, and up, due to the variation of the difference potential with rAB. noted, is to put into context current attempts to develop a spectroscopy of transition states in chemical reactions. which best describes the gateway to product formation, It is only in exceptional reactions that the intermediate i.e., which give the best rate constants). We shall employ is a long-lived complex, and hence the reactive event can the term here in its wider sense to denote all configurations be regarded as involving the formation of an energized through which the system passes in transition to products. adduct that subsequently forms a transition-state species Because of successes in applying spectroscopy (translacapable of yielding product^.^*^ The direct observation tional, rotational, vibrational, and electronic spectroscopy) of such long-lived complexes by spectroscopic means to the determination of energy states in chemical reagents certainly represents an important challenge related to the and products for processes such as A + BC AB + topic of this paper. It is a problem that has been addressed C,6,7J3-16there has been a burgeoning interest in the posin an ingenious fashion by Gordon and co-workers1° for sibility of developing a spectroscopy of the transitory inH-atom complexes (section 1I.B). It could advantageously termediate ABCt. Till now most of the activity has been be examined by the techniques suggested for direct entheoretical; it has been well reviewed by George17 and counters below. It involves, however, two successive proLau,18who have played a leading part in these developcesses each with its own dynamical intricacies: the inments. The current status of experimental efforts has also tramolecular energy flow that converts the energized been the subject of a recent reviewlgand will be summamolecules into transition states, and the molecular process rized in section 1I.C. by which transition states separate into reaction products. An approach that is being used in this l a b o r a t ~ r y " ~ ~ @ ~ ~ We restrict ourselves here to the problem of elucidating is the study of reactions A + BC AB + C* that yield the second enigma which is fundamental to chemical reelectronically excited product with an allowed atomic action and to many related physical conversions of chemtransition. This makes possible the observation of an ical species. emission spectrum from the transition state ABC**.11,2@23 In order to observe emission as a transition state sepaSimilar transition states AB$*and ABCt* can be formed, rates in l vibrational period to form reaction products,'l and their emission spectrum recorded, using physical, one should seek to observe (allowed) electronic transitions rather than chemical, processes-as outlined in sections since the density of emitters will, in general, be low. In 1I.A and 1I.B. the present work we shall be referring to emission from In the third section of this paper we present some new AB$* or ARC$* as it falls apart, the asterisk denoting calculations for the photodissociation of NaI (currently the electronic excitation and the double dagger indicating that subject of experiments in this laboratory) to show that both the species is a t,ransition state. In rate calculations a spontaneous and, under proper conditions, stimulated restricted family of unstable configurations AB$*or ABCt* emission should be observable during the course of disare collectively referred to as "the transition state" (for sociation. We show that this should be informative in example, Truhlar and co-workers in a recent study" have regard to the potentials, and hence the dynamics, of the compared four such families of transition states, to see dissociation into Na*(32P) and I. It should, moreover, be possible to employ field-trapped NaI(J)*as the working

, ~

1

-

-

-

(3) I. Oref and B. S. Rabinowitch, Acc. Chem. Res., 12, 166 (1979). (4) B. E. Holmes and D. W. Setser in 'Physical Chemistry of Fast Reactions", Vol. 2, I. W. M. Smith, Ed., Plenum Press, New York, 1980, Chapter 2, p 83. (5) J. G. Moehlman, J. T. Gleaves, J. W. Hudgens, and J. D. McDonald, J . Chem. Phys., 60,4790 (1974); J. G. Moehlman and J. D. McDonald, ibid., 59, 6683 (1973); J. F. Durana and J. D. McDonald, ibid., 64, 2518 (1976). (6) R. D. Levine and R. B. Bematein, 'Molecular Reaction Dynamics", Oxford University Press, New York, 1974, p 105. (7) I. W. M. Smith, 'Kinetics and Dynamics of Elementary Gas Reactions", Buttenvorths, London, 1980, p 149. (8) D. R. Herschbach, Faraday Discuss. Chem. SOC., 55, 233 (1973). (9) M. Parson, K. Shobotake, Y. T. Lee, and S. A. Rice, Faraday Discuss. Chem. SOC., 55,344 (1973); J. M. Farrar and Y. T. Lee, J. Chem. Phvs. 65. 1414 (1976). , ~ ?lOfE. B.-Gordon, B. I. Ivanov. A. P. Perminov, and V. E. Balalaev, Chem. Phys., 35, 79 (1978). (11) J. C. Polanyi, Faraday Discuss. Chem. SOC.,67, 129 (1979). (12) B. C. Garrett, D. G. Truhlar, and R. S. Grev, J.Chem. Phys., 73, 235 (1980). - I

(13) M. R. Levy, Prog. React. Kinet., 10, 1 (1979). (14) R. N. Zare and R. B. Bernstein, Phys. Today, 33, 43 (1980). (15) M. Kneba and J. Wolfrum, Annu. Reu. Phys. Chem., 31, 47 (1980). (16) R. B. Bernstein, "Chemical Dynamics via Molecular Beams and Laser Techniques", Oxford University Press, New York, 1982. (17) T. F. George, J. Phys. Chem., 86, 10 (1982), and references therein. (18) A. M. F. Lau, Adu. Chem. Phys., 50, 191 (19821, and references therein. (19) P. R. Brooks, R. F. Curl, and T. C. Maguire, Ber. Bunsenges. Phys. Chem., 86, 401 (1982). (20) P. Arrowsmith, F. E. Bartoszek, S. H. P. Bly, T. Carrington, Jr., P. E. Charters, and J. C. Polanyi, J. Chem. Phys., 73, 5895 (1980). (21) J. C. Polanyi and R. J. Wolf, J. Chem. Phys., 75, 5951 (1981). (22) T. Carrington, J. C. Polanyi, and R. J. Wolf in "Physics of Electronic and Atomic Collisions", S. Datz, Ed., North-Holland, Publishing Co., Amsterdam, 1982, p 393. (23) P. Arrowsmith, S. H. P. Bly, P. E. Charters, and J. C. Polanyi, submitted for publication in J. Chem. Phys.

The Journal of Physical Chemistry, Vol. 86, No. 26, 7982 5029

Feature Article

material for a versatile “photon-catalyzed laser”.

tribution over collision energies at temperature T

n(r) = no exp(-[U,(r) - Ultr)l/kn

11. Examples

(3)

A. Emission in the Course of Collision. As noted above, emission (or absorption) of light can occur during the 51

where no is the total density of inert gas. The term Idv/drl in the denominator of eq 2 is closely related to the term ps during which an unbound pair of atoms are in collision. that gives rise to (common-a-garden or) quantum-scatThis is illustrated schematically in Figure 1 for the case tering rainbows. In the present context if a range of inof emission: ternuclear separations all contribute radiation in the interval vto v + dv, i.e., dvldr = 0, then there will be a A” + B t AB * * ( h ~ ) (1) maximum in the intensity. Such rainbows when they The emission is indicated parenthetically since it repreappear in the far wings of collision-broadened atomic sents a minor pathway. In the case illustrated in Figure emission l i e s are termed “satellites”. Clearly their location 1 both the upper potential energy curve, UU(r),and the adds yet another definitive item to the information that lower one, Ul(r),are purely repulsive. This is an idealican be culled from the far-wing spectra and can then be zation since one can expect a shallow minimum in the exploited in order to map the potential energy of interpotentials at large r (=rm) corresponding to the van der action. Waals attraction. Gallagher’s laboratorg2has been particularly active in The two potential curves approach one another at small exploiting the possibilities of line-broadening studies as internuclear separations where strong repulsion sets in due a means to obtaining interaction potentials (see ref 33 for to substantial overlap of the charge clouds. The charge a recent review). The satellites referred to above are not clouds (loosely speaking) differ more in their outer than the only type of structure to be found in the wings. In in their inner regions; hence, the difference between UJr) addition, there may be structure due to transitions from and Ul(r)becomes less. Assuming only vertical transitions, “quasi-bound” states due to rotational barriers.% Further as in the classical Franck-Condon or “quasi-static”picture, structure can arise from quantum undulations, due to the the emission of AB$* will constitute a wing on the A* interference between contributions to the emission from (atomic line) emission toward longer wavelengths-we call two (or more) internuclear separations r, and r b for which this a “red wing”. U, - Ul is identical.35 The limit of this red wing will be sharpest if the collision The power of this method is further enhanced by the energy, ET,of A* + B is well-defined, as it is in Figure 1. fact that complementary studies can be performed in abClearly increased collision energy will shift the limit of the sorption using laser excitation wavelengths displaced to wing further to the red, as illustrated in the figure. The varying extents from the atomic line e m i ~ s i o n . ~ ~ , ~ ~ extent of the shift to the red consequent on a known inThis line of experimentation is not restricted to the crease in ETgives a direct measure of the decrease in the determination of interaction potentials between atomic potential difference U,(r) - Ul(r)for a given increase in A few years ago Gallagher’s group considered the pairs. U,(r). Ancillary information is required in order to draw contribution to the wing emission from the triatomic U J r ) on a known scale of r. Fortunately for a number of species Na*Xez and Na*Kr2.38 Variations in the wing alkali-inert gas systems atomic-beam scattering meaintensity were expressed in terms of concentrations [IG] surements are available for U,(r)(e.g., ref 24). In addition, and [IGI2. At densities above 1020cm-3 evidence for still laser spectroscopic measurements of UJr) - Ul(ro),where higher-order terms was found. A more significant watro is the (known) internuclear separation in the weakly bound van der Waals molecule, is becoming a ~ a i l a b l e . ~ ~ershed ~ ~ ~ was crossed when, in the most recent experiments,% nitrogen was employed as the perturbing collision partner. This general field of study is termed line broadening. Collisions between Na* and Nz, as has long been surFor alkali-metal atoms, M*, plus inert gas, IG, the field m i ~ e d , 3can ~ 1 result ~ in electron transfer to yield Na+N2-. has a fairly extensive h i ~ t o r y . ~ -At ~ l sufficiently large IG This change in electronic state provides an avenue for pressures the collision process becomes as probable as the quenching. This should evidence itself as a truncation of radiative one; hence, the wings become comparable in total the red wing in the region of a frequency vx corresponding intensity to the line emission. However, in modern studies to the configuration rx at which the system crosses to the designed to elucidate the nature of the binary interaction, ionic state. Wing emission experiments designed to uni.e., Uu(r),the pressure of the perturber, IG, is 1 atm or cover this new category of information are underway.33 less, and the intensity I for emission in the frequency Finally it should be noted (as mentioned in section I) interval v to v + dv at a gas temperature T can be written that other types of line-broadening experiments have alas ready been applied to collisions involving polyatomic, I(v,T)dv = N*n(r )hvA (r)(4ar2)dv / Idv / drl (2) yu

