Rare-gas Matrices, Their Photochemistry and Dynamics-cage Effect

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10 Rare-gas matrices, their photochemistry and dynamics:

recent advances in selected areas

Vladimir E. Bondybey,Markku Rasanenand Andreas Lammers

Institut fur Physikalische und Theoretische Chemie der TU Munchen, 85747

Garching, Germany. E-mail: [email protected]

Department of Chemistry, University of California, Irvine, CA 92660, USA

Laboratory of Physical Chemistry, PO Box 55, FIN-00014, University ofHelsinki, Helsinki, Finland

In this article we give a brief overview of the current understanding of the dynamics ofmatrix-isolated molecules, their photophysics and relaxation. Various types of non-radiative transitions, energy transfer and relaxation processes occurring in the matrix

and their theoretical description and modelling will be discussed. The recent introduc-tion of picosecond and femtosecond techniques coupled with molecular dynamicssimulations provides new insights into the details of guesthost interactions.In situUV photolysis of matrix-isolated species has recently resulted in the characterizationof an entire series of novel rare-gas compounds. We will also review studies of themobility of guest species in rare-gas matrices with emphasis on the diffusion ofhydrogen atoms and protons.

1 Introduction

When the idea of investigating atoms and molecules in inert cryogenic solids emerged,and the name of matrix isolation was coined, the emphasis clearly was on spectro-scopic investigations of transient, highly reactive molecules.Very soon it was, how-ever, realized that even the inert rare-gas matrices are not really inert, but can perturb,in some cases quite considerably, the isolated species and their spectra. Furthermore,investigations of the, in general, nonrotating molecules in the matrix naturally meantthe loss of the precise structural information available in the gas phase from therotational structure. When then, with the emergence of lasers and the development ofsupersonic beam sources,new gas phase methods for obtaining cold spectra of trulyfree molecules became available, it seemed that the days of the matrix isolationtechnique were numbered.

Even though such gas phase methods have now been available for some twodecades, the steady flow of interesting new results obtained using matrix methods goeson, and as evidenced by the attendance at the numerous meetings and conferences

Annu.Rep.Prog.Chem.,Sect.C, 1999,95, 331372 331

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dealing with low-temperature solids and matrix isolation, the number of laboratoriesand researchers active in this area appears undiminished, and a steady development ofthe field continues. It is the purpose of the present article to review some of the morerecent of these developments. Naturally, there have been a number of previous reviews

of matrix isolation, some of them rather comprehensive.Since, in a paper from ourown group several years ago, we have concentrated on the spectroscopic aspects ofmatrix isolation,we will in the present work focus more on the photophysics anddynamics of processes proceeding in low-temperature solids.

As noted above, nowadays gas phase methods, which often combine lasers withsupersonic expansion, can indeed provide detailed information about free gas phasemolecules, but from the chemical and technical point of view, often more important aremolecules which are not free, but interact with their environmentspecies in the solidor liquid phase, or in frequent collisions with high pressure gas. In fact, most of the

technically important processes occur in solutions and in the condensed phase. Raregases represent perhaps the simplest possible solvent, which can be easily handledexperimentally, and lends itself readily to theoretical modelling.

Matrix spectra also provide, in addition to information specific to the guest, infor-mation about the solventsolute interactionsvia the medium shifts and spectral lineshapes. Even in the gas phase species, line shapes contain information about thelifetimes of the states involved in a given transition. Compared with the gas phase, thelifetimes in a solid matrix are usually shortened due to fast nonradiative processes, andstates which can in the gas phase be to a good approximation viewed as stationary

states of the system evolve rapidly in time in the matrix. The study of the profiles ofspectral lines allows one to gain some insight into the processes proceeding in thematrix.

Current progress in laser technology and the production of short pulses make itpossible to follow the temporal development of the system in real time, usingtime-resolved, femto- or picosecond techniques, and to obtain the same informationabout the dynamics of the system in a more direct way. Studies of spectra both in thefrequency and time domain may thus in principle provide the same information. Forcomplex systems studies of the frequency spectrum and temporal evolution are highly

complementary, and by combining the two a more complete understanding can beobtained. In fact, following the temporal development of the system may provideconsiderable insight, and there are details of spectral information even in cases whenthe spectra themselves appear to be almost completely featureless.

Rare-gas solids are systems which are very simple and complex at the same time.The simplicity consists in the fact that the binary potentials between the solvent atomsare all the same, isotropic, and are relatively well known. The complexity lies in theguesthost potentials which are in general anisotropic, state-dependent, and not wellknown, and beyond that there is the sheer size of the system, the number of atoms and

modes which have to be considered to provide a realistic description of the system.Besides the lack of knowledge of the binary potential, the contribution of three- andmultibody effects is also unknown. In spite of this complexity, progress in this area hasbeen nothing short of amazing. From the beginnings some 25 years ago where just afew atoms could be explicitly considered, progress in hardware and modellingtechniques has made it possible today to simulate the dynamics of systems withhundreds of atoms, solve the equations of motion to follow the trajectories of individ-

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ual particles, and then invert the time-dependent trajectory information to simulatethe spectra of the isolated guest, and in turn obtain a deeper understanding of theguesthost dynamics.

The development of the matrix method with its idea, implied by the name, of

isolating the species of interest from the reactive environment, preceded only by a fewyears the discovery of Bartlett that rare gases themselves are not as inert as believed.It did not take long to realize that matrices can be an excellent medium to investigaterare-gas compounds.Using rare gases as a reactive medium, several rare-gas com-pounds were characterized. After a span of some twenty years when virtually nothinghappened in this field it was suddenly discovered a few years ago that rare-gaschemistry may be much richer and more varied than originally believed.In the lastfew years a whole series of new compounds, including xenon dihydride, have beengenerated and spectrally characterized in the rare-gas matrices.

The above mentions just a few of the areas where impressive progress has occurredrecently. Here we will first give a short overview of the current status of our under-standing of low-temperature matrices and their dynamics in general, and then in a fewmore specific sections sketch briefly recent developments in some of the most excitingareas.

2 Photophysics of matrices and guesthost interactions

As noted above, the original goal of matrix isolation, to establish the spectra oftransient species in an inert environment, which permitted a leisurely study of theotherwise reactive guest, was based on the assumption (or hope) that the spectra will beonly weakly perturbed and so give a realistic picture of the free molecule. The extent towhich this hope is founded depends on a number of factors. In general, ions and ionicor strongly polar species interact more strongly with the host than covalently stronglybound, non-polar neutral ones.The assumption is also more justified for the groundstate than for excited electronic states, and the higher the excitation energy of the statesinvolved, the stronger is, usually, the interaction with the medium. Thus high Rydberg

states are usually very strongly perturbed and shifted in the matrix. Similarly,strong spectral shifts will occur if the electronic transition involves a charge transfer,and a considerable change in the charge distribution within the molecules.

As far as the original goal of the technique is concerned, the guesthost interactions,and most of the effects of the solid environment, were regarded as obstacles, restrictingthe techniques usefulness and general applicability. Methods such as supersonicbeams are nowadays available to study truly free, cold molecular species.On theother hand, most of the interesting chemistry, at least here on Earth, does not occur inisolated molecules in the gas phase, but in a condensed environment. Chemistry occurswhen bonds break, form or rearrange, when molecules and atoms interact with eachother, and the interactions of molecules with their environment thus become a topic ofconsiderable interest. Molecular guests isolated in rare-gas solids are very simplesystems, where such interactions can be investigated in microscopic detail, and withrelative ease modelled theoretically. The guesthost interactions in matrices, formerlyviewed as annoying side effects, are therefore now increasingly becoming the mainfocus of study.




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The solid environment affects the spectral properties and photophysics of the guestin various ways. A free gas phase molecule excited into a bound level can only disposeof its energy by radiation. In a condensed environment, transfer of part or all of theenergy to the host and nonradiative relaxation may take place. While a molecule

excited in the gas phase into a dissociative or predissociating state will smoothly fallapart, interaction with the matrix cage effect will hinder dissociation, and alternativeprocessesrecombination, isomerization, or reaction with the matrixmay takeplace. In contrast to dissociative processes, the condensed environment may assistionization of the guest molecule or atom and other charge separation processes. Thesolvation by the solvent atoms or molecules invariably strongly stabilizes ionic speciesthat result from ionization, and the energies required for ionization may be drasticallylowered in the matrix. We will briefly review our state of knowledge about these effectsof the medium upon the photophysics of the guest in the following subsections.

