Nesbitt JPhysChem1996

8/18/2019 Nesbitt JPhysChem1996

1/22

Vibrational Energy Flow in Highly Excited Molecules: Role of Intramolecular Vibrationa

Redistribution

David J. Nesbitt*,†

Department of Chemistry and Biochemistry, UniV ersity of Colorado and JILA, National Institute for Standardand Technology and UniV ersity of Colorado, Boulder, Colorado 80309-0440

Robert W. Field Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

ReceiV ed: March 6, 1996; In Final Form: May 30, 1996 X

A pedagogical overview of intramolecular vibrational redistribution (IVR) phenomena in vibrationally excimolecules is presented. In the interest of focus and simplicity, the topics covered deal primarily with IVin the ground electronic state, relying on examples from the literature to illustrate key points. The experimentopics discussed attempt to sample systematically three different energy regimes on the full potential surfacorresponding to (i) “low”, e.g., moderate- to high-resolution vibrational spectroscopies, (ii) “intermediate.g., stimulated emission pumping and high overtone spectroscopies, and (iii) “high”, e.g., photofragmepredissociation dynamical spectroscopies. The interplay between experiment and theory is highlighted h

because it has facilitated enormous advances in the field over the past decade.

I. Introduction

At the very core of all fundamental chemical transformationsis the making and breaking of bonds, yet in most molecularsystems beyond simple diatomics this process has proven to beone of the most difficult and challenging to understanddynamically. The reason for this is intimately connected withthe nature of highly vibrationally excited states near dissociationand the importance of “intramolecular vibrational redistribution,”or IVR, toward which this review is addressed. The impact of IVR phenomena in all of chemistry1-9 can hardly be overstated

and is at the heart of any first principles description of rates of chemical reactions.10,11 Although particularly stunning progressin this field has recently been possible through technologicaladvances in both experiment and theory, an appreciation of theimportance of IVR is nearly as old as The Journal of PhysicalChemistry itself and therefore an eminently appropriate topicfor a pedagogical overview in this 100th-year issue.

One simple way to see why IVR and chemistry are sointimately connected is shown schematically in Figure 1, whichdisplays a typical reaction coordinate diagram for transformationbetween reactants and products. Near the regions of thepotential energy surface corresponding to reactants and products,motion of the nuclei is constrained near local minima, wherethe restoring forces for sufficiently small displacements are

purely quadratic. From such a “ball and spring” Hooke’s lawmodel of nuclear motion in rectilinear coordinates, we are ableto use normal mode analysis and simple quantum mechanicalideas to solve exactly for the appropriate linear combinationsof nuclear displacements, which correspond to perfectly “un-coupled” harmonic oscillators. Vibrational energy placed in oneor several of these oscillators therefore remains localized in agiven normal mode. From a time-domain perspective, there isno opportunity in a purely harmonic system for energy to flowfrom a collective excitation of oscillators into a specific low-frequency mode mimicking a weak bond. On the other hand,

as one systematically proceeds up in energy toward the topa barrier or out along some dissociation coordinate, tharmonic description begins to break down, both necessarand catastrophically. Consequently, as is true in many of most challenging fields of science, what we as chemists seto understand (i.e., bond breaking and chemical reactions) reon understanding the systematic “crumbling” of the origiparadigm, in this case for nuclear motion as a function of interenergy! Of course, the long-hoped-for “blessing” implicitthis “curse” is that IVR might therefore exhibit sufficisensitivity to molecular system, energy, and vibrational degof freedom to allow us to influence and/or control chemireaction pathways with laser light excitation. Even though thas been largely achieved for relatively small systems such

vibrationally excited triatomics,12-15 it is fair to say that suc

* To whom correspondence should be addressed.† Staff Member, Quantum Physics Division, National Institute of

Standards and Technology.X

Abstract published in Ad V ance ACS Abstracts, July 15, 1996.

Figure 1. Schematic potential energy cartoon indicating how neharmonic concepts of vibrational motion (which are often approprin the reagent and product well regions) necessarily break down intermediate stages in the chemical transformation, which is thus key reason why IVR phenomena play an ubiquitous role in chemis

127 J. Phys. Chem. 1996, 100, 12735-12756

S0022-3654(96)00698-3 CCC: $12.00 © 1996 American Chemical Society


2/22

goal has proven substantially more elusive in larger poly-atomics than perhaps was initially appreciated.