Here N* is the steady-state number density of M*, n(r) is the density of M*-IG colliding pairs at a separation r, A ( r ) is the Einstein radiative transition probability of M*-IG at the stated internuclear separation, and hv converts the photon density into an itensity in energy units. The quantity n ( r ) is determined by the Boltzmann dis(24)R. Diiren and W. Groger, Chem. Phys. Lett., 56,67 (1978). (25)J. Tellinghuisen, A. Ragone, M.-S. Kim, D. J. Auerbach, R. E. Smalley, L. Wharten, and D. H. Levi, J . Chem. Phys., 71, 1283 (1979). (26)W. P. Lapatovitch, R. Ahmad-Bitar, P. E. Moskowitz, I., Renhom, R. A. Gottscho, and D. E. Pritschard, J. Chem. Phys., 68,5419(1980). (27)A. Jablonski, Phys. Reu., 68,78 (1945). (28)S.-Y. Ch’en and M. Takeo, Reu. Mod. Phys., 29,20 (1957). (29)S.-Y. Ch’en and R. A. Wilson, Jr., Physica, 27,497 (1961). (30)J. Cooper, Reu. Mod. Phys., 39,167 (1967). Ch’en, Phys. Reu., 188,40 (1969). (31)D. E. Gilbert and S.-Y.

(32)(a) R. E. Hedges, D. L. Drummond, and A. Gallagher, Phys. Reu. A, 6,1519(1972);(b) D. L.Dnunmond and A. Gallagher, J. Chem. Phys., 60,3426(1974);(c) G. York, R. Scheps, and A.Gallagher, ibid., 63,1052 (1975). (33)A. Gallagher in “Physics of Electronic and Atomic Collisions”, S. Datz. Ed.. North-Holland. Publishine Co.. Amsterdam. 1982.D 403. (34)C.’ G. Carrington, ’D. L. Drummond, A. Gallagher, and A. V. Phelps, Chem. Phys. Lett., 22,511 (1973). (35)C. G. Carrington and A. Gallagher, Phys. Reu. A, 10,1464 (1974). (36)J. L. Carlston, A. Szoke, and M. G. Raymer, Phys. Reu. A , 15, 1029 (1977). _.__ - -,\--

(37)M. C. Castex, J. Chem. Phys., 66,3854 (1977). (38)W. P. West, P. Shuker, and A. Gallagher, J. Chem. Phys., 68,3864 (1978). (39)E.Bauer, E. R. Fisher, and F. R. Gilmore, J . Chem. Phys., 51, 4173 (1969). (40)I. V. Hertel in “The Excited State in Chemical Physics”, Vol. 2, J. W. McGowan, Ed., Wiley Interscience, New York, 1981,Chapter 4,p 341.

5030


SADIATIVE ASSOCIATION, A ~

*+0

Foth et al.

I

I

EMISSION DURING PHOTODISSOCI ATION

I

1

!

“I

U

‘AB

‘AB

Figure 2. Schematic diagram of radiative association; colliding atoms with relative kinetic energy E, are stabilized by emission of radiation at frequency Y to yield AB.

potentially reactive, collision partners. The collisions were between atomic H and such species as SOz, CO, CzH2, CzH4, etc.1° Reaction did not take place, but the collision complex re-formed H + collision partner after the lapse of W-103 ps. The interaction time was obtained from the extent of broadening of a hyperfine state of H, using an H maser. If such methods can be refined to yield the shape of the broadened line, they will represent an intriguing alternative route to the determination of interaction poten tials. Doubtless other variants on the theme of line broadening in atom-atom and atom-molecule collisions will emerge in the future. B. Emission in the Course of Dissociation. Though this paper deals primarily with the emission spectroscopy of dissociating unstable species, it would be a peculiar omission were we not to mention related converse processes. In the present section we shall be concerned with light emission from molecules undergoing photolytic rupture, i.e., photodissociation. The converse process in which light is emitted by molecules that are in the course of forming a chemical bond-termed radiative association, or photoassociation-has been a topic of many investigations over an extended period. Having said this we should add that the number of undoubted cases of radiative association that have been identified in the laboratory is small. There can be no doubt that radiative association does take place.41 For example A*

-

9

-

A3**

(---

AB)

(4)

Once again minor pathways are indicated parenthetically. This process is exemplified in Figure 2. Since AB$*exists for 51 ps, and the radiative lifetime is s for an allowed electronic transition, the collision efficiency of radiative association is SO4. Under laboratory conditions there is likely to be some doubt whether the vessel wall or a ternary collision in the gas was involved in stabilizing AB*, which then had a much longer time, and correspondingly higher probability, of radiating to yield the observed AB product and the observed emission at frequency v. The most favorable circumstances in which to look for radiative association require a very large reaction vessel and very low pressure. The upper atmosphere, and also (41) T. Carrington and D. Garvin in “Comprehensive Chemical Kinetics”, Vol. 3, C. H. Bamford and C. F. H. Tipper, Eds., Elsevier, Amsterdam, 1969, Chapter 3, p 107.

Figure 3. Schematic diagram of photodissociation. The unstable intermediate ABt’, excited by radiation at frequency vl,emits during the course of dissochtbn, elther at v2 adjacent to v 1 (transition moment diminishes as rAB increases) or at a wide range of frequencies: v2, vg, etc. (transition moment still high in the asymptotic limit).

interstellar space, meet these requirements fully. Thus, the radiative association of oxygen atoms

-

2 ~ 1 ~ ~ ) $+

**

!-

0,)

(5)

j hill

is believed to contribute to the near-infrared spectrum of the night-glow c o n t i n u ~ m .The ~ ~ ~atomic ~ ~ reagents are thought to approach along the repulsive 311ustate and to radiate to high vibrational levels of the 32; state. This could account for the high vibrational excitation of oxygen found in the thermosphere. To cite a further example the radiative association C+

iY

-

[CH+(A’njlt*

(-

CB’IX’

Xl)

(6)

( h i

may account for the presence of CH+ in interstellar space. The reverse of radiative association is simply photodissociation, the employment of light as a means to rupture a bond. By varying the wavelength of the photodissociating radiation one could develop this into an absorption spectroscopy which probes unstable species, i.e., the species formed as a result of light absorption. Our interest here is, however, in emission processes. In Figure 3 we show how emission during the course of photodissociation can constitute a spectroscopy of an unstable, photolytically formed, electronically excited species, AE

h

AB**

-

A*

+

e

(7)

(hv)

Emission during the course of photodissociation also has a history extending over a number of years. Since, however, the studies were not described in these terms, they are much less well-known than is radiative association. The process has gone under the name of “continuum resonance Raman ~ c a t t e r i n g ” . ~It~ ’is termed “resonance” (42) E. Herbst, Astrophys. J., 205, 94 (1976). (43) B. A. Murtov, Geomagn. Aeron., 14, 63 (1974). (44) W, Holzer, W. F. Murphy, and H. J. Bernstein, J . Chem. Phys., 52, 399 (1970). (45) W. Kiefer and H. J. BernsteinJ Mol. Spectrosc., 43,366 (1972). (46) D. L. Rousseau and P. F. Williams, J. Chem. Phys., 64, 3519 (1976).


Feature Article

!

RAMAN SCATTERING

(AB*) FREOUENCY IWAVENUMERSI

Figure 4. Observed spectrum of continuum resonance Raman scattering from I,. The excitation wavelength was 488 nm. Reprinted with permission from ref 46. Copyright 1976 American InstLute of Physics.

A*+ B A + B

Raman since the excitation is to a real electronically excited state; it is, however, an excitation either to an unbound electronically excited state (as in Figure 3) or to an energy above the dissociation limit in a bound electronically excited state. Both of these types of continuum resonance Raman emissions have been recorded for halogen and interhalogen molecules; the purely repulsive excited state, in this case, is a 'II, state, and the bound state is B3110+.48949 This process is called "continuum" Raman spectroscopy by the authors in view of the excitation intothe continuum; the observed emission is, however, structured, as one would expect for freebound transitions. Figure 4 exhibits part of the structure for the case of I2excited by XI = 488 nm&

'AB Flgure 5. Schematic diagram of continuum resonance Raman scattering. Excitation into the continuum of AB$' results in Raman scattering into various vibrational levels of AB, e.g., with frequencies Y:, and ug (see section 1I.B).