2.1 Nonradiative relaxation processes in matrices

Even though in principle nonradiative relaxation of an excited state of an impurity ina rare-gas solid might seem to be a very simple problem, actually the internal energy ofthe guest is relatively rarely transferred directly to the delocalized lattice phonons ofthe host. Depending on the specific nature of the guest, of its excited staterotational,vibrational or electronicand on the strength of the guesthost coupling, the relax-ation may proceed by a number of different mechanisms, and the rates may span many

orders of magnitude. The simplest nonradiative process, relaxation between two levelsof the guest, converting the internal guest energy into delocalized lattice vibrations,can be seen when the level spacing is relatively small in molecules in highly dilutedmatrices, but is most often accompanied or masked by other, more efficient processes,such as intramolecular VV energy transfer, transfer of energy to rotation (VRtransfer), or transfer of vibrational or electronic energy to other guest molecules. Theprinciples which govern nonradiative relaxation are relatively well understood, andnumerous previous reviews dedicated to this topic summarizing both the availableexperimental data and the theoretical modelling, have appeared.

2.2 Intermolecular energy transfer and vibrational ladder climbing

If the concentration of molecules in the matrix is relatively high then a long-range,Forster type transfer of vibrational or electronic energy between them may take place.Thus in an early study of matrices containing both OH and OD the A statelifetimes of OD were found to be consistently shortened due to intermolecular elec-tronic energy transfer to OH:

OD A(v 0)OH X(v 0)OD X(v 0)OH A(v0)E 90cmVibrational energy transfer to impurity molecules has been systematically inves-

tigated by Goodman and Brus.They found that the vibrational relaxation rates ofexcited Astate levels of NH and ND were significantly increased in doubly dopedmatrices that also contained other small molecules due to the intermolecular vibra-tional energy transfer. Somewhat surprisingly, not only the dipoledipole transfer toCO was rather efficient, but so was the presumably dipolequadrupole transfer to the




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nonpolar N.

Even more efficient is, of course, the resonant energy exchange between vibration-ally excited molecules in their ground states, in particular if they are strongly polar,and this can naturally be a problem when one tries to establish experimentally their

vibrational lifetimes. This was first observed in the classic studies of CO relaxation indilute argon matrices.Similarly in later studies of hydrogen halides in the matrix itwas realized that the excitation does not necessarily stay with the originally excitedmolecule, but by resonant transfer wanders from guest to guest through the solid:

HCl(v 1)HCl(v 0)HCl(v0)HCl(v 1) (E)

Such a diffusion can eventually result in a transfer to a molecule whose relaxation isparticularly efficientperhaps due to the proximity of a polyatomic impurity, whichmay act as an acceptor of the vibrational energy. This will result in a quenching of the

infrared fluorescence, and effectively shorten the measured lifetimes, and one finds thatthe lifetimes are strongly guest concentration dependent. It should also be noted thatwhile for such a resonant transferE 0, if, for instance, two different isotopes areinvolved then this will not be the case. The process will be exothermic if Cl is theheavier isotope, and at very low temperatures there is a tendency to concentrate theexcitation in the heavier isotopic species, which can, in fact, be conveniently used intwo-photon schemes to excite or react selectively one isotope. If several trapping sitesare present, there is also a preferential population of the site with the lower vibrationalfrequency.

A particularly interesting situation arises when not only the concentration of theguest but also the excitation rate is high, so that interactions to two vibrationallyexcited molecules may take place. In this case, as shown in a series of elegant studies byDubost and co-workers, besides CO, and also for instance for NO and other mol-ecules, a slightly off-resonant energy transfer between them can occur:

NO(v 1)NO(v n)NO(v0)NO(v n1)E

Such a process is usually exothermic in view of the anharmonicity of molecularvibrations; once a molecule is in a v 1 level, the excitation is effectively localized since

v 1 processes are inefficient. If the density of excited molecules is high, energyexchange with furtherv 1 NO molecules can result in an energy pooling and ladderclimbing process, resulting eventually in a distribution of vibrationally excited mol-ecules extending to very high v levels. The high efficiency of such processes is aconsequence of the exothermicity of the reaction, and of the fact that entropic con-siderations are not important at the low temperature of the matrix. This process canpopulate extremely high vibrational levels of the ground state, with levels up tov 27in NO andv 38 in CO having been observed.

For such highly vibrationally excited molecules an intramolecular vibrational-to-

electronic energy transfer can in fact occur, populating excited electronic states andresulting in visible or UV fluorescence or phosphorescence, and does in fact eventuallyalso result in molecular dissociation as demonstrated in the case of NO.

2.3 Theoretical studies of multiphonon processes

The energy level separation of the relaxing molecules, the energy gap

, is usually




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much larger than the highest frequency phonons , so that relaxation requires

simultaneous formation of a large number of lattice phonons (N/

), and is

inherently a high-order process. A concise review of the various theoretical ap-proaches to this problem with extensive references is given in the recent work of

Egorov and co-workers.Most approaches are based on perturbation theory, andusually partition the overall Hamiltonian into three terms: a Hamiltonian describingthe guest, H

, a Hamiltonian describing the harmonic phonon modes of the host

lattice,Hand a potential providing the coupling:

H HH

V(q)

In general, the interaction potential Vis assumed to be linear in the vibrationalcoordinateq of the relaxing molecule, but nonlinear in the phonon coordinates toallow for higher-order processes. If the interaction term is assumed to be an exponen-

tial function of the phonon coordinate, one obtains the well-known energy gap lawderived by Nitzan and co-workers some 25 years ago. The law essentially predicts anexponential decrease in the relaxation rates with the increasing energy gap, that is theenergy separating the guest levels involved in the relaxation process. The theory alsopredicts a steep temperature dependence of the relaxation process. Physically, therelaxation is based on the stimulated emission of phonons and depends thus on theBoson thermal occupation number n(

) [exp(/kT) 1]it is easier to pro-

duce phonons, when phonon levels are already thermally populated.The rate of impurity relaxation obviously also depends strongly on the extent to

which the intramolecular transition is coupled to the lattice. Experimentally one canoften get information about the magnitude of this coupling by examining line shapes inthe spectrum of the isolated guest. Specifically a useful indicator of the strength of thecoupling is the ratio of the integrated intensity of the phonon sideband to that of thecorresponding zero phonon line, often denoted S

. This parameter, often also referred

to as HuangRhys factor, represents essentially the FranckCondon principle appliedto lattice phonons, and is indicative of the mean number of phonons directly created inthe absorption (or emission) process. It is an experimental fact that in the vibrationalspectra (IR or Raman) of matrix-isolated molecules the phonon sidebands are usually

insignificant andS 1, and the coupling is weak. As a consequence one often findsthat pure vibrational multiphonon relaxation is quite inefficient, and the lifetimes ofthe excited vibrational levels very long.

2.4 Experimental studies of multiphonon vibrational relaxation

Vibrational relaxations of molecular guests with large vibrational spacing thereforefrequently proceed very inefficiently, and in fact the observed vibrational relaxationrates span some 16 orders of magnitude. A very thorough study of vibrational

relaxation and lifetimes of the vibrational levels v 420 in the ground electronicstate of O

in an argon matrix has been carried out by Salloum and Dubost.Since

the homonuclear O

vibrational levels cannot be populated directly, an indirecttechnique of energy transfer from vibrationally excitedCO was used. The authorsfind that in the range where the band gap changes from 1500 to 1100 cm, the ratesof the multiphonon vibrational relaxation change by three orders of magnitude from2.5 10sforv 4 to 2.5 sforv 19. For many similar molecules which have




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Fig. 1 The top trace shows the excitation spectrum of the B(0)X

transi-

tion of Cl

in solid argon near the convergence limit. The bottom trace is a moleculardynamics simulation of the same spectrum,which reproduces qualitatively the sameshift of intensity into the phonon sidebands for higher v levels. The relative vintensities are not correctly reproduced, since a synthetic function, rather than the trueground statev 0 wavefunction, is used in the simulation. Note the changes in the

widths of the zero phonon lines due to lifetime broadening in the experimentalspectrum.

comparably high vibrational frequencies such as O

but are polar, e.g. NO, CO or CN,one finds that the rates are often controlled by infrared radiation, rather than non-radiative processes. The authors found that they can fill relatively well their resultsusing the theoretical treatment of Nitzanet al.,and more recently a good fit of thedata was shown by Egorov and Skinner. Interestingly though, the relaxation ratesdo not seem to exhibit the strong temperature dependence predicted by theoreticalmodels.