Since the key issues of IVR deal with vibrational behaviorat chemically significant energies, and which historically havebeen more easily accessed via visible/UV excitation, the fieldof IVR has received considerable stimulus from studies of electronically excited states.16-26 From laser-induced fluores-cence (LIF) studies, manifestations of IVR as a function of vibrational excitation in S1, T1, etc., have been extensively

investigated. Since the dynamics occur on electronically excitedsurfaces, however, there can also be additional interactions dueto nonadiabatic radiationless transitions such as internal conver-sion and intersystem crossing.19-21,27,28 Although of consider-able interest and importance in their own right,29-31 suchelectronic effects do not reflect intrinsic IVR dynamics. Thishas stimulated a particularly heightened interest in spectroscopicprobes of IVR phenomena exclusively in the ground electronicstate manifold, based on techniques such as high-overtonevibrational pumping,32-50 high-resolution IR absorption spec-troscopy in supersonic jets,51-71 and stimulated emission pump-ing (SEP) methods.72-82 Indeed, it is toward IVR dynamics inthe ground state that this review is primarily focused, althoughwe also consider relevant examples from the literature on

electronically excited states. Of equal importance in this reviewis the very exciting parallel theoretical efforts83-100 towardinterpreting these ground-state experimental results and, inparticular, attempts to develop a more predictiV e understandingof IVR. Our goal is an easily read introduction and overviewto IVR phenomena, accessible to people outside of the field,rather than an exhaustive summary aimed at experts. Thischoice always runs the risk of annoying our closest andmost valued colleagues, but in the spirit of this CentennialIssue and in the interest of pedagogy we feel such a risk worthtaking.

The organization of this review therefore is as follows.Section II establishes what is meant by IVR, zeroth-order modelsof the phenomenon, and the spectral and time-domain mani-

festations of this process. The next three sections discussselected experimental and theoretical studies of IVR, mostlyspectroscopic in nature, that correspond to three different energyregimes on the molecular potential surface. Specifically, sectionIII describes the effects of vibrational excitation relatively lowin the potential well, where high-resolution IR methods haveproven particularly powerful in probing relatively weak IVRmode couplings and correspondingly long-time IVR behavior.Section IV considers intermediate excitation of states progres-sively higher up the potential ladder, such as has been accessedvia high-overtone vibrational pumping or stimulated emissionpumping and dispersed fluorescence spectroscopies and whichcan sample much larger regions of the full potential surface.Section V addresses the manifestations of IVR in the high-

energy limit, where excitation can be above barriers to uni-molecular dissociation, isomerization, etc. Section VI discussesthe structural dependence of IVR and prospects of predictingor influencing IVR in specific molecular systems. Section VIIpresents some brief concluding remarks.

II. What Is IVR? A Pedagogical Tool Kit

A. Background. As physical chemists, it is natural for usto think of molecules as a collection of balls and springs. Weknow that if one spring were to be stretched and then suddenlyreleased, the initial bond-localized excitation would spreadquickly and in an apparently complex manner over the entiremolecular framework (see Figure 2); this is the essentialphenomenon of intramolecular V ibrational redistribution. Three

long-standing goals in the study of IVR have been (i) to find a

concise language to describe and quantify this complex intmolecular ballet, (ii) to predict the energy flow rates apathways for any imaginable initial excitation (i.e., dependenon excitation energies, type of bond(s) excited, excitattemporal profile, etc.), and (iii) to extract information about IVthat is encoded in both frequency- and time-domain experimenMore specifically, however, chemists are in the businessmaking and breaking chemical bonds. If it were possibleinsert a chemically significant amount of energy in one boand keep it there for a chemically relevant time, this could crewonderful possibilities for external manipulations of chemireactivity. Many such schemes have proven naive, yet dream of external control101-108 over chemical procescontinues to fuel the study of IVR. IVR has proven a woradversary!

Even though IVR is a simple and ubiquitous concept, italso extremely subtle and has been made even more difficby seemingly contradictory descriptions of the process. Tkey to this semantic difficulty is that the ball-and-spring pictof IVR is inherently dynamic, yet below the lowest dissociatlevel all molecules have sharp, well-resolved energy levelsmolecular eigenstates, which are inherently static. Even wh

an eigenstate, ψn, which belongs to an energy eigenvalue,

is written as a solution of the time-dependent Schrödinequation (for a time-independent H ˆ ),

the probability distribution, Ψ*Ψ, and all expectation valof dynamically relevant quantities (e.g., functions of positor momentum), ! Â", are time-independent. Simply stated, probabilities associated with molecular eigenstates do not mo

The motion associated with IVR arises because the localiinitial excitations in which we are interested are not eigenstaof the molecular Hamiltonian. However, any arbitrary inistate, Ψ(t )0), can always be expressed as a superpositionthese eigenstates

where

and for which the time evolution of this initial state is giventhe simple prescription

This non-eigenfunction does have a probability distribution t

Figure 2. Intuitive classical mechanical “ball and spring” model

IVR, indicating how a localized vibrational excitation inevitably spreover the entire molecular framework. A description of the detailed tscale and pathway for energy flow of an arbitrary localized vibratioexcitation (i.e., the dependence on both location and total excitatenergy) is the ultimate goal of any satisfactory model of IVR.