0

0 0

0

0

0

gSCALE

CHANGE

330

320

310

3xop, ml+

290

280

Gk

Figure 8. Observed photoemission spectrum of ozone excited at 266-nm wavelength; from ref 55.

ihU,)

The observed spectrum comes from I?* emitting from configurations adjacent to those in which this species was below); this is shown formed (as will be the case for 03** schematically as emission at v2 in Figure 3. Analysis of the spectrum for a single excitation frequency reveals numerous overtones comparable in intensity to the fundamental and the Rayleigh line. The band envelope in scattered intensity for each Au transition (Figure 4, and frequencies beyond) shows considerable vibrotational structure. This is due to the fact that excitation from any populated level in the ground state is in resonance with some continuum level in the upper electronic state. Following excitation the molecule returns to a differing quantum level (Au = 1,2, ...) in the ground electronic state. The total intensity I , in photons per molecule per second, for a transition from the ground state, Ig), to a final state, If), is given by the standard expression

1(v2) = (1/1a a n o ~ (J ;~ T)I~S,~(+I~ ,

0 0

(9)

Here P(u, J ; T ) is the relative probability of state (u,J) in a thermal distribution at temperature T (total density no);Ilis the incident laser intensity at frequency vl, and v2 is the frequency of the scattered radiation; SJ is the rotational branch intensity factor; ( ( u )is~ the polarizability tensor, containing the transition moments connecting the initial and final states, and also the extent to which the excitation frequency is displaced from a resonant frequency.2>46 The continuum resonance Raman effect has been treated theoretically by using analytic models which sep(47)D.L.Rousseau, J. M. Friedman, and P. F. Williams in 'Topics in Current Physics",Vol. 11,A. Weber, Ed., Springer-Verlag, New York, 1979. _. .., Chanter _ ~ . _ r . .6. . ~ (48)P.Baierl, W. Kiefer, P. F. Williams, and D. L. Rousseau, Chem. Phys. Lett., 50, 57 (1977). (49)J. A.Coxon, N. Gramani, and M. Jacon, J. Raman Spectrosc., 8, 63 (1979). (50)E. J. Heller in "Potential Energy Surfaces and Dynamics Calculations",D. G. W a r , Ed., Plenum Press, New York, 1981,p 103.

arate the polarizability tensor into a real part and an imaginary part (the latter describing the transition to and from the c o n t i n u ~ m ) . ~Modern ~ - ~ ~ developments in the time-dependent approach to semiclassical dynamic^^!^^ allow one to treat the problem in the time domain (propagation of a Gaussian wavepacket as a function of r(t))and arrive in the frequency domain by simple Fourier transforms; this is the approach used by Heller,2 as noted in section I. Heller's description illuminates the somewhat blurred distinction between resonance Raman scattering and (resonance) fluorescence. In the former case the excitation frequency is sufficiently removed from resonance that the upper-state lifetime is significantly less than a vibrational period (Figure 5 ) ; in the latter case excitation is at the resonance frequency and the upper-state lifetime is comparable to, or exceeds, a vibrational period (Figure 3). If the upper state is repulsive, then resonance fluorescence will be accompanied by photodissociation, but resonance Raman excitation may not provide sufficient time for the excited molecule to fragment. Another example of emission during the photodissociation of a molecule was reported very recently. The molecule under study was

(51)L.A.Nafie, P. Stein, and W. L. Peticolas, Chem. Phys. Lett., 12, 131 (1971). (52)M.Jacon, M.Berjot, and L. Bernard, Opt. Conmun., 4,117,246 (1971). (53)J. P. LaPlante and A. D. Bandrauk, J.Raman Spectrosc., 5,373 (1976). (54)E. J. Heller, J. Chem. Phys., 62, 1544 (1975). (55)D.G. Imre, J. L. Kinsey, R. W. Field, and D. H. Katayama, J. Phys. Chem., 86, 2564 (1982).

5032


The excitation of O3involved X1 = 266 nm, from a Nd:YAG laser. The emission from 02* is reproduced in Figure 6. The structure corresponds to overtones and combination bands in the symmetric stretch and eyen-numbered levels of the antisymmetric stretch of the XIAl ground state of ozone. The process could be continuum resonance Ftaman scattering. Alternatively it may be better described as fluorescence from 03** which is in the process of dissociating to yield O*(lD) + 02*(1$).Neither of these product species is an emitter (0*and 02*are metastable); consequently, the transition moment decreases as 03** begins to come apart, and the spectrum that is obtained comes from 0$* at moderately extended configurations, as compared with its original geometry when formed photolytically. The information being obtained relates (a) to the form of the upper repulsive state in this region of configurations for 0J*,i.e., near to the saddle point of the upper potential energy surface (pes), and (b) to the highest vibrational levels of the ground (bound) electronic state to which the emission takes place. The information about the upper pes is most relevant to reaction dynamics and illustrates the possibilities of the method. The upper pes appears to accord with recent ab initio computation^.^^ Our final example of emission from photolytically generated unstable species relates to the alkali halides. We are presently studying, in our laboratory, the process ;.r.

*

NOI**

i JhV2 3

-

N0*!3‘P,

+ I

(11)

5 ’1

3

The NaI absorbs h v l and dissociates directly. The distinctive characteristic of this system is that the radiative transition moment remains large throughout most of the process of dissociation, since the product has a strongly allowed radiative transition to give D-line emission, vD (where the ionic and covalent ground-state potentials for NaI cross, the transition matrix element could exhibit interesting a n o m a l i e ~ ~ ~Schematically ). this process is represented in Figure 3 by emission at v2 and v3 across the full range of rAB. Photodissociation of NaI by ultraviolet radiation (-230 nm) has been the subject of quantitative studies for over half a century. For example, Hognes and Franck5’ inferred the repulsion in the unstable intermediate NaP* from measurements of the Doppler width of the D-line emission which results from photodissociation. For work in the intervening period, particularly experiments of Herm and his group in the 1970’s, the reader is referred to two recent v01umes.~~~~~ Curiously no attempts have been made until now to observe the wing emission due to NaS* formed en route to Na*(32P).61 When one uses a Xe/Cd lamp and a monochromator as the source of UV in the 220-260-nm region and a cell with 510-ltorr of NaI, the atomic line emission measured on a double monochromator is found to be >,lo6counts/s ensuring that the wing can be observed. Since only preliminary results have been obtained (56) P. J. Hay, R. T. Pack, R. B. Walker, and E. J. Heller, J. Phys. Chem., 86, 862 (1982). (57) T. R. Hognes and J. Franck, Z.Phys., 44, 26 (1927). (58) Y. Zeiri and C. G. Balint-Kurti, to be submitted for publication. (59) H. Okabe, “Photochemistry of Small Molecules”, Wilev. New York, 1978, p 192. (60) R. S. Berry in “Alkali Halide Vapors’, P. Davidovits and D. L. McFadden, Eds., Academic Press, New York, 1979, Chapter 3. (61)H.-J. Foth, J. C. Polanyi, and H. H. Telle. to be submitted for publication.

Foth et al.

Ul

‘AB

Flgure 7. Schematic diagram of radiative trapping. High field intensity of nonresonant radiation at frequency vd resuits in a significant avoided crossing between the repulsive state and the “radiativeiy dressed” ground state. TIW trapped AB“)* emits iargeiy at the outer turning point of its vibration; hence, absorption of h v , gives substantial emission at h v2.

for the wing emission at this time, we defer discussion of the experimental findings.61 The system is, however, simple enough to be amenable to theoretical treatment; a discussion of the anticipated form of the wings and their dependence on some parameters of the system is to be found in the following section. It should be noted that photodissociation of diatomics and polyatomics to yield radiatively allowed atomic fluorescence is a fairly widespread phenomenon; 62 consequently, the application of this approach to the study of interaction potentials over a broad range of internuclear separations should be extensive. Under the conditions that we have considered till now, the emission from the transition state will be feeble. The total lifetime of NaI**,for example, is only times that of Na*(32P)(i.e., s / W 8 9). If the spectrum of the NaI** is divided into as few as 100 spectral intervals, the intensity of the wing at some wavelength X relative to the D line becomes IW(X)/I,, -lo4.” It is interesting to note, however, that this fraction can be greatly increased by the application of an intense nonresonant radiation field. We discuss this procedure in some detail in section 111. In outline this consists in “dressing” the bound potential energy curve by means of intense laser radiation at frequency vd. The effect of this radiation can be represented by picturing a new energy state displaced upward by hvd (see, e.g., ref 17 and 18);this dressed state is shown as a broken line in Figure 7. Provided that the electric field gradient associated with the dressing laser is sufficiently great to give rise to an avoided crossing (or “splitting”) between the dressed state and the repulsive state, a potential well has been created in which AB(*)*can oscillate. This energy state is shown by a horizontal line beneath the symbol AB(*)*in Figure 7. AB is transferred to this temporarily bound state by absorption of hvl and can leave this trapped state either by dissociation-i.e., by hopping to the A* + B outrun in the figure-or by radiating hv2. The intensity of the radiation is greatly enhanced since the concentration of the temporarily trapped species AB(:)*, in a restricted range of configurations, greatly exceeds that of free AB**. The “trapping” of NaIt* that we shall propose depends on an increased splitting at (what in the zero order would be) the intersection of two potential curves. In the present example one of these two curves is a “dressed“ potential. The suggestion that trapping of this sort can take place

-

(62) P. Pringsheim, “Fluorescenceand Phosphorescence“,Interscience, New York, 1949, p 208.


Feature Article

'I

TRANSlTiON STATE EMISSION AtBC-+

ABC*

I

*

+AB+Cx

~

I

SEACTN PROPS. SEPARATE

-

5700

Flgure 8. Schematic diagram of emission from the transition state in a chemical reaction. Emission from the intermediate ABCt' during separation to products results In "wings" on the atomic transition (hu,); h v, exemplifies a transition in the red wing, and h v 2 a transition in the blue wing.

is derived from discussions of predissociation in intense fields to be found in the work of Lau and Rhodess3 and of George and c o - w o r k e r ~ .WeineP ~ ~ ~ ~ has applied this principle in a different context, one where no dressed states are considered. He computed the effect of intense laser fields on the relative probability that a (bound) groundstate alkali halide MX decomposed along one potential curve to ions, M+ + X-, or switched to the alternate curve leading to neutral M + X. In section I11 we shall be concerned with the effect of an intense laser field on the probability that an (unbound) electronically excited state MX** is held captive in a dressed potential curve. The phenomena are different, but each depends on increased splitting between potential curves. It is understandable therefore that the laser intensity calculated to be necessary for a significant effect ( 10'" W/cm2) is similar in the two instances. C. Emission in the Course of Reaction. In section ILA the species ABC**was formed in a nonreactive collision A* + BC and in section 1I.B by photolysis of ABC. Here we consider the possibility that ABC**can be formed in the c o m e of a chemical reaction, en route to the formation of electronically excited product. We select a case in which the electronically excited product is an atom with an allowed radiative transition to the ground (or some lower) state. Then the atomic chemiluminescence should be accompanied by a feeble luminescence from transition states ABCT* N

A t

ac

-

ABC**

I

-

AB t

c*

(12)

I

Here uc is the frequency of the atomic line emission, and Y represents a broad range of frequencies corresponding to the range of configurations for the transition state. It is instructive to consider in what way this process, pictured schematically in Figure 8, differs from the collision-induced line broadening discussed in section 1I.A. The obvious difference is that AB + C* does not approach to form ABC**;we deal only with the retreat of AB from C*. The less obvious, but even more important, difference (63) A. M. F.Lau and C. K . Rhodes, Phys. Reu. A, 16, 2392 (1977). (64) P. L. de Vries, M. S. Mahlab, and T. F. George, Phys. Reu. A, 17, 546 (1978). (65) J.-M. Yuan and T. F. George, J. Chem. Phys., 70, 990 (1979). (66) J. Weiner, Chem. Phys. Lett., 76, 241 (1980).