Very slow vibrational relaxation was recently found even in the ground electronicstate of various isotopic species of diatomic tungsten oxidewhere intense emissionfrom levels up tov 8 is observed. The nonradiative relaxation is apparently insig-nificant, and in spite of the relatively small vibrational spacing, ranging from 1056 (forthe 10 transition of WO) to 950cm (the 87 transition of WO), vibrationalemission seems to be the dominant relaxation channel.

In contrast with molecules with relatively high vibrational frequencies, those whose




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vibrational modes approach the Debye frequency of the lattice can decay by low-orderphonon processes, and their vibrational relaxation is often extremely fast. This can beseen for instance in the fluorescence of Ca

, or in the excitation spectrum of Cl

in solid

argon, reproduced in Fig. 1. Here one observes that the higher vibrational levels are

severely lifetime-broadened, implying relaxation rates of10 s, corresponding tolifetimes in the subpicosecond range.

2.5 Subpicosecond time-resolved studies of guesthost dynamics

Rather than relying on linewidths as an indicator of vibrational relaxation rates, theavailability of pico- or femtosecond lasers now allows direct lifetime measurements. Asan example, the vibrational relaxation rates in the B (1/2) and C(3/2) states ofXeF could be measured.After exciting the molecules by 250fs pulses at 355 or

320 nm, the time-dependent profiles of various levels populated during the relaxationprocess is probed by selecting 2 ps segments from their fluorescence signal using a Kerroptical shutter. The CS

Kerr cell is triggered by 640 nm, 150 fs pulses, whose delay

with respect to the pump signal is varied with an optical delay line, with the 2 ps timeresolution being limited by the CS

relaxation time. By analysing the time profiles, the

relaxation rates could be determined. Thus in the B state the lifetimes decrease from300ps forv 1 to30 ps forv 4. Even faster relaxation is found in the C statewhere following excitation aroundv 2 the population reachesv 0 in 13 2ps.

Relaxation is often found to depend strongly also on the mass and other properties

of the host matrix, as well as on the specific nature and geometry of the matrix site. It isnot uncommon for the same molecules isolated in two different sites in an identicalmatrix to exhibit considerably different relaxation behaviour. It should also be notedthat the relaxation of the guest is not only affected by the level spacing, but depends onother properties of the guest. In general, ions or strongly polar molecules relaxnonradiatively much more readily than comparable neutral, nonpolar species.

As noted above, the spectral line widths and shapes are often the products of, andcontain information about, the system dynamics. In the case of low vibrational levelsof Cl

the coupling of the guest vibration to the lattice is relatively weak, and

broadening of the zero phonon line (ZPL) due to relaxation small, so that well-resolved spectra, providing insight into the dynamics, are obtained.It is, however,also obvious, and can be seen by examining the right-hand part of the spectrum in Fig.1, that, in the limit of very strong homogeneous phonon broadening and fast relax-ation, the spectra become essentially continuous. In a regime where no zero phononlines are resolved, and the spectra are featureless, little detailed information will beobtained. A classical example is molecular iodine: its vibrational frequency is smallerand relaxation correspondingly faster than in Cl

, and the transitions of the polariz-

able I

molecule couple more strongly to the lattice, leading to broad and intensephonon sidebands, which results in continuous absorption spectra entirely devoid ofvibrational structure.

Fortunately, in the same way that spectra can provide information about theguesthost dynamics, direct time-resolved measurements can conversely provide spec-tral information. This has recently been demonstrated experimentally by Apkarianand co-workers.When a continuous spectrum such as that of iodine is excited,due to the high density of states one does not excite a single eigenstate of the system but




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Fig. 2 (a) Schematic of the I

potential energy and the femtosecond pump experi-ment. The broad fs-pump pulse (left-hand arrow) excites a nonstationary state, whose

time development is monitored by the time-delayed probe (right-hand arrow) whichexcites the molecules near the outer turning point to the higher lying charge transferstate. The dashed extension of the potentials refers to the cage potential. Panel (b)shows relaxation in the bound B0

potential, while in panel (c), where the A1

state

continuum is excited, a more complex process involving transient dissociation andrecombination is probed.

a superposition of many states which then evolves in time. Typically, if one examinedthe spectroscopy of the system during this relaxation process, one would obtain atime-integrated emission or absorption spectrum containing little information. This is

as if one were to take a 2 h movie, overlap all the frames and project them simulta-neouslyone would just get a black screen. On the other hand, projecting one frame ata time will yield the information contained in the movie (which might or might not bean improvement). Modern femtosecond technology permits doing just that with arelaxing molecule.

Exciting a molecule with a short-pulse femtosecond laser accomplishes two things.In the first place, since the pulse is, in view of the uncertainty principle, spectrally broad(a 100 fs pulse corresponds to a spectral width of60cm), and will thus not excite asingle stationary state but a superposition of many states from the dense manifold.

Following the excitation, the system will start to relax, and in the course of the motionthe spectra of the molecule will change as a function of time. The second thingaccomplished by the short-pulse excitation is that the molecular motion during therelaxation will not proceed with a random phase, but in a coherent fashion, since allthe molecules were essentially simultaneously excited. If one could now photographthe spectrum with a sufficiently short shutter, one would see the temporal developmentof the spectrum, and follow the coherent motion of the excited molecules and the




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dynamics of their relaxation. In typical femtosecond experiments a second short pulseprobing the system at a variable delay provides such a shutter.

The spectra of Cl

discussed above, as well as the states excited in the iodineexperiment of Apkarianet al. involve excitation from the X

ground state into the

spinorbit components of the lowest lyingelectronic state, as shown schematicallyby the left-hand arrow in Fig. 2(a). From this lowest triplet state, the halogen moleculescan then be further excited into the components of a higher triplet, often referred to ascharge transfer state, because it correlates with an ionic IIlimit. The molecules inthis state are known to fluoresce in matrices with high quantum efficiency on the fullyallowed transition back into the lowest triplet. As the molecule excited by the probepulse to the excited state oscillates back and forth within its bound potential, theabsorption spectrum changes with the frequency of the oscillations. These spectralchanges can be monitored by a time-delayed probe pulse exemplified by the right-hand

arrow in Fig. 2(a). This is tuned to a frequency capable of promoting the molecules intothe higher triplet, and excite its fluorescence. The fluorescence as a function of the delaybetween the pump and probe pulses then provides a window on the time-dependentabsorption spectrum of the excited lowest triplet. By varying the probe wavelength,one can shift this window, and analysis of the time-resolved signal at a number ofdifferent wavelengths can then provide a very detailed picture of the photophysicsoccurring following the initial dissociation.

The experiment naturally requires two independently tunable femtosecond lasersources, which are nowadays available if one can afford them. The basis of a typical

system such as used in the elegant experiments of Apkarian et al. employs a tunable,pulse-amplified Ti:sapphire laser, which pumps a cascade of optical parametric oscil-lators (OPO). In the iodine experiments, the OPO output is used as the pump, whilethe doubled Ti:sapphire laser provides the probe pulses. The ability to vary the delayand the frequencies of both the excitation and the probe pulses permits obtaining avery complete understanding of the guesthost dynamics of the system.

The result of such an experiment where the exciting laser populates the bound levelsof the 0 B state below the dissociation limit is shown in Fig. 2(b), where thefluorescence is shown as a function of delay between the pump and the probe pulse.