H ˆΨ(t ) ) ip∂Ψ

∂t ) E nψne

-i E nt /p (2

Ψ(0) ) #ciψi (2

ci t !ψi|Ψ(0)" (2

Ψ(t ) ) #i

ciψie-i E it /p (2

12736 J. Phys. Chem., Vol. 100, No. 31, 1996 Nesbitt and Fi


3/22

evolves in time, with the time-dependent probability distribution,P(Q,t ), given by

and a time-dependent autocorrelation given by

There are several commonly misunderstood points that shouldbe clarified with regard to the initially excited state. First of all, many spectroscopic studies of IVR are conducted with cw,nearly monochromatic lasers. These lasers typically exciteeigenstates; they neV er prepare the initially localized excitationwith which one associates a time-dependent relaxation. Infrequency-domain studies of IVR, it is from the frequencysplittings (related to E i) and relatiV e intensities (related to |ci|2)in a high-resolution spectrum that the nature of the initiallylocalized excitation and its subsequent dynamics are inferred.If this initially localized excitation were produced by a suitablelaser pulse, then the time-domain behavior of the autocorrelation!Ψ(t )|Ψ(0)" would be exactly predicted by the results from thesefrequency-domain experiments. A second point of clarificationis that such a short pulse (or pulse sequence) prepares a ratherspecial class of initially localized excitations, which by virtueof its special coupling to the external laser field is referred toas a “zero-order bright state” (ZOBS). Although called a “state”,a ZOBS is not a molecular eigenstate; it moves! Since ourpicture of what the initial vibrational motion looks like (seeFigure 2) is rather good at early times, the ZOBS is often labeledby 3 N - 6 vibrational and 3 rotational quantum numbers ( J ,K a, K c). However, most of these quantum numbers correspondto operators which may not commute with the exact molecularHamiltonian, from which the true eigenstates are obtained. Asa final note of caution, the same sets of quantum numbers areoften used to label both ZOBS and eigenstates. This labelingfor the eigenstates is, of course, approximate, but it is intendedto provide useful labels that express the dominant (or nominal)character of that eigenstate.

B. An Example. An explicit example may help solidifythese concepts. Consider, for example, a 2:1 bend-stretchanharmonic term in the potential energy functionV (Q1,Q2,...,Q3 N -6) ≡ V (Q), namely k 1,22 Q̂1Q̂22. In a productbasis of harmonic oscillator functions (i.e., our zero-orderpicture), this term will couple modes 1 and 2, following theselection rule 2∆V 1 ) -∆V 2 (with ∆V i ) 0 for all other normal

modes) by a matrix element that scales rigorously as109

Each vibrational basis state, which has the form

belongs rigorously to a set of 3 N - 6 vibrational quantumnumbers. These basis states are mixed by the bend-stretchanharmonic interaction to yield vibrational eigenstates, whichare perhaps misleadingly (but still usefully) labeled by the same

3 N - 6 vibrational quantum numbers. For the above example,

the |1,0" and |0,2" basis states mix to form the “|1,0"” and “|0eigenstates

In eqs 2.8a,b, θ is the mixing angle calculated from the ratio(i) the off-diagonal matrix element V ) !1,0| H ˆ |0,2" (obtainfrom eq 2.6) to (ii) the difference in zero-order energies,

by tan(2θ) ) V /∆. This is equivalent to solving the 2 ×secular determinant

which yields the true molecular eigenenergies

where E h° is the average of the zero-order energies, E h°( E °10 + E °02)/2.

Now suppose that we excite this molecule from its vibratioground state, |0,0", to the energy region of the ν1 fundamenby using a light pulse that is sufficiently short to overlap bthe E + r E °00 and E - r E °00 transitions, but not so short asoverlap other zero-order transitions such as ν2, 2ν1, 3ν2, eSuppose also that |1,0" is a “bright state” and |0,2" is a “dstate”; i.e., |1,0" r |0,0" (ν1) is an electric-dipole-allowinfrared transition, and the overtone transition |0,2"r |0,0" (2is forbidden (or so much weaker as to be negligible). At t )the system will therefore be in the ZOBS (for notatioconvenience we choose R ≡ sin(θ) and ∆ E ° > 0),

which will explicitly evolve in time according to

Since we are interested in energy flow out of the initial ZOBa particularly relevant quantity to consider is the square moduof the time-dependent overlap (or autocorrelation) of Ψ(t ) wΨ(t )0), given by

where ω ) ( E + - E -)/p. The system starts out with uprobability in |1,0" at t ) 0 and reaches a minimum probabiin |1,0" at t ) π /ω, given by

When θ ) π /4 (i.e., ∆ ) 0), the initial state mixing is compleand the system oscillates from the pure |1,0" state at t )2π /ω, . .., 2nπ /ω to the pure |0,2" state at t ) π /ω, (2n + 1)π /ω. This simple description correctly predicts early time dynamics observed in, for example, quantum bspectroscopies6,22-26,110,111 and isolated anharmonic resonanc

where only two states contribute to the time dependence. T

P(Q,t ) ) Ψ*