- -

5900

5800

6000

x GI-+

6100

+

Figure 9, Observed wings of the sodium D line in the reaction F Na, FNaNat" NaF Na'. Experiments under a variety of conditions; from ref 20 and 23.

+

is that ABC** separates from a selection of configurations which is governed not by the favored angles of approach for a collision AB + C* but by the favored mode of approach of A to BC, Le., by reaction dynamics. This approach to the study of reaction dynamics has been a p p l i e d " ~ ~to~ the , ~ ~following reaction, studied in crossed uncollimated beams of reagents at a reagent pressure of -lo+ torr; F t NG,

-

FNcING**

-

NaF

+

Na*(3'P)

t

t

(hv)

hv,

(13)

The frequency vD is that of the D line. The D line exhibits wings extending over several hundred angstroms. The results of a number of experiments on this system, performed in this laboratory, are collected in Figure 9. Kinetic studies confirm that the wings arise from FNaNA**, en route to NaF Na*. The wing intensity at a given wavelength (spectral resolution 8.5 A) can be seen from Figure 9 to be -lo* times the D-line intensity. This is approximately the same ratio IW(A)/IDquoted above for emission from NaI** transition states formed photolytically. Wings of somewhat different shape and intensity have been recorded in preliminary experiments performed here on 0 Naz NaO Na* and C1+ Naz NaCl + Na*.67 For none of these systems does the transition-state spectrum, at the present time, have adequate signal to noise to reveal structure. Preliminary theoretical studies21p22 link such factors as the total integrated intensity of the wings, the breadth and spectral distribution of the wings, and the (yet to be observed) structure in the wings to dynamical variables, such as the time that ABC**spends in traveling along the exit valley of the pes, the extent to which ABCt* is initially compressed, the bending in ABC** at enhanced reagent collision energy, and the configurations in which ABCt* is most likely to ricochet from one side of the pes exit valley to the other-i.e., the preferred phase of vibration of AB as it retreats to successive distances from C*. The calculations that illustrate these causal links involve running batches of about 1000 three-dimensional classical trajectories (Monte Carlo selected for some experimentally plausible reagent conditions) across a pes which serves as a model for the upper of the optically linked energy surfaces (see Figure 8 for a schematic one-dimensional cut through the exit valley). The transition state ABC**sig-

+

+

-

+

-

(67)S. H. P. Bly, Ph.D. Thesis, University of Toronto, Toronto, Canada, 1982.

SO34


nals its presence and the time it spends at successive configurations by emitting radiation of corresponding frequency (such as v l and v2 in Figure 8) and intensity.21i22 It hardly needs to be said that, in view of the multidimensionality of the problem, there is no way of inverting the experimental findings (even at such time as they will reveal structure) in order to obtain two optically linked pes unambiguously; the upper pes on which the dynamics unfolds, and the lower to which radiative transfer occurs. Regrettably much the same can be said of the other tools in the reaction dynamicist's kit. Invariably it is necessary to proceed a posteriori, Le., to see whether the clues that we have regarding the reaction dynamics are consistent with postulated models. In the past two decades these clues have come to include a considerable variety of indicators of molecular motions in reagents and in products. The time seems to be at hand when we can begin to add some further clues coming in this instance from the most interesting part of the reactive event-the transition region. We have spoken so far of emission from ABCt* as it comes apart to yield AB C*, i.e., as it moves along the exit valley of the pes. This restriction is not a necessary one.22 Wings on the atomic line (for example, the sodium D line) will be observed as A* approaches BC, where A* and BC are en route to form products such as AI3 + C, AB -tC*, or AB* C. This type of experiment would yield information regarding the motion along the entrance valley of the pes. An example would be provided by the study of the photodissociation of NaI, to yield Na*(32P) of selected translational energy, in the presence of excess HX (X 5 F, C1, ...). The work of Gallagher and co-workers on Na*(32P) N2 2 Na+N2-represents a first stage along this route. It should be remarked that intensity is not the only spectroscopic parameter that one might obtain from the transition-state "wing emission". If phase and polarization can be characterized for the atomic species, either as reagents encounter one another (A* + BC ABCt* products) or as products separate (reagents ABC** AB + C*), then the transition-state dynamics could be further elucidated by recording these quantities. The most readily accessible attribute of the wing emission (apart from intensity) should be its polarization, with respect to the polarization of the reagent A* electronic angular momentum, or with respect to the direction of motion of A* in the laboratory. Zare and co-workers have obtained evidence of the importance of the alignment of the p orbital in an atomic reagent, on the reaction dynamic^.^^,^^ They have also exploited chemiluminescence polarization to determine the plane of rotation of new-born reaction produ~ts.'~*~' A favorable case for a comparable study of transition-state emission would appear to be that alluded to above; Na*(3P) with kn_ownp-orbital polarization and known velocity vector, i.e., Na*, would be formed by photodissociation using polarized light, in the presence of excess hydrogen halide. The polarization of the wing emission arising from NaXH** would furnish information regarding the rotation of the plane of NaXH** as the reagents approached. (Despite the random orientation of HX, it is reasonable to expectgreferred planes for the consecutive configurations as Na* approaches HX.)

+

+

+

-- --

(68) C. T. Rettner and R. N. Zare, J. Chem. Phys., 75, 3636 (1981). (69) C. T. Retter and R. N. Zare, to be submitted for publication. (70) M. G. Prisant, C. T. Rettner, and R. N. Zare, J.Chem. Phys., 75, 2222 (1981). (71) M. G. Prisant, C. T. Rettner, and R. N. Zare, to be submitted for publication.

Foth et

al.

The enormous successes of laser spectroscopy (we cite three of particular interest to chemists seeking to detect trace ~ p e c i e s ~leave ~ - ~ ~no) doubt that the emission spectroscopy of reactive transition states will ultimately be supplemented or supplanted by absorption spectroscopy. Both approaches will yield data that require for their interpretation some knowledge of an upper and a lower pes. Absorption studies, since they explore the dynamics of normal ground-state reactions, will have a wide range of interest and app1icability.l' Our reason for favoring emission spectroscopy as a means to obtaining spectra of ABC**was (and is) the fact that structural features will be broad for these short-lived species (0.1 ps implies -102-cm-' line width); consequently, the intrinsically high resolution of lasers is not, in general, required. One can, therefore, profit by the fact that lowresolution emission spectroscopy measures concurrently all the photons within a selected (wide) spectral bandwidth. It is, of course, regrettable (if one may deplore physical laws) that systems in a state of flux yield only broad spectral features-in emission or absorption. However, spectroscopists whose interest is in the condensed phase have learned a great deal about liquids and solids despite the fact that they are restricted to examining the location and the breadth of rather poorly defined features. Early attempts to study transition states in absorption have been reviewed recently by Brooks and co-workers.lg Preliminary evidence for transition-state absorption at X = 606 nm was reported in a crossed molecular beam study of the reaction K + HgBrz KBr* HgBr,75but later work, designed to move from single-wavelengthabsorption to a spectroscopic study, has so far failed to confirm this.lg Meanwhile, Grieneisen, Xue-Jing and K ~ m p obtained a~~ evidence of transition-state absorption at X = 158 nm (XeF laser) under bulb conditions in the reaction Xe Clz XeC1* C1, as proposed earlier by Dobov et al.77 The wavelength of an ArF laser (193.3 nm) is thought to be too long to provide the endoergicity of the Xe + Cl2reaction, Le., to excite the transition state XeClJ to XeC12**that leads to XeCl* + C1; accordingly no XeCl* fluorescence was observed with this source of irradiation in the work of Grieneisen et al. However, a concurrent study of the same system in another laboratory yielded XeCl from ArF (193.3 nm) irradiation, indicative, instead, of a two-step process: Xe + C1, + hv [XeC12]*followed by [XeCl,]* + M XeC1* + C1 + M.78 Some further work will be required to establish whether or not a reactive transition state XeClzt is absorbing radiation.lg The prospects for success in absorption studies are particularly good if the absorption in the transition states ABC*or ABC**is induced as the reagents approach at long range, or as the products separate to substantial dist a n c e ~ . In ~ ~these regions the upper and the lower potential curves have moderate slopes; hence, Idv/drl is small (cf. eq 2) and the system spends a maximum time in resonance with the incident radiation. A similar factor ex-

-

+

+

-

+

-

-

(72) R. N. Zare and P. J. Dagdigian, Science, 185, 739 (1974). (73) W. M. Fairbank, Jr., T. W. Hansch, and A. L. Schawlow, J . Opt. Soc. Am., 65, 199 (1975). (74) G. S. Hurst, M. H. Nayfeh, and J. P. Young, Appl. Phys. Lett., 30, 229 (1977). (75) P. Hering, P. R. Brooks, R. F. Curl, Jr., R. S. Judson, and R. S. Lowe, Phys. Rev. Lett., 44, 687 (1980). (76) H. P. Grieneisen, H. Xue-Jing, and K. L. Kompa, Chem. Phys. Lett., 82, 421 (1981). (77) V. S. Dobov, L. I. Gudzenko, L. V. Gurvich, and S. I. Yakovlenko, Chem. Phys. Lett., 45, 330 (1977). (78) B. E. Wilcomb and R. E. Burnham, J . Chem. Phys., 74, 6784 (1981). (79) J. C. Light and A. Altenberger-Siczek, J. Chem. Phys., 70, 4108 (1979).