Each time the outer classical turning point is approached as the molecule vibrateswithin the bound B-state potential, the probe pulse excites it into the charge transferstate, and one can see a periodic recurrence of the fluorescence signal. As shown by thedashed arrow in Fig. 2(a), with the available photon energy the upper potential cannotbe reached near the inner turning point. By changing the probing photon energy, onecan effectively change the observation window. A similar experiment, where the probelaser excites the dissociative continuum of the lower 1,2

spinorbit compo-

nents, so-called A and A states, is shown in Fig. 2(c), where the signal appearssomewhat more complex. This is due to the increased complexity of the process itself,

with the molecule first transiently dissociating, the fragments colliding with the latticeatoms and rebounding, and finally the molecule oscillating and relaxing within thecage. For a probe laser wavelengths above about 705 nm, the molecules from thelowest A state levels can no longer be promoted into the charge transfer state, and onesees a signal decaying with a time constant of about 12 ps, corresponding to the overallvibrational relaxation rate in the A,Amanifold. Perhaps the biggest surprise in theseexperiments came from the observation that the coherence of the excited I

molecules




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can survive many collisions with the lattice, and persist for times of at least 510 ps. ByFourier transforming the oscillatory signal one can then obtain spectral informationabout the excited state vibrations. The spectrum shows a red-shaded peak near80cmwhich corresponds to the I

vibrational frequency within the anharmonic A

state potential, as well as several lower frequency features due to motions of the latticecage atoms coupled to the molecular vibration.

Using the theoretical descriptions and trajectory calculations which will be dis-cussed in one of the following sections, one can model the multibody guesthostdynamics, and the response of the system to the guest excitation, and simulate almostquantitatively the time-resolved transient signals. In this way, by combining construc-tively theoretical modelling with the experimental observations from femtosecondpumpprobe experiments, one can obtain a detailed understanding even in the case ofsystems whose spectra appear completely featureless.

2.6 Molecular rotation, and the V R process

While, as discussed above, the nonradiative relaxation of molecules such as O

, N

orCN, with high vibrational frequencies in the 15002300cmrange is extremely slow,so that the excited state decay is governed by radiation, for many simple hydrides thisis not the case, and they relax nonradiatively. The first demonstration of this effectresulted in fact from experiments designed to test multiphonon relaxation theories

by comparing the lifetimes of matrix-isolated hydrides with the corresponding deuter-ides. While the theory would require, in view of the factor of2 larger energy gap,a much less efficient relaxation in the hydride than in the corresponding deuteride, theexperiment gave exactly the opposite result: the hydrides relaxed up to three orders ofmagnitude faster than the deuterides. The first experiments involved excited electronicstates of the OH and NH radicals,but subsequent measurements of vibrationallifetimes in ground electronic states confirmed that this result is not some exoticproperty of an excited electronic state, but that indeed hydrides systematically relaxmuch faster than deuterides, and this has been attributed to the effect of molecular

rotation in the matrix.One might expect that the interactions of the guest with the matrix will result in

barriers and arrest the molecular rotation, and indeed one can often find this to be thecase. Thus, for instance, the laser-induced fluorescence of halogens in matrices is foundto be polarized, and careful measurements yield almost exactly the polarization ratiosexpected for photoselection from an ensemble of randomly oriented, nonrotatingmolecules.On the other hand, for many matrix-isolated molecules this is not thecase, and in particular, light hydrides can rotate relatively freely even in the matrix, andtheir spectra exhibit a clear, albeit somewhat perturbed, rotational structure. A well-resolved and almost unperturbed rotational structure was recently found in thevibrational fluorescence spectrum of matrix-isolated CN, and the rotation is alsoevidenced by completely depolarized electronic fluorescence.Interestingly, dopingfor instance an Xe matrix containing CN with about 1% of Ar is sufficient tocompletely quench the rotation. Strong interaction of the guest with the cage will notinterfere with the rotation, as long as it is fully isotropic. The presence of the Ar atom inthe neighbourhood of the substitutional CN impurity, even though it would presum-




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ably make the cage looser, breaks the isotropy of the interaction and introduces abarrier to rotation.

The energy of a vibrationally excited gas phase molecule can, in the absence ofcollisions, not be converted into rotational energy, since the angular momentum has to

be conserved. This is, however, no longer the case in the matrix, where the molecule isin the asymmetric field of the matrix cage, and where the effect of the barrier to freerotation will be a partial mixing of the pure vibrational or rotational levels. As a result,in a matrix-isolated molecule, VR transfer can, and does take place. The rotationallocal mode is in general more strongly coupled to the vibration than to the delocalizedlattice phonon. This is also reflected in the appearance of a discrete rotational structureand of the J 0 transitions, rather than of a featureless phonon sideband, in thespectrum. The rotational quanta which grow quadratically with Jare in general largerthan the lattice phonon. As a consequence, the V R conversion is a lower-order

process, and prevails over the multiphonon vibrational relaxation. When deuterium issubstituted for the hydrogen, the energy gap is reduced by a factor of approximately1.4, while the rotational quanta, which are the primary acceptors of the vibrationalenergy, are reduced by a factor of two. The net result is that relaxation of a hydride is alower-order process than that of the corresponding deuteride, and this is reflected inthe much more efficient relaxation.

One of the well-studied examples is the v 1 level ground state ND level in solid Krwhose lifetime of about 34 ms is probably purely radiative, while the correspondinglevel of NH relaxes three orders of magnitude faster with a lifetime of 30s.The same

effect has now been established for a number of other hydrides, and was very carefullystudied by Nitzan et al. and Wiesenfeld and Moore in HCl. It now seemswell-established that a VR process that creates highly excited rotational levels is theprimary step in the relaxation of these hydrides, with the rotational energy then beingconverted into the delocalized lattice phonons in the second step. The efficiency of thisrelaxation is confirmed by the experimental observation that excited rotational levelsobserved in matrix spectra exhibit strong lifetime broadening. While the rates maydecrease with increasing rotational quantum number and level spacing, the rotationalrelaxation is still likely to proceed on a picosecond timescale. Classical simulations,

as well as the theoretical model of Gabriel and co-workers, who described themotion of a host atom classically, but treat rotation of the HCl guest quantummechanically, predict rotational relaxation to be very fast. In the latter model, it isconcluded that a considerable part of the energy is relaxed in 100200fs.

The effect of rotations is not restricted to diatomic hydrides but is also observed inpolyatomic molecules,with for instance CH

F in matrices relaxing much faster

than CD

F. A related observation made for a number of systems was that theintroduction of a group with a low barrier to free rotation, such as methyl, into anotherwise rigid, e.g. aromatic molecule, may increase by more than an order of

magnitude the rate of its vibrational relaxation.This was again explained by theintramolecular rotation being the primary acceptor of the energy, and it was suggestedthat, since in such a case a barrier to free rotation is present even in a free molecule, asimilar effect on vibrational relaxation could be expected even in the gas phase.Following this suggestion this has indeed been confirmed experimentally and studiedin a large number of gas phase species by Parmenter and co-workers.




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2.7 Excited electronic states and interelectronic cascade processes

Nonradiative transitions between vibrational levels belonging to two different elec-tronic states are often considerably more efficient than intrastate vibrational relax-

ation, which is due to the magnitude of the electronphonon coupling. The relaxationprocess requires a conversion of the internal energy of the guest molecule into thedelocalized phonons of the lattice, and this is greatly facilitated if the transitionrequires a rearrangement of the lattice atoms. The geometry of the guest solvation andof the lattice cage depends on the electronic properties of the guest, and is in generaldifferent for different electronic states, but is usually little affected by a change in thevibrational quantum number within a given electronic state. The resolvation requiredto accommodate a transition of a guest from one electronic state to another providesthe electronphonon coupling necessary to dissipate the intramolecular energy into

the delocalized lattice phonons. The same change in geometry which leads to intensephonon sidebands (and a large coupling parameter S

) in an optical transition also

facilitates the simultaneous generation of a large number of phonons needed to absorbthe energy gap in a nonradiative process.

For pure vibrational transitions the coupling is weak, as can be deduced from IR orRaman spectra which typically show only sharp ZPLs, and virtually no phononsidebands. Conversely, electronic transitions in the matrix often exhibit intensephonon sidebands, indicative of a much stronger electronphonon coupling. This hasthe consequence that, in the matrix, transitions between vibrational levels of different

electronic states are often much more efficient than intrastate relaxation within thevibrational manifold of a given excited state. One then observes a relaxation cascadeinvolving vibrational levels of several electronic states. A very clear, well-studiedexample of such a cascade process is the CN radical, where at lower energies therelaxation is governed by internal conversions between the levels of the A excitedstate and the X ground state.Analysis of the data revealed that the rates of theinternal conversions can be well reproduced by a simple theoretical model taking intoaccount the intramolecular FranckCondon factors v v, the energy gap E

,

and the strength of the electronphonon couplingS

.