The Journal of Physical Chemlstry, Vol. 86, No. 26, 1982 5035

Feature Article

plains the higher intensity in the AI3Cl* emission spectrum at wavelengths adjacent to the atomic line (Figure 9). When absorption or emission of a reactive transition state is observed, the problem of interpretation is greatly simplified if the slope of one pes is negligible in some region of ~onfigurations,2~ or if one of the pair of pes is known. The latter situation would apply in spectroscopy of the transition state of the celebrated reaction D + H2 DH + H. The ground pes for H, has been computed to a high level of precision.@' Laser spectroscopy of DHJ reacting across the lower pes would trace out the first excited pes along the D + H2 DH H (ground state) reactive pathway. Such an experimen; is now in reach since translationally excited atomic D can be formed in high concentration under bulb conditions by excimer photolysis of DI, DBr, or D2S?1982 Tunable vacuum-UV lasers in the region of the Lyman-a line for atomic D are also available.s3*s4 If, therefore, DX were photolyzed in the presence of excess H2 and a tunable vacuum-UV laser were used to probe the wing absorption due to D-H2 collisions (absorption being evidenced by D*Lyman-a fluorescence if the reagents re-form, or by H* Lyman-a fluorescence if products are formed), a spectroscopy of DHH* would result. The vacuum-UV transition-state spectrum could be taken some nanoseconds after the photodisjociation laser pulse generated the translationally "hot" D; hence, only the initial D + H2 collision need be sampled at total pressures up to -10 torr. The anticipated spectrum can readily be computed from ab initio data;@ the actual spectrum will provide a test of the quality of that ab initio data.

-

-

+

111. Spontaneous and Stimulated Emission from Photodissociating NaI In this section we shall consider in some detail the links

between the potentials and the spectra for the (to a reaction dynamicist) simple example of NaI, in which only one internuclear distance need be considered. A. Free Nalt*. As noted in section ILB, we are presently engaged in an experimental study of the wing emission originating from NaI** in the process of falling apart.61 Enough is known about the spectroscopy of NaI to allow one to make rough predictions in regard to the intensity, spectral range, and principle features of this transition-state emission. A . l . Potential Energy Curves. The ground-state potential of the alkali halide molecules can be described to a good approximation by the ionic model M+X-, especially in the neighborhood of the equilibrium separation. The interactions between the two charged particles is usually expressed in terms of a multipole expansion for the electromagnetic forces. In the diabatic picture the corresponding potential is, in general, described by the Rittner models8

Vi,, = -e2/r - (1/2)e2(a1+ a&/+ - 2e2ala2/r7CG/T6 + A exp(-r/p) + AE (14) (80)P. Siegbahn and B. Liu, J. Chem. Phys., 68, 2457 (1978). (81)C. R. Quick, Jr., R. E.Weston, Jr., and G. W. Flynn, Chem. Phys. Lett., 83, 15 (1981). (82)F. Magnotta, D. J. Nesbitt, and S. R. Leone, Chem. Phys. Lett., 83, 21 (1981). (83)R. Schmiedl, H. Dugan, W. Meier, and K. H. Welge, 'Laser Doppler Spectroscopy of Atomic Hydrogen in the Photodissociation of HI", Festschrift Phys. A , special issue (1982). (84) R. W. Dreyfus, P. Bogen, and H. Langer, Int. Quantum Electron. Conf., Ilth, Appl. Phys. B, 28, 292 (1982). (85)H. R. Mayne, R. Poirier, and J. C. Polanyi, to be submitted for publication. (86)E. S. Rittner, J. Chem. Phys., 19,1030 (1951).

Na(3p) t

I

4-

-t -

3Na't

I

5 d 2% 3

I-

Na(3s)t I

2-

I-

2

3

4

5

6

7

8

9

Flgure 10. Potentlals of NaI. The ground-state NaI(X) is calculated from the lonlc Rlttner model and the excited-state potential represents a 6-12 LennardJones potential fitted to the data (full circles) of ref 90. The crossing between the lonlc and covalent curves is marked r x . Photodissociation at frequency v resuits in products Na' 4- I with relative kinetic energy E,. A nonresonant radiation field (frequency vd) shifts the adiabatic potential by the energy h vd (indicated by the dashed line).

where r and e denote the internuclear separation and the electric charge of the particles, respectively. The first term describes the Coulomb attraction, the second and third terms give the ion-induced dipole interactions, and the following terms stand for the long-range van der Waals attraction and the short-range repulsive forces. The ionization limit is given by AE = I - EA (Iis the first ionization energy of the metal atom; EA is the electron affinity of the halogen atom). Since the term proportional to r-7 results from higher-order perturbation theory, whereas all other contributions stem from second-order effects,87a truncated form of the Rittner potential which omits this term is frequently used. We have, however, retained this term. In the adiabatic picture (as in normal thermal dissociation) the molecule separates into neutral atoms. This means that a transition must take place from the ionic to a covalent curve at the crossing radius rx, as shown in Figure 10. Covalent interaction between a pair of atoms is often described by a simple two-parameter LennardJones potential

V,,, = A'/r2 - B'/r6

+ AE

(15)

where AE now stands for the energy of the neutral atoms at infinite separation. To complete the required adiabatic representation one has to combine the potentials 14 and 15 through a coupling potential. In the region of the crossing the interaction between the two curves can be reasonably well approximated by an exponential representations8

VI, = A" exp(-r/p")

(16)

where A" and p" are constants. At rx in Figure 10 the splitting between the covalent and ionic states is 2V1,.89 (87)P. Brumer and M. Karplus, J. Chem. Phys., 58, 3903 (1973). (88)M. B. Faist and R. D. Levine, J. Chem. Phys., 64,2953 (1976). (89)R. Grice and D. R. Herschbach, Mol. Phys., 27, 159 (1974).

5036

The Journal of Physical Chemistty, Vol. 86, No. 26, 1982

This coupling term is not valid over the entire range of internuclear separations; we have corrected for this. For the construction of the relevant potentials of NaI we have chosen forms for the ionic and covalent potentials of the ground state which resemble eq 14 and 15 but represent the repulsive slopes somewhat better at small internuclear separations; details can be found in ref 88. The numerical values of the constants were taken from the same reference. The adiabatic representation of the ground-state potential was obtained from a fit of the ionic curve and the coupling potential to a calculated RKR potential. In this way a pseudopotential Vlz for the coupling was obtained, which was fixed to an overall exponential behavior at the crossing (eq 16) with the correct Landau-Zener splitting, VI2;the numerical value for the splitting was taken from ref 89. For the upper potential the experimental data of Davidovits and Brodheadgo were fitted to a simple 12-6 Lennard-Jones potential. It should be pointed out that the choice of the constants for the electronically excited state is in doubt; experimental data measured by different authors differ by some 1000 wave number^.^^^ The potentials used in our model calculations are shown in Figure 10. A.2. Excitation Process. Earlier experiments measuring the photodissociation of NaI have shown that absorptionw or emission from the final Na*93-95can be observed over a wide range of excitation wavelengths. This is mainly due to the fact that in the usual vapor-cell experiments many vibrational and rotational levels are thermally populated, all of which contribute to the transition to the repulsive upper state. Moreover, even in a simple Franck-Condon approximation, the overlap between discrete levels in the bound ground state and the continuum state distribution in the upper state is significant for many transitions. The width of the energy distribution in the upper state due to the absorption of radiation is determined by the line width of the excitation source. If one assumes that only a single level is populated in the ground state, a narrow-band laser would result in a very narrow kinetic energy for the dissociating NaIi* in the upper electronic state, whereas broad-band excitation with a continuum source produces a wider distribution of kinetic energies for the dissociating molecule. In initial experiments currently being performed we use a continuum source (Xe/Cd lamp) whose output is filtered by a small monochromator.61 Let us assume for purposes of calculation that the NaI vapor is present only in a single initial vibrational-rotational state and that the dissociating radiation at frequency v has a narrow spectral distribution (i.e., a tunable W laser as proposed for a later stage of experimentation). Then the kinetic energy of the dissociating molecule is nearly 6 shaped, and consequently the recoil velocity uK of the Na* relative to the center of mass of NaI is also well described by a 6 function. Numerical values can be obtained from conservation of energy and momentum mNaUK2/2

= EK= (ml/”NeI)t

(17)

where mNa, ml, and mNaI represent the masses of the (90) P. Davidovits and D. C. Brodhead, J. Chem. Phys., 46, 2968 (1967). (91) H. Levi, Doctoral Dissertation, Humboldt University, Berlin, Germany, 1934. (92) R. F. Barrow and A. D. C a n t , R o c . R. SOC.London, Ser. A , 219, 120 (1953). (93) H. G. Hanson, J . Chem. Phys., 23, 1391 (1955). (94) B. L. Earl, R. R. Herm, S.-M. Lin, and C. A. Mims, J. Chem. Phys., 56,867 (1972). (95) B. L. Earl and R. R. Herm, J. Chem. Phys., 60, 4568 (1974).

Foth et al.

subscripted atoms and molecules, and uK is the velocity corresponding to the kinetic energy EK. The energy t available for distribution between the separating atoms is obtained from the energy balance in the excitation process e =

hv

+ E(u”,J‘? - D e -

E(Na*)

(18)

The symbols De and E(Na*) denote the dissociation energy of the ground state of NaI and the electronic energy of the excited Na atom. In general, however, the initial states have a thermal velocity distribution, and the kinetic energy of dissociation mirrors that distribution (see, e.g., ref 94 and 96). For the sake of simplicity in the calculations, since we initially only want to trace the influence of the change in kinetic energy, we assume a simple 6 function rather than a more realistic distribution. The population density of NaIi* at one specific energy of the repulsive state will be normalized to unity. The velocity extracted from eq 17 is of importance for a rough estimate of the total emission during the separation of the particles, as compared to the intensity in the atomic transition of the products. The velocity distribution can also be used to determine the time the system spends at a certain internuclear separation, and hence the intensity of the emission from that configuration during the dissociation process. In the case under consideration the emission at a separation of 10 A is already in the Lorentz core of the Na D line, Le., within the natural line width. The time needed to reach this point on the potential is approximately 2.0 ps for a kinetic energy of 100 cm-’ (-0.3 kcal/mol) and 0.5 ps for 2000 cm-’ (-6 kcal/mol); this corresponds to a total intensity in the wing of roughly 1.2 X and 3 X of the D-line intensity, respectively. This already gives an idea of the requirements in terms of spectral sensitivity for an experiment designed to detect the wing emission during photodissociation. Wavelength-selectiveobservation in 100 spectral intervals would have to detect intensities on the order of 10-6-10-7 of the D-line intensity. A.3. Emission from Dissociating Nag*. A calculation of the expected emission in the wings can only be as good as our knowledge of the potentials, the energy spacing, and the electronic transition moment. The potential of the upper state of NaI has not yet been characterized out to large internuclear separations, nor is the vibrational structure available for high energies in the ground state. Little information exists regarding the electronic transition moment between the two states; only the transition dipole moment for the atomic transition Na(2P is known. Consequently we shall not attempt a fully detailed modeling of the wing spectrum at this stage. Our objective is to arrive at an understanding of the elements of the problem and to give an approximate value for the expected intensities. In principle, the dipole moment function D ( r ) can be obtained from the conventional definition of the oscillator ~ t r e n g t h ~but, ’ , ~ ~to our knowledge, no attempt has been

-

(96) J. R. Barker, R. E. Weston, Jr., J. Chem. Phys., 65, 1427 (1976). (97) R. W. Nicholls and A. L. Stewart in ”Atomic and Molecular Processes”, D. R. Bates, Ed., Academic Press, New York, 1962, p 47. (98) J. P. Woerdman, J. Chem. Phys., 75, 5577 (1981). (99) For example, in Na2(A-X); see, e.g., L. K. Lam, A. Gallagher, and M. M. Hessel, J . Chem. Phys., 66, 3550 (1977). (100) A. M. F. Lau and C. K. Rhodes, Phys. Rev. A , 15, 1570 (1977). (101)J.-M. Yuan and T. F. George, J. Chem. Phys., 68,3040 (1978). (102) A. M. F. Lau, Phys. Rev. A , 16, 1535 (1977), and references therein. (103) J.-M. Yuan, J. R. Laing, and T. F. George, J. Chem. Phys., 66, 1107 (1977), and references therein. (104) K. P. Huber and G. Herzberg, ‘Molecular Spectra and Molecular Structure”, Vol. IV, Van Nostrand, New York, 1979. (105) H. H. Telle and U. Telle, Comput. Phys. Commun., in press.

The Journal of Physical Chemistry, Voi. 86, No. 26, 1982 5037

Feature Article

I 3

m

I

I

I

I

-5

-51

% I

50cm-’

I

,

I

>

1900L

L

L

1

200

300

1

1

400

500

A

600

200

made so far to apply this to the case of bound-free transitions in NaI. To obtain a sufficiently realistic transition moment function for our calculation, we have constructed a function which is equal to the transition moment for the D line at large internuclear separations ( r > rx in Figure 10) and decreases linearly from r = rx to half the asymptotic value at the equilibrium separation of the ground state. The decrease to half the D-line value was selected since the transition probability at equilibrium separation for many diatomics that dissociate to give strongly allowed atomic emission is approximately a half of that for the excited atom.58J25J26 The emission during the separation of the N d * complex was calculated for a set of internuclear separation intervals [ri,ri+J. The time that the system spends in each interval of separation was given by

300

400

500

600

WAVELENGTH [nm]

WAVELENGTH [nm]

Flgure 11. Computed wing emission Intensity from unstable NaIt’ relative to the D line. The potentials used in the calculations were those in Figure 10, with a well depth of 850 cm-I in the upper state potential. Kinetic energy ET of the dissociating molecule: (a) 35, (b) 350, (c) 1200, and (d) 3500 cm-’. (Note: photodissociation by X = 235 nm gives E, = 312 cm-’, and 1 = 220 nm gives ET = 3127 cm-’.) I n reality the wings will exhiblt structure, since the emission takes place to a bound state. L symbolizes the Lorentz wing of the Na D line.

A

I

Flgure 12. Computed wing emission intensity from NaIt’ (cf. Figure 11). The kinetic energy of the dissociating molecule was 3500 cm-’. The well depth in the upper-state potential was varied: (-) 50, (- - -) 900,(- -) 2100, and (-) 5200 cm-’. L symbolizes the Lorentz wing of the Na D line.

-

Well depth, DL

50 cm-‘ -__ 900 2100

4400

Flgure 13. Energy differences between the upper and lower states for the potentials used to generate the wing shown in Figure 12.

where um is the average velocity between ui at ri and ui+l at uiand ui+l being obtained from the kinetic energies (106) L. W. Grossman, G . S. Hurst, M. G. Payne, and S. L. Allman, Chem. Phys. Lett., 50, 70 (1977). (107) J. C. White. ADDLPhvs. Lett.. 33. 325 (1978). (108j R.Burnha&, &pl. Piys. Lett., 30, 132‘(1977). (109) P.Burkhtud, W. Lathy, and T. Gerber, Opt. Lett., 5,522 (1980). (110) A. Owyoung, IEEE J. Quantum Electron., QE-14, 192 (1978). (111) S. R. Nestor. J . Chem. Phvs.. 69. 778 (1978). (112) W. R. Bennett, Appl. Opt: Sup&, 1, 24 (1962). (113) J. P. Girardeau-Montautand G. Moreau, Appl. Phys. Lett., 36, 509 (1980). (114) See, e.g., H. Welling and B. Wellegehausen in “Laser Spectroscopy 111”, Springer-Verlag, New York, 1977, p 365. (115) E. J. Schimitschek, Laser Focus, 18, no. 1, 53 (1982). (116) H. Egger, H. Pummer, and C. K. Rhodes, Laser Focus, 18, no. 6, 59 (1982). (117) K. L. Hohla, Laser Focus, 18, no. 6, 67 (1982). (118) H. P. Kortz. Laser Focus. 18. no. 7. 57 (1982). (119) A. E. Siegman, “An Introduction to ‘Lasers and Masers”, McGraw-Hill, New York, 1971. (120) P . J. Kuntz, M. H. Mok, and J. C. Polanyi, J. Chem. Phys., 50, 4623 (1969). (121) J. C. Polanyi and J. C. Schreiber in ‘Physical Chemistry, an Advanced Treatise”, Vol. VIA, W. Jost, Ed., Academic Press, New York, 1974, Chapter 6, p 383. (122) P. 3. Kuntz in ”Modern Theoretical Chemistry” Vol. 2, Part 3, W.H. Miller, Ed., Plenum Press, New York, 1976, Chapter 2, p 53. 55,233 (1973). (123) D. R. Herschbach,Faraday Discuss. Chem. SOC., (124) R. M. Harris, Ph.D. Thesis, Harvard University, Cambridge, MA -. __ -, 1971) - - . -. (125) W. J. Stevens, M. M. Hessel, P. J. Bertoncini, and A. C. Wahl, J. Chem. Phys., 66, 1477 (1977). (126) H. Kat0 and C. Noda, J. Chem. Phys., 73,4940 (1980).

at the corresponding points. The fraction of emission into a given wavelength interval, according to the FranckCondon principle (i.e,, assuming vertical transitions), was accumulated for all intervals ri to r,+l. It should be stressed that the spectral emissions shown in the figures (see below) are smoothed spectra, since vibrational structure in the ground state has been omitted. In actual fact one would obtain structure, due to the vibrational-rotational spacing in the ground state and the corresponding free-bound Franck-Condon overlap integrals. Figure 11shows the relative intensity in the wings for some chosen kinetic energies. The spectral width for individual data points in the plot was chosen according to the resolution normally employed in our detection system, namely, 10 It is clear from Figure 11that excitation to energies only slightly above the Na* + I limit give the highest spectral intensity but that the interesting part of the potential around the minimum in the upper state is better probed by higher excitation energies which give less intensity but greater changes in the very-far wing, i.e., 220-250 nm (see also the difference potential in Figure 13). A compromise for a best signal-to-noise ratio and information content has to be made. The well in the potential is mirrored by a minimum in the emission (at 225 nm in Figure l l ) , since the time the molecule spends in the corresponding configuration is also minimal as a result of acceleration in “rolling” into the well.

-

5030


To test the influence of the well on the emission intensity we have varied the well depth and position in a systematic manner; the results are shown in Figure 12 for some well depths close to the experimentally measured value, as well as for an “extreme” well depth which results in a minimum in the difference potential, U(NaI*) - U(NaI) (see Figure 13), and therefore in a satellite in the emission (the maximum in the dotted line in Figure 12). Satellites have been observed in line broadening due to this cause,32and also in bound-bound molecular transitions, e.g., ref 99. The two figures, 11 and 12, clearly demonstrate that from very-far-wing spectra obtained in the photodissociation of molecules one should be able to extract the complete potential of a dissociative state up to the point of excitation, although in practice the procedure can be arduous as, in general, the distribution in the kinetic energy is not a 6 function as assumed in these model calculations. Experiments underway in our laboratory are providing data for a test of this procedure. In addition, vibrational structure in the wing spectra should give information regarding the level spacing in the ground state of NaI up to (close to) the dissociation limit. A similar approach has been demonstrated successfully for continuum resonance Raman scattering in and also, very recently, for laser-induced fluorescence of dissociating as noted in the previous section. B. Field-Trapped NaI(*)*. In this section we examine, in some detail, the feasibility of “trapping” the unstable NaI**in the electric field of an intense nonresonant laser. The principle is not new,looJolbut examples have until now been lacking. The case of NaI**seems well adapted to a demonstration of this principle. I t has become evident in recent years that molecular properties can be modified drastically by interaction with the strong electromagnetic fields associated with highpowered lasers. Such molecules are termed “radiatively dressed”. The whole field of “dressed states”, in which theory still predominates but experiments are beginning to appear, has been surveyed in a recent feature article in this journal.” Applications to field-induced effects in molecular dissociation and predissociation have been discussed; new channels to dissociation can be opened that were previously closed, and vice versa. The way this comes about is that the electric field interacts differently with various electronic states, thereby (in general) increasing the splitting where field-free states approach each other. We shall illustrate how this affects the dynamics for the case of NaI**. A noteworthy aspect of field-induced processes is that they may be achieved at no expense of photon energy, since no actual absorption or emission of a photon need be involved; the laser that dresses the state is in this case nonresonant with any electronic transition. B.l. Potentials and Wave Functions. The ground-state potential in its adiabatic representation is the same as described earlier. Again we use the experimental data of DavidovitsgOto fit the potential for the upper electronic state. To provide the dressing radiation we have chosen a frequency-doubled Nd:YAG laser whose wavelength, Ad = 532 nm, is well off resonance with Na* + I. In the very weak field limit the new dressed state, i.e., the ground-state potential displaced upward by the dressing radiation energy, hvd, crosses the excited NaI state as illustrated in Figure 10. When the laser field is strong, the adiabatic potential of the field-dressed molecule shows a significant avoided crossing around the resonance point (the diabatic potentials are represented by the dashed lines in Figure 17*639102

Foth et al.