The gas phase selection rules are often modified in matrices, and in particular theimportance of the spin in matrix nonradiative processes is greatly reduced. Theinterelectronic cascade process therefore often prevails over direct multiphonon relax-ation even when the states involved differ in their multiplicity. An early example ofsuch a case is C

, where the relaxation is governed by intersystem crossings between

the singlet and triplet manifolds. This process is so efficient that a consecutive absorp-tion of two visible photons actually populates the d

excited electronic states, and

leads to population inversion and a strong stimulated emissiononthed a

Swan bands transition, at higher energy than the pumping laser photons.

More recently, numerous further examples of such cascade processes have beenreported. A very suitable and intensively studied example is NO, which has severalinteresting features. Its spectroscopy both in the gas phase and in the matrix is wellunderstood, and the relative state energies are well known. The molecule has a doubletground state, and several relatively low-lying excited states, both doublet and quartet.Besides valence states, it also has Rydberg excited states in an experimentally readilyaccessible spectral region. The matrix spectroscopy of NO has recently been ex-




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plored in a series of thorough studies by Chergui and co-workers.These investiga-tors have also employed monochromatized synchrotron radiation to examine thepattern of NO fluorescence following excitation ofv 04 b levels, as well as ofseveral levels of the Bstate.

The difficulties of direct excitation of the high B state levels of NO from theground state, resulting from poor FranckCondon factors and from the overlap withthe broad A Rydberg absorptions, were circumvented by Dubost and co-workers.They took advantage of the ladder climbing mechanisms described above to populatehigh ground state vibrational levels (up to v 27), and then used a pulsed tunable dyelaser to excite selectively thev 06 B vibrational levels.With the help ofthese experiments it was possible to map the energy flow between the excited states,and establish that the relaxation proceedsvia a cascade involving vibrational mani-folds of the electronic states present in this region: B , b , a , and A .

Bachir et al. have analysed the results with a theoretical model similar to thatused for the CN relaxation, with the rates being computed fromK 4c/Av veS/N!, where A is the electronic interstate coupling el-ement,v vrepresents the intramolecular FranckCondon factors, and the termin the braces represents the phonon FranckCondon factor. HereNE/is theorder of the multiphonon process, that is the number of phonons needed to dissipatethe energy gapE. The authors conclude that the agreement with the experimentaldata is only semiquantitative, and that, in particular when either the intramolecularFranckCondon factors are very small ( 10) or the energy gap is large

(E 400cm), significant deviations from the model do occur.The authors also find that the ladder climbing process also leads to electronic

fluorescence, and eventually dissociation of the NO molecule. A careful analysis of thedata shows that this is, however, in this case not due to an intramolecular conversion ofvibrational energy into electronic energy, that is to the inverse of the processesdescribed in the case of CN or that which occurs between the excited states of NO. Theprocess responsible for the electronic excitation is found to be an intermolecular,nearly resonant energy transfer of the type:

NO(X,v)

NO(X,v)NO(X,v

n)

NO(B,v)

(E)In such a process several quanta of vibrational energy are exchanged en bloc

between two molecules, both of them vibrationally excited, leading either to furthervibrational excitation, or as shown above to electronic excitation, and perhaps com-plete dissociation. While the stronger localization of the NO molecules with anincreasing value ofvwill counteract this type of transfer process, they are assisted bythe significantly increased strengths of the dipoledipole interactions with increasingv, and by the near resonant nature (E 0) of selected transitions.

The interelectronic cascade relaxation was observed in a number of other molecular

species, including O, S, SO, Pb, and many others. Compounds of transition metalswith their open d-electron shells in particular have a very complex electronic structure,with a multitude of low-lying electronic states, and WO represents an interestingrecently investigated case in point. The molecule has numerous excited electronicstates in the visible, which can be easily selectively excited by tunable lasers.Onefinds that the relaxation in this region involves manifolds of numerous electronicstates, and proceeds via an interelectronic cascade, until the lowest excited state




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Fig. 3 The right-hand inset shows part of the potential energy diagram of WO.Following electronic excitation a nonradiative interelectronic relaxation cascadepopulates the lowest levels of the astate, from which thev 7 and 8 levels of theground state are reached. Further relaxation in the ground state proceeds by infraredradiation. The spectrum taken with an InSb detector shows the v 2 overtonesequence. Thev 1 fundamental emission near 1000 cm can also be observedwith a HgCdTe detector. The inset on the left shows the isotopic structure of one of thevibronic bands. The origin of the splitting of all the vibrational bands ofWO is notunderstood.

located in the NIR near 7500 cm is reached, which based on theoretical prediction isprobably an astate. As shown schematically in the inset of Fig. 3, from the lowestvibrational levels of this state the relaxing molecules cross into thev 7 or 8 levels ofthe ground state. Since the interstate cascade path is now closed, further relaxationproceeds radiatively down the ground state vibrational manifold, as exemplified by thespectrum of the Fig. 3, showing the v 2 overtone infrared fluorescence. Thegeneral conclusion is that whenever two or more electronic states are available in theregion of interest, unless either the molecular FranckCondon factors and the inter-

state coupling are quite unfavourable, or the vibrational frequency is quite low, theinterstate relaxation is likely to prevail over direct multiphonon vibrational relaxation.Such an interstate cascade is controlled by accidental, isotopically dependent nearresonances, with the rates being at least semiquantitatively determined by the energygap law modulated by the intramolecular FranckCondon factors.




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2.8 Relaxation processes in polyatomic molecules

Much of what was said above for multiphonon relaxation of diatomics hold also forpolyatomic molecules. In these the density of states is naturally, in view of the presence

of low-frequency bending and deformation modes, considerably higher than in dia-tomic molecules, and the relaxation processes are accordingly higher. Furthermore,one has to deal with additional processes, such as mode-to-mode energy transfer, andintramolecular vibrational energy redistribution. In view of the, in general, fasterprocesses and larger complexity, studies of relaxation in polyatomics are more diffi-cult. This topic has been dealt with several times previously, in particular in the ablereview by Dubost and Legay.

Laster-induced fluorescence techniques allow relaxation studies in excited elec-tronic states, and such studies were carried out for several triatomic radicals,as well

as for several fluorinated benzene cations, and larger organic molecules. Incontrast with diatomics, in view of the more efficient intrastate relaxation the crossingto different electronic states is of less importance. Relaxation most often proceedswithin the vibrational manifold of a given electronic state, with nonradiative crossingto other electronic states then possibly taking place in the relaxed molecule from thevibrationless level of the excited state. One also finds that for low levels of excitation,up to about 0.5 eV, the vibrational energy redistribution may be nonstatistical, withthe relaxation proceeding by specific pathways determined by the intramolecularintermode coupling. In particular, where strong coupling due for instance to Fermi

resonance is present in the free molecule, the relaxation rates in the matrix (as well as ofcollisional relaxation in the gas phase) are greatly enhanced, often by many orders ofmagnitude.

A further general observation is that everything else being the same, molecules oflow symmetry relax faster than comparable, more symmetric species, with vibrationalrelaxation in for instance the C

symmetry 1,2,4C

H

F

cation being much fasterthan in the symmetricD

1,3,5C

HF

isomer. This is undoubtedly due to the effectof symmetry on the intermode coupling. Furthermore, relaxation is found to be lessefficient in rigid molecules than in floppy ones and, as mentioned above, the introduc-

tion of a freely rotating methyl group can often result in an enhancement of the rate ofrelaxation by more than an order of magnitude.