4 4651)

! I

d

Q I

3

4

5

6

7 ~

8

9

1

0

01

r !A,-

Flgure 14. Adiabatic potentials for NaI. “Dressing” energy hvd originates from the radiation of a Nd:YAG laser (532 nm), with power density of 3 X 10“ W/cm2. Experimental data points (full circles) from ref 90. Excitation of the P(51) rotational transition from v” = 2 to v’ = 15 (the latter is the second vibrational level above the Na’(3*P) I limit).

+

14). The excited-state potentials in Figure 14 can be written in the general formlo3

Wi,z = ‘/(Hi1 + H z z

* [ W z z - HiJ2 + 4di&zi11”)

(20)

where Hll and Hzz are the field-free “diabatic” surface which are coupled through d12 and dzl. It should be pointed out that Hll here represents the adiabatic ground-state potential shifted by the energy of the dressing radiation. The strength of the interaction between the molecular system and the laser field is17 dij = c(ilD(r)k) (21) where t is the field strength and D(r) is the dipole operator between the electronic levels i and j . The potentials shown in Figure 14 are for a dipole moment of approximately 7 D and a laser field strength of 3 X 1O’O W/cm2. The influence of field strengths on the Landau-Zener splitting, 2d,, and on the shape of the adiabatic potentials, as well as the wave functions in the quasi-bound potential for Na* + I + hvd, will be discussed below. Excitation of the molecule to energies somewhat higher than the dissociation limit, Na* I, now no longer leads to a continuum state but rather to a discrete vibrational-rotational level, for the time that the “dressing” field is applied. The known spectroscopic constants for ground-state NaI(X)lWwere used to construct a RKR potential for low vibrational states. Wave functions for the ground and electronically excited states were obtained from a numerical integration of the Schrodinger equation.lo5 For the upper state the adiabatic potential (solid line in Figure 14) W z from eq 20 was used for the solution of the Schrodinger equation. As pointed out earlier, the experimental data for the upper stateg0are uncertain. In addition, the Na* + I energy (i.e., the NaI bond energy) is not known very precisely. As a consequence the potential W zis approximate. Nevertheless, it serves as a reasonable potential for the calculation of the excited-state wave functions needed to investigate the emission spectra from the radiation-trapped molecule. The low vibrational states in the van der Waals well of the upper state (see Figure 14) are basically determined by the diabatic Lennard-Jones potential. Only close to the diabatic dissociation limit does

+

Feature Article


TABLE I : Diabatic Landau-Zener Crossing Probabilities f o r Electronic Field Surfaces f o r V a r i o u s D r e s s i n g Laser Powersa Id,b

d,,,

W/cm2

cm-I

lo9

121

1 X 10''

191

2 X 10"

270

4 X 10"

381

7 X 10''

505

4X

(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)

241.9 241.5 240.1 241.9 241.5 240.1 241.9 241.5 240.1 241.9 241.5 240.1 241.9 241.5 240.1

0.360 1.5 0.548 0.33d 0.09d 0.725 0.078 8.1 0.223 0.9 0.448 0.1 6.13 X 1.07 X l o z 4.5 0.050 0.201 0.3 3.94 X lo-' 1.67 X 91.0 2.55X 0.041 1.5 1.83 X lo-* 3.67 x 2.78 X l o - ' 8.30 X 3.68 X 17.6

a T h e values i n c o l u m n s 3-5 c o r r e s p o n d t o kinetic energies of (1)35 c m - ' (crossing velocity ux = 1.46 x l o 4 c m / s), ( 2 ) 100 c m - ' (ux= 2.48 x l o 4 c m / s ) , a n d ( 3 ) 3 5 0 c m - ' ( U X = 4.64 x l o 4 c m / s ) . T is the t i m e a f t e r which the p o p ulation d e n s i t y has decayed to l i e . Dressinglaser intensity. Crossing probability. d Probability > 0.5 for dissociation within t h e first vibrational period. e When the c a l c u l a t e d t r a p p i n g t i m e is this long, t h e n t h e lifetime of NaI(*)* will be strongly a f f e c t e d by radiation decay (Tmd

- 10 ns).

the adiabatic potential start to play a more important role. Above the Na* + I limit the vibrational spacing differs significantly from that below this limit. For most of our calculations we have used the rotational transition P(51) from the vibrational level u" = 2 in the ground state to the second vibrational level above the dissociation limit in the upper state, u'= 15. All significant quantities, such as the Franck-Condon factors and dipole transition matrix elements, were calculated from the wave functions. B.2. Spontaneous Emission from Field-Trapped Nul(*)*.At the diabatic crossing point there is a local probability for a transition between the electronic field surfaces Wl and W2which can be described by the Landau-Zener expressionlo3

P12= e x ~ ( - 2 7 ~ d ~ ~ d ~ ~- /s21)) ( u ~ h l s (22) ~ Here s1 and s2 are the slopes of W, and Wz (assuming Wl and W2 to be linear functions of r in the region of the crossing, and dlz and dzl to be constant in the same region), and the local velocity ux is defined as ux = (2EK/m).Since d12and dzl are linearly dependent on the field strength (see eq 21), the probability P12in eq 22 varies linearly with the radiation intensity. The difference in potential slopes is moderate at the crossing; this is advantageous since it makes PI, small and helps trap the NaI**. There are two further factors that will assist trapping. First, the intensity of the dressing-laser radiation should be high: -lolo W/cm2. Second, the local velocity ux should be small; i.e., the photoexcitation should bring NaIt* to a level marginally above the Na* + I limit. Table I gives the crossing probabilities, P12,and "trapping times", 7 , of the molecule for various dressinglaser intensities, I,, and local velocities, ux (Le., photoexcitation wavelengths). As can be inferred from Figure 14, the highest probability density for the molecular state is in the vicinity of the crossing. When the Franck-Condon principle is applied, it is found that transitions to high vibrational levels in the ground state are favored. If the dressing-laser wavelength is altered, the outermost maximum in the vibrational wave function in the upper state

shifts (along with the crossing point); consequently, the emission spectrum probes different regions of the ground-state potential, close to the dissociation limit. For low crossing probabilities, P12(high dressing-laser intensity, and/or low local velocity), the lifetime of the dissociating species is increased significantly, and consequently enhanced fluorescence will be observed in the desired wavelength region. It is noteworthy that for dressing-laser intensities within a practical range for focussed radiation (see the following section), the lifetime of the trapped species can be varied over 8 orders of magnitude (Table 1). The proposed method of fluorescence from radiatively trapped dissociating molecules probes the high-energy part of the ground electronic state, at least in the example of the alkali halides. This represents a unique spectroscopic tool for determining the potential in this region of configuration. It should be possible to test the validity of the ionic Rittner potential, as well as the coupling matrix element, H12,in the region of rx (provided the electronic transition probability is nonzero in the crossing region). B.3. Stimulated Emission from Field-Trapped Nul($)*. Recently some experiments have been reported in which saturation was achieved in the photodissociation of alkali halides. An experiment in CsI vapor made use of this saturation effect to demonstrate low-density detection of these molecules.lM Another experiment, on photodissociation of NaI, showed the ability to invert the population of sodium atoms, Na*, with respect to the ground level, Na." In this study superradiance from N ~ * ( ~ P ~ Pwas ,,~) observed when dissociating NaI with moderately intense radiation of the fifth harmonic of a Nd:YAG laser. Furthermore, photodissociation of In1 and ThI yielding electronically excited metal atoms has been used in efficient atomic transition lasers.108J09 The usefulness of stimulated emission processes for the detection of low-density gases is well established-for example, in the method of stimulated resonance fluorescence.lloJ1l An intriguing question in this context would be the possibility of stimulating emission from the dissociating intermediate MXt*. We remarked above that the population density in a given configuration interval, during the dissociation process, is very low. We would expect, therefore, that gain in probe laser intensity incident on NaI** would, in general, be too weak to detect, and densities would be too low to result in detectable superradiance from a vessel of convenient length. On the other hand, the time that the particles spend in a given configuration can be significantly increased by the field trapping described above. We have, therefore, performed model calculations for the time dependence of the population inversion in a field-trapped state of NaI(f)*. To obtain the population density in a specific vibrational-rotational state, we have solved the rate equations

+ (BluI+ AlU)nu = + BuJnl - (BIJ + Alu + LR + &,)nu ri, = -Bullnl

ri,

(234 (23b)

where nl and nu are the number densities in the lower and upper electronic states, LR stands for the radiative losses other than the return to the pumping level, and LD i s the dynamic loss via the diabatic channel (its value is obtained from the crossing probability, P12,given in eq 22). For simplicity both the dissociating light pulse and the dressing field pulse are assumed to be square and of equal time (but the method is by no means restricted to this model case). The transition (u" = 2, J" = 51) (u' = 15, J' = 50) was used once again as the photoexcitation pathway. The requisite wavelength of 241.5 nm can be obtained by fre-

-

5040


7

7

2000

t

Torr

--.

4

Foth et al.

25 it is evident that the gain coefficient is strongly dependent on the population inversion An = (nl - nz(gl/gz)). The population densities in NaI‘f)’ (see Figure 15) together with a bandwidth Av 1O’O Hz result in a gain coefficient of cyl2 0.18. Therefore, the resulting number density in the trapped state during the pumping process is high enough to obtain superradiance from an active length of approximately 10 cm. These values agree reasonably with the results from superradiant molecular lasers. For example, superradiant laser action has been obtained in sulfur dimer with An 10l1cm-3 and cyl2 0.05, from an actrive medium of 1 = 25 cm.I13 We have so far ignored collisional redistribution of the population in the molecular ground state. This would replenish the lower pumping level which otherwise is emptied very quickly due to photodissociation in the upper state. Under low pressure conditions it would be more appropriate to use a picosecond laser source to give photoexcitation on a time scale that matches the dissociation losses. However, the addition of buffer gases to the NaI vapor can be made to repopulate the depleted ground state collisionally,the collision rate being selected to offset the dissociation losses. In this way one should be able to maintain a significant population in the upper state for nearly the complete duration of an excitation pulse of some nanoseconds (see upper part of Figure 15) for a buffer gas pressure of -2000 torr. A t these pressures the collisional redistribution is on the order of the dissociation loss rate. It should be pointed out that a gas with a high dielectric strength has to be used, otherwise the high field strength of the dressing laser may cause gas breakdown.127 If one wants to set up a laser cavity operating on N a P ’ collisional repopulation becomes vital. The round-trip time in an external resonator is on the order of 1 or more ns depending on the length of the resonator. From the previous discussion it is evident that ? l atm of buffer gas would be required. Without going into details of the calculations,we outline below a simple scheme for a photon-catalyzed laser. The laser output would comprise a line spectrum, as is general for diatomic gas l a s e ~ 3 . lDue ~ ~ to Franck-Condon overlaps of the field-trapped vibrational-rotational wave function with those of the ground state, the example discussed in this paragraph would result in laser lines with wavelengths in the range approximately 490-540 nm. In order to obtain a large Landau-Zener splitting, and therefore a low crossing probability, Plz,and hence a long lifetime for the radiatively trapped molecule, one needs power densities around -1O’O W/cm2. A t present one is restricted to powerful lasers with fixed frequency since only these lasers offer such energies without extreme f o ~ u s i n g . l l ~ExJ~~ amples are excimer lasers, such as XeCl at 308 nm, KrF at 249 nm, and dissociation lasers, for example, HgBr at 502 nm. Another possibility is the Nd:YAG laser fundamental at 1024 nm or the second harmonic at 535 nm. However, efficiencies for dye lasers pumped by these lasers are 20-40% ,117J18 so that tunable pulses with energies in the required range should soon become available. One will then be free to choose the position of the photon-catalyzed curve crossing. This will result in optimal Franck-Condon overlap for other downward transitions, and hence lasing to shorter wavelengths approaching that of the excitation laser, using a short-wavelength dressing laser. The region being scanned is that of the wings in Figure 11.

-

-

-

-(L---. -

iC

_J_-__

- \’E

__ -

..A r in ”

L@ceil

Figure 15. Population density in the “trapped” molecular state calculated for the transition indicated in Figure 14. The fractional number density in the lower pump level corresponds to a NaI vapor temperature of 600 O C ; n(v”= 2,J“ = 51) = 1.86 X 10” cm3. Lower part of figure: power densities of the excitation radiation are (a) 0.4, (b) 1.O, and (c) 4.0 MW/cm2. Upper pari of flgure: power density of the excitation radiation is 4.0 MW/cm2; buffer gas at the indicated pressures is added to collisionally repopulate the lower pumping level.

quency doubling of a coumarin dye laser. Pulse energies of 1-3 mJ can be easily realized, corresponding to peak powers of approximately 0.4 MW. Figure 15 shows the number density vs. time for different laser powers. It can be seen that the available laser power for the dissociation process is sufficient to saturate the transition within a few picoseconds. The fractional population (Boltzmann distribution) in the lower vibrational-rotational state of NaI was chosen to correspond to our experiments (vapor temperature around 800 K; corresponding to a vapor pressure 70 mtorr and a density 8 X 1014~ m - ~ ) . Superradiance from a population-inverted medium can be observed in the case112 1s = IF exp(alzl) >> 1 (24)

-

-

i.e., when the emission is no longer dominated by simple fluorescence. Here Is and IF stand for the stimulated and spontaneous fluorescence emission intensity, 1 is the length of the active medium, and a12is the gain coefficient. The customary expression for the small-signal gain (i.e., with gain saturation due to stimulated emission still negligible) at the line center is112 where g(vo)is the line-shape function (in first approximation l/g(uo) Av; Au is the half-width of the line); vo is the transition wavelength between state 1 (degeneracy g,, population density n,) and state 2 (degeneracy g,, population density n2),and A12is the corresponding Einstein coefficient (Alz 1/7,,d). It should be noted that the Einstein coefficient can only be replaced by the inverse of the radiative lifetime so long as transitions to all vibrational levels in the lower state are being measured, since A12 = &A,,(u”). The individual A12(u’9 has to be calculated for a particular vibrational transition. From eq

-

-

(127) V. E. Mitsuk, V. I. Savonskin, and V. A. Chernikov in “Phenomena in Ionized Gases”, Vol. 1, B. PeroviE and D. TolniE, Eds.. Gradevinska Knjiga Publishing House, Beograd, 1966, p 813.

Feature Article


IV. Conclusion

In addition to the broad range of laser transitions accessible, such a laser should have another advantage. By varying the field strength for the "catalyzing" laser (or the choice of kinetic energy in the dissociation), one can alter at will the lifetime of the radiatively trapped state. The uncertainty principle links the lifetime of a state with its energy width; the shorter the life time, the broader the state. From the trapping time 7 in Table I it is evident that in some cases the lifetime of the radiatively trapped state is s; i.e., it corresponds to the fluorescence decay time; the natural line width is then -0.01 cm-'. At the other extreme 7 is SlO-I3 s; i.e., it corresponds to the time required for NaI(f)*to pass through the relevant region of internuclear separations; the line width in this case is 2102 cm-'. The special properties of this photon-catalyzed laser, as exemplified for the case of NaI as the working substance, can be summarized as follows: pulse duration, 0.1-104 ps; tunability, 220-580 nm; line width, 0.01-210 cm-'. A requirement for realizing such a laser is that the length of the active medium must be subjected to a dressing laser of intensity in the region of 1O1O W/cm2. Fortunately (as indicated above) it is feasible to obtain powers of this magnitude by focusing commercially available lasers (Nd:YAG and excimer lasers with output energies of -1 J/pulse116)to give a beam waist of -1 mm in diameter and several centimeters in length. In the example treated here the green line of the Nd:YAG laser, at 532 nm, can have a pulse energy -0.3 J/pulse. If this is focused to a 0.5-1-mm waist, the power of 1O'O W/cm is obtained. Presently available commercial dye lasers give a pulse energy within a factor of 3 of this; 1' consequently a continuously tunable dressing laser is also within reach. It might be thought that the line width of the photoncatalyzed laser could be increased almost without limit, by decreasing the lifetime of the upper electronic state (i.e., shortening A, for excitation, or decreasing the intensity Id). However, the Lorentzian (homogeneous)broadening of the levels in the upper state will then cause them to overlap, in their wings, with the dressing laser. In place of a tunable laser one would then have an amplifier for the dressing laser at Vd. Fortunately, for reasonable dressing-laser powers the field-induced splitting has the consequence that the peak of the laser transition at v2 is detuned by several hundred cm-' from vd. Even for a Lorentzian line breadth this is sufficient to reduce the stimulated emission at V d to a sufficiently low level that population inversion is maintained, and tunable lasing is expected. The minimum population inversion Anth at laser threshold is119

We have sought to show that the luminescence of molecules in the process of falling apart constitutes a young but established field for spectroscopic studies. The unstable molecules in the examples that we cited were formed (1)in nonreactive collisions or (2) by photoexcitation or (3) as transitory intermediates in chemical reaction. This is not an exhaustive list; for example, electronic or ionic impact, or energy transfer from an electronically excited collision partner, could replace the photon in the second category. In all three categories it is likely that what has been accomplished so far will before long be eclipsed by what can now be done. The newest and rawest category of investigation is 3; the spectroscopy of transition states in chemical reactionsthis term being used to describe states intermediate between reagents and products. We have pointed out that in the future such studies will be made for the entry channel of the reactive potential energy surface (pes)-just as in category 1emission occurs along the approach as well as in the retreat coordinate. However, in the present paper we have stressed the category of processes in which the emitting species is falling apart. In the reactive context this means that the products are separating, moving along the exit valley of the pes. The importance of the forces released in this second stage of the reactive event, in determining such attributes as product excitation and angular distribution, has been stressed in models of the dynamics such as the DIPR model (direct interaction with product repulsion).'20-122 One outgrowth of the DIPR model was the even more euphonious DIPR-DIP model of Herschbach and coworkers; 123~124the DIP stands for distributed as in photodissociation. These authors obtained the form of the repulsion, required for the DIPR model, by recourse to an electronically analogous process of photodissociation. There should, therefore, be instances in which the spectroscopy of molecules in the process of photodissociation (our category 2) bears more than a formal resemblance to the spectroscopy of reaction intermediates in the process of dissolution (category 3). There will also be cases in which the spectroscopy of molecules falling apart subsequent to a strong thermal collision (category 1) has points of resemblance to the spectrum of reacting species retreating from their configuration of closest approach. These similarities, and (even more) the differences, will shed light from a new direction on all three processes, of which the most mysterious and tantalizing is chemical reaction.

An, = (4x2/3)(AV/v)(7,,d/7~)(no/A)3 (26) Here 7c = (n&/c)(l/S) is the product of the one-way transit time in the cavity of length L with the inverse of the total power losses per pass (diffraction, absorption, transmittance of mirrors). With total losses of 6 0.1 and a bandwidth of Av 1O'O Hz (as above) the minimum population inversion for a cavity length L of 10 cm (assumed to be equal to the length 1 of the active medium) is Anth 1.6 X 1O'O ~ m - ~This . value is well within the population inversions achievable by using the dressing laser to trap NaI(f)*(see Figure 14). We conclude that a photon-catalyzed laser should be realizable.

Acknowledgment. J.C.P. thanks his colleagues at the California Institute of Technology, most especially A. H. Zewail, A. Kuppermann, and R. A. Marcus, for their advice and stimulus during the tenure of a Sherman Fairchild Fellowship there. These topics have also been the subject of helpful discussions with R. B. Bernstein, W. Demtroder, E. J. Heller, and J. L. Kinsey, to whom we extend our thanks. H.J.F. thanks the Deutsche Forschungsgemeinschaft for the award of a fellowship. This work was supported by the Natural Sciences and Engineering Research Coucil of Canada and, in part, by grants from the U S . Air Force Office of Scientific Research and the Occidental Research Corp. of Irvine, CA.

-

-

-

-

Emission from molecules and reaction ... - ACS Publications

Recommend Documents