In view of the fact that interstate cascades, which are often important in diatomicmolecules, are much less common in polyatomics, there is also less difference betweenrelaxation in the excited electronic states and that of the ground state. The lack ofavailability of broadly tunable infrared sources also makes studies of ground staterelaxation still more difficult. In early work, coincidences with fixed frequency laserlines were often exploited. For instance Abouaf-Marguin and co-workershaveused CO

laser lines in a series of elegant studies of NH

and CH

F already mentioned

above. Tunable Nd-Yag pumped OPOs can reach the higher vibrational levels or thehigh frequency hydride stretching modes, and were used in several thorough studies byAbbate and Moore who examined the relaxation of several isotopic species of HCN,and explored also the dependence of the rates on matrix material, temperature, andconcentration.While free electron lasers, which have increasingly become avail-able in the last few years, provide in principle intense, broadly tunable sources ofradiation, they have thus far only sporadically been used for studies of matrix relax-




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ation processes.In general one finds that the relaxation of the lowest frequency level of a polyatomic

molecule is in principle not much different from the relaxation of a diatomic moleculewith a similar frequency. The relaxation at higher energies is governed by the energy

gap law, but is also strongly modulated by intermolecular intermode coupling. Atenergy levels typically above a few thousand cmthe density of states becomes verylarge, and the level spacing small compared with the phonon frequencies of the lattice,and the relaxation becomes statistical. One usually observes a homogeneous broaden-ing of all the vibrational levels due to a rapid intermolecular vibrational energyredistribution (IVR).

2.9 Stimulated emission in matrices

The solid rare-gas medium, transparent from far infrared into vacuum UV provides avery favourable medium for the observation of stimulated emission. Several circum-stances facilitate establishing an inverted population and increase the gain available inthe solid medium, as compared with the gas phase system. In general, the density of themolecular guests in the solid can be quite high and, at the low temperatures of typically410 K, all molecules are in the zero point level. At the moment when a molecule isexcited, there therefore automatically exists population inversion between the pumpedlevel and all the levels below it with the exception of the ground state. Furthermore, theabsence of rotational dilution, and the sharpness of the individual transitions favour

and increase the available gain, which is thus much easier to establish in the matrixthan in a gas phase system.

The presence of stimulated emission in the matrix is therefore not uncommon, andhas been observed in a number of molecules. As previously noted, the C

molecule is an

early example, where strong stimulated electronic emission was observed. A consecu-tive absorption of two red photons resulted in a strong population inversion on thed

a

Swan band transition, and a strong blue stimulated emission.

Stimulated emission is mostly easy to diagnose, since it exhibits a clear thresholdbehaviour, with the character of the emission changing drastically when the pumping

efficiency is raised above this threshold, as can be exemplified on the case of C.(a) Below the threshold the spectral distribution of emission from a given level is

governed by the FranckCondon factors, while above it the bulk of intensity shifts intoa single vibronic transition, often with a several orders of magnitude increase in itsintensity.

(b) While below the threshold the line widths are 45 cm, above it they narrowand become limited by the experimental resolution of 1 cm.

(c) The emission is anisotropic, and in the case of C

where the reflection from the Ptmirror substrate provided feedback it was oriented perpendicular to its surface.

(d) The time-dependent profile of the emission above the threshold is nonexponen-tial, consisting of a spike due to the stimulated emission, followed by an exponentialdecay.

A similar electronic stimulated emission was observed for a number of othermolecules, including CN, NCO, and several metal oxides. In studies of lifetimes andnonradiative relaxation processes this can, in fact, be a problem since the stimulatedemission distorts the relaxation process. One therefore has to reduce the pumping rates




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and specifically take care to avoid stimulated emission and lasing.Similarly, given efficient pumping of higher vibrational levelsovertone or combi-

nation bandsin the matrix, stimulated emission can also take place in the infrared onvibrational transitions. Dubost and co-workers have excited matrix-isolated CO or

NO molecules using a Li-KCl colour centre laser tuned to the v 2 overtone transi-tion, with ladder climbing processes populating levels up to v 30. They found thatthe observed kinetics of the system could only be satisfactorily modelled by assuming av 2 1 relaxation by stimulated emission.The fluorescence was indeed found toexhibit an unusual time profile with a short spike, indicating that stimulated emissionwas occurring.

Even more favourable from the point of view of stimulated emission may be smallpolyatomic molecules, which possess relatively low-lying frequency bending or defor-mation frequencies, which are more effectively depopulated than high frequency

stretching modes. With a rapidly relaxing lower level, it is easier to maintain thepopulation inversion and sustained stimulated emission. Abouaf-Marguin and co-workers have excited the

combination band of ozone by a tunable infrared

source, using frequency difference generation between an Nd-Yag and a dye laser in aLiNbO

crystal. A fast relaxation populating the nearby 2

level is then followed by

2

stimulated emission.Free electron lasers also provide convenient, in-

tense and broadly tunable sources of infrared radiation, and this was recently used byChabbi et al. to pump the

level of CO

in solid argon. They observed a strong

stimulated emission in the 16m region, corresponding to transitions between the

, 3and, 2Fermi resonant doublets, as well as from the lower frequencydoublet into the

level. These same transitions are, in fact, also well known to lase in

the gas phase.While lasers operating on vibrational transitions of matrix-isolated molecules are

not very likely to lead to useful devices, lasers operating on electronic transitions in theinfrared could prove more interesting. Atoms and ions of metals, and in particulartransition metals, often possess numerous low-lying electronic states. These states areoften metastable and exhibit long lifetimes, which should make it easy to establishpopulation inversion. Furthermore, if two such states arise from different electronic

configurations, the transitions between them frequently exhibit large homogeneousbroadening. Such transitions, with phonon sidebands extending over several hundredwavenumbers, might make it possible to generate widely tunable infrared radiation.

3 Photochemistry, dissociation, and matrix cage effect

Excitation of a small gas phase molecule above its dissociation limit may haveessentially only two outcomes: either the excited state is stable and the moleculefluoresces back into the ground state, or it irreversibly dissociates. The matrix cage hasa substantial effect upon the dynamics of the isolated molecule, and often preventsdissociation even when a considerable excess of energy is available. This may appearsomewhat surprising if one imagines that, e.g., a hydrogen atom with 2eV kineticenergy is moving at some 20kms, corresponding to a temperature of nearly25 000 K. In spite of that, one finds direct dissociation and ballistic exit of the frag-ments from the cage is a rather uncommon event, and the variety of possible outcomes




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is greatly increased.(a) Due to the cage effect, the molecule may relax into the ground state.(b) The molecule may transiently dissociate, and recombine to form an isomer.(c) The molecule may dissociate, resulting in fragments trapped in the same cage.

(d) One of the fragments may succeed in exiting the cage, leading to permanentdissociation.

(e) The molecule may react with the matrix cage.

All of these processes can be, and have been, investigated in detail in matrices, andwe will deal with them in the following sections.

3.1 Geminate cage recombination

Most commonly one observes that the cage effect prevents, especially for heavierfragments, permanent dissociation, and the molecule relaxes nonradiatively and re-turns eventually back into the ground state. In the adiabatic sense the barrier todissociation is typically low, since the binding of the rare-gas atoms is weak, and verylittle energies are needed for their displacement. In equilibrium, naturally,E/q

0

and one can, with relatively little energy, significantly enlarge the cage exit, if oneallows the distortion to propagate far into the matrix. It may be noted that an excessenergy of 2 eV deposited in a typical 10 K matrix can melt more than 200 Ne, 45Ar,35 Kr and 23 Xe atoms. One may thus contemplate a process in which in the excited

molecule repeatedly dissociates and recombines, with the fragments transferring theirexcess energy in collisions with the atoms. This would result in loosening the cage,and an eventual delayed fragment exit.

In spite of that, one mostly observes that even with a considerable energy excess thedissociation quantum yields are vanishingly small.For instance for Cl

and ICl in

solid argon and krypton upper limits of10 were found for permanent dissociationwith energies up to 2.5 eV. The fact that no such local melting takes place is alsoevidenced by the observation that even for excitation with 2 eV excess of energy abovethe gas phase dissociation limit, the Cl

fluorescence remains polarized, with a ratio of

I 0.7. This is close to what is expected for a nonrotating molecule,and indicates

that during the transient dissociationcage recombination process, vibrational andelectronic relaxation into the long-lived emitting A

state, as well as during the

subsequent time preceding the radiative decay, the molecules have not changed theirorientation. Similar observations of polarized fluorescence following cage recombina-tion were also made for ICl and other species.

A lack of permanent dissociation was observed for numerous other molecules,including I

,Br

as well as ICNand O

. The dissociation event can be

viewed as a collisionof the dissociating fragments with one or several of the cage atoms,transferring to them part of their kinetic energy. If the energy is not sufficient to force animmediate, ballistic cage exit, the fragment atoms rebound, reforming the molecule,while the kinetic energy which the cage atoms have gained is in turn transferred to themore remote atoms in the second and further solvation shells. Since in each dissocia-tionrecombinationevent the molecule loses a substantial fraction of the initial energy,the fragments typically have only few chances to exit the lattice cage. The energypropagates rapidly from the lattice site, preventing local melting of the solid.




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Interestingly, if the atomic states produced in the dissociation process correlate withexcited molecular states, these states rather than the ground state may be populated inthe recombination.This provides a useful and often employed method for reachinginto the matrix states which are, because of selection rules, not directly accessible in

absorption from the ground state. Examples are the A 2 states of halogens, or forinstance triplet states of metal dimers like Cu

or Mo

.

3.2 Dissociation with cage exit

While for small and moderate excess energy in the 12 eV range perfect caging is morea rule than an exception, there is also a number of systems where a rather efficientdissociation in the solid was found. The most prominent and general exceptioninvolves hydrides and hydrogen atoms. In contrast to heavier atoms, H atoms often

exit the lattice cage with relative ease, and this fact has been frequently exploited as avery useful method for generating a variety of transient species in the matrix. When aspecific unstable molecule or radical is desired, one deposits a suitable precursorcontaining the same heavy atom configuration, with one or more additional hydrogenatoms. UV photolysis then usually leaves the heavy atom configuration unchanged,but the hydrogen atom or atoms which are able to exit the cage are removed. Thus C

and C

are produced by photolysis of acetylene,allene or methyl acetylene yield

C

, and NCO and CNO can be generated by photolyzing HNCO and HCNO,respectively.

This facile cage exit of hydrogen atoms is due to several reasons. In the first place, thedissociation of a XH molecule imparts most of the energy to the light atom, which alsoloses the energy much less readily than the heavier atoms. As an example, upon Cl

dissociation each of the Cl (mass 35 u) atoms will receive half of the available excessenergy, and will lose about half of it in each collision with an argon lattice atom (mass40 u). It thus has virtually no chance of exit, unless this happens directly, or at leastwithin the first few collisions, or unless it has enough energy to actually fully displacethe lattice atoms, and completely disrupt the cage.

On the other hand, the hydrogen atom upon dissociation of HCl will receive most of

the excess energy, and lose only about 3% of it on each collision. It will thus require anumber of collisions before an appreciable fraction of the initial kinetic energy is lost.There is thus an increased possibility of a substantially delayed exit after a number ofunsuccessful attempts. Furthermore, the barrier to cage exit will typically be muchhigher for the heavier atoms than for the small and compact hydrogen. Finally,quantum mechanical tunnelling may be of importance for light atoms, and in particu-lar hydrogen. These cage effects on photodissociation have been more quantitativelydiscussed by Tarasovaet al.,who predict an increased possibility of local melting inhydrides where the energy is more slowly released into the lattice. They also concludethat the local heating is, particularly in argon, dependent on the bulk temperature.They suggest that the decrease in thermal conductivity with temperatures will enhancethe local melting and dissociation quantum yield. Experimentally, however, no tem-perature effect is found,and the local melting model was disputed by Cenianetal., who propose a rapid shock-wave-like propagation of the energy away from thetrapping site, preventing local melting.

Schwentner and co-workers have carried out a series of thorough investigations of




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the dissociation of diatomic HCl, as well as of H

O, and their deuteratedanalogues in rare-gas solids. They irradiated the matrices containing H

O

with dispersed synchrotron radiation (BESSY), and monitored the OH produced bylaser-induced fluorescence. For both matrices they found a nearly identical dissocia-

tion threshold near 6.9eV, with only a slightly higher value for DO. This result,combined with theD

value of 5.118eV for water molecules in the gas phase, would

place an upper limit on a matrix-induced barrier of about 1.8 eV. Chenget al.havemore recently carried out very similar experiments, and established a nearly identicalHO photodissociation threshold in solid neon of 6.87 0.02 eV. A careful examin-

ation of the results revealed, however, that the 6.9 eV dissociation threshold alsocoincides with the onset of absorption, so that little could be said about the actualbarrier height in the matrix. The photodissociation of H

Sand of other hydrides

was also studied.

Also important in the dissociation process is the initial alignment of the molecule. Ifone considers a substitutional impurity in an otherwise perfect rare-gas lattice, thelowest energy dissociation pathway passes through the centre of an equilateral triangleformed by the three nearest neighbour atoms of the lattice cage. A molecule orientedtowards the lattice atoms will obviously have a smaller chance of exiting the cage thanwhen it is appropriately oriented in the direction of the lowest barrier path. A niceexample demonstrating this point and explored in a series of careful investigations byApkarian and co-workers is molecular fluorine. An efficient dissociation hasbeen found for F

in solid argon and krypton, where the minimum energy configur-

ation has the fluorines properly oriented for the lowest energy cage exit. Above 2.5 eVexcess energy, the yield for cavity exit is essentially unity, in essential agreement withclassical molecular dynamics simulations.What is interesting is in this case isthe observed anomalous temperature dependence, with the photodissociation prob-ability decreasing with increasing temperature. At increased temperatures the fluorinerotates freely, destroying the appropriate alignment, as observed experimentally andconfirmed by theoretical simulations.A contributing factor to the rate decreasewith temperature may be due to the destruction of the alignment of the channelsthrough the lattice, and scattering of the propagating atoms caused by lattice vibra-

tions.

3.3 Forced cavity exit

The complete caging discussed for instance for Clrefers to experiments carried out

with typical sources available in the laboratory, such as xenon, mercury or halogenlamps, where the intensities are weak to moderate, and where the photon energiesusually do not exceed 67 eV. Considering typical chemical bond energies, this leavesonly a moderate energy excess of 23 eV. In cases where a much larger energy excess isavailable, the exciting fragment can force its way out of the matrix cage. This is, in factwell known to anyone who has worked with vacuum UV sources such as -Lyman orthe argon or krypton resonance lamps, with photon energies of 1012 eV. One of theproblems with the use of such sources is the radiation damage they induce even in thestrongly bound salt (LiF or MgF

) windows used, and the defect centres which often

rapidly reduce their transparency, and thus limits the efficiency of the lamp. Thefragment from molecules excited in this energy range possess enough kinetic energy to




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force impulsively cage exit. The same is, of course, true for very intense, short-pulsedlaser sources, where again a consecutive absorption of several photons can provideenough energy to overcome the cage effect.

The currently available broadly tunable VUV synchrotron sources provide ideal

means for quantitative studies of such a forced cage exit and its efficiency as a functionof photon energy, matrix material, and temperature.A series of elegant studies ofthis nature was carried out by the group of Schwentner, as well as several otherinvestigators. Kunz et al. irradiated their molecular Cl

containing matrices

with monochromatic VUV, and determined the extent of permanent dissociation byexciting the Cl atoms at 168 nm and monitoring the Ar

Cl emission at 260 nm. In their

reinvestigation of Cl

in argon they found, in agreement with the previous investiga-tion,that excitation of the repulsive

continuum near 3300, with excess

energies of 12 eV, results in no observable permanent dissociation. A relatively sharp,

weak permanent dissociation threshold is detected at 6.2 eV, that is with an energyexcess of about 3.7 eV. Dissociation with a low, about 10, quantum efficiencypersists throughout the range up to 9.2 eV, where a much stronger threshold isobserved. Excitation above this threshold, due to a well-known electronic transition ofmolecular chlorine centred near 130 nm, leads to a much more efficient permanentdissociation, and the authors estimate the quantum yield in this region to be about30%. Interestingly, the authors find that the quantum yield associated with the lowerenergy threshold is strongly dependent on the quality and morphology of the sample,and is increased considerably in samples rapidly deposited at low substrate tempera-

tures.

3.4 Permanent dissociation within the matrix cage

If the activation barrier for reformation of the photolyzed molecule is not zero, thefragments which failed to exit the cage may lose their energy and remain in the originalcage. Examples of such cases where at least one of the fragments is a stable moleculeabound in the literature. Thus the photolysis of cyanogen azide, NCN

, in a rare-gas

matrix yields first NCN and CNN species,with a second photolysis step yielding acarbon atom with, presumably, two N

neighbours. The CNN produced in this way in

an argon matrix is trapped next to a N

molecule, and exhibits IR absorptions at 1241and 2847cm, intermediate between their positions in pure argon (1235 and2828cm) and pure neon (1252 and 2856 cm). Binary complexes, dimers, or trimerscan often be cleanly prepared by this method.

An interesting case is the matrix photochemistry of the H

O

molecule, in which thedominant primary step is fragmentation into two OH radicals.If both of them failto exit the cage, they can either recombine back to peroxide or form a H

OO complex,

that is a water molecule trapped next to an oxygen atom. While continued irradiationat 230 nm was also found to photolyze this complex, so that ultimately only OHradicals remained apparently as the stable photoproducts, irradiation of the H

OO

complex with 250 350 nm resulted in regeneration of the peroxide. This processmight be of considerable interest in environmental and atmospheric chemistry.




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3.5 Cage isomerization

It is well known that the cage effect, and the lack of permanent dissociation, can beused to excite optically matrix-isolated species and accomplish their isomerization.

Perhaps the first study of cage dissociationrecombination appeared in 1963, whenMilligan and Jacox irradiated, in matrices, HCNand later also XCNspecies togenerate the corresponding XNC isomers. The ICN dissociation was studied exten-sively in molecular beams, and it became one of the first reactions to be studied byfemtosecond techniques.Haas and co-workers have investigated in detail theisomerization of ICN in low-temperature matrices.They find that upon irradi-ation of the matrix-isolated ICN with a low pressure mercury lamp at 253.7 nm there isnegligible permanent dissociation, but the growth of an absorption at 2057.5cm dueto INC indicates that isomerization takes place. Only about 2.6% of the ICN mol-

ecules can be isomerized in this way, suggesting that this corresponds to a photo-stationary state at this wavelength. Irradiation of the 253.7nm photolyzed samples at388 nm, where the ICN molecule does not absorb, results in a complete disappearanceof INC, presumably due to its reconversion into the more stable ICN isomer.

The isomerization in matrices due to rotation of the CN group in the lattice cageappears quite general. Thus CNO, when excited into an excited electronic state in thenear infrared, is found to isomerize readily into NCO,NCN isomerizes to CNN,and even fulminic acid, HCNO, is converted into HNCO. In addition, organicnitriles are converted efficiently into the corresponding isonitriles. Thus, irradiation of

dicyanoacetylene, NCCCCN at 235nm results in its efficient conversion intoCNCCCN and eventually CNCCNC, isomerizing both of the nitrile groups.The same authors also attempted without success to isomerize longer chain dinitriles,including dicyanodiacetylene. This was, however, recently accomplished using theshorter wavelength and intense ArF excimer laser source by Kolos, who recentlyidentified the NCCCCCNC isomerization product.

The power of todays ab initio computational methods has been vividly demon-strated on this problem of nitrile isomerization. The product identification has in allcases be confirmed with the help of state-of-the-art ab initio calculations by Bot-

schwina and co-workers.These computations predicted amazingly well notonly the vibrational frequencies of the products, but also the relative intensities of theinfrared absorptions, as well as the remarkable, more than hundred-fold increase in theabsorption cross-sections which accompanies isomerization of the nitriles to isonit-riles. The computations also predicted not only the fundamental frequencies, but alsothe intensities of the combination bands and overtones. In fact, all such combinationbands predicted by the computation to be strong could actually be found experimen-tally, while those predicted to be weak were missing.

The facile rotation of the relatively nonpolar CN radical during the dissociation

process is perhaps not surprising. One might note in this connection that the barrier tofree rotation of matrix-isolated CN is quite low, and the CN infrared emission spectraexhibit, in matrices, a well-resolved rotational structure, indicating little perturbationby the solid medium. Also, the laser-induced fluorescence of the CN radical is, unlikethat of, for instance, halogens, almost completely depolarized, indicating that also theexcited electronic states undergo free rotation, or at least change the molecularorientation on the timescale of the upper state radiative lifetime.




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Chlorine dioxide is another example of cage isomerization observed already in theearly days of matrix spectroscopy in Pimentels group. In 1967, Rochkind and Pimen-tel as well as Arkell and Schwager reported that photolysis of the symmetric OClOmolecule results in its isomerization to the asymmetric ClOO species.In more

recent years there has been a renewed interest in this and similar systems in viewof the importance of halogens and their oxides in stratospheric chemistry, and in thecatalytic destruction of ozone. This OClOClOO system was very recently reinves-tigated in detail by Y. P. Lee and co-workersusing a Fourier transform spec-trometer with the help of both absorption spectroscopy and, following selective laserexcitation, fluorescence. The quantum yield of the fluorescence is low, since the lifetimeof the upper state is severely shortened due to predissociation. In view of the very fastpredissociation rate, vibrational relaxation cannot compete successfully, and mainlyvibrationally unrelaxed fluorescence from the directly excited low vibrational levels of

the A state levels is observed. As is usual in molecules of this type, vibrationalrelaxation is found to be more efficient for the lower frequency bending mode than forthe symmetric stretching mode

, so that, when the (0,1,0) bending level is excited, a

weak relaxed (O,O,O) fluorescence is also observable.Particularly interesting is the mode selectivity of the isomerization. Even though

levels involving overtones of the asymmetric stretching mode, 2

, are very weak in thespectrum, their excitation plays a prominent role in the isomerization process. Thus, insolid Ar, irradiation into the very weak (1,0,2) level results in a considerably moreefficient isomerization to ClOO than the almost an order of magnitude stronger

nearby (2,1,0) and (2,0,0) levels. This result appears consistent with the excited stateabinitiopotential surfaces of Peterson and Werner,which suggest a mode-selectivecouplingbetween the predissociating AA

state and the nearby C

symmetry

B

state, leading to predissociation to X ClO and O(P), whose cage recombina-tion may then produce the ClOO product.

The authors also observe interesting medium effects, with both the predissociationrate and the rate of isomerization being a factor of 23 higher in solid neon than inargon or krypton matrices. The situation is somewhat complicated by inhomogeneouseffects, with both OClO and ClOO occurring in several distinct matrix sites. There

appears to be a one-to-one relationship between the sites of the two molecules, with thephotolysis of an OClO molecule in a given site yielding ClOO in the correspondingsite. Part of this site selectivity appears to be lost when higher levels above (2,0,0) areexcited, possibly due to local melting or annealing as more energy becomes available.

3.6 Infrared-induced isomerizations in matrices

Quite soon after the development of matrix isolation it was realized that isomerizationprocesses do not necessarily require visible or UV light, but can be induced by aninfrared source of the infrared spectrometer, with several examples having beenobserved in the early studies in the Pimentel laboratory. Renewed interest in thisprocess emerged some twenty years later, with the fairly general observation that manycompounds or complexes which occur in the gas phase as mixtures of several intercon-verting conformers can in the matrix be isomerized, often just by the light of thespectrometer source.This is, for instance, the case with many linear-chain saturatedhydrocarbons, where rotation around a single bond, be it CC, CO, or CN, and




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transgauche isomerization occur. This was first observed for 2fluoroethanol, but hassince been detected in various compounds. The interest in this area arises from twosources.

In the first place, this easy isomerization, in conjunction with the capability of

modern instruments to carry out efficient spectral subtraction makes it possible toidentify small changes in the absorption bands, and assign them to the specific isomers.With broadband excitation the process usually does not proceed to completion but toa photostationary state. Using spectral subtraction one can, however, still compute thecomplete spectra of the individual conformers, a task which would be rather difficult todo in the gas phase. In this way, for instance, the spectra ofgaucheandtrans-butanecould be identified.

As a more recent example of application, in this way the cis-HCOOH has beenprepared, which is the higher energy rotamer of formic acid.In this case the barrier

is fairly high, and therefore the overtone of the OH stretch at 6934 cmwas pumpedby a tunable OPO. Unlike broadband irradiation, use of tunable infrared permitscomplete conversion. Furthermore, the use of the gentle IR radiation prevents thepossibility of decomposition and other competing processes. The infrared isomeriz-ation is not restricted to alkanes and molecules of this type, but may also occur inmatrix-isolated dimers and clusters. As an example, the HDO dimer forms twodifferent species bound eitherviaa proton or a deuteron, which differ by their spectraand can be interconverted by IR radiation.Again the band can be assigned with thehelp of spectral subtraction.

Another interesting system was recently examined by Rasanen and co-workers.They fou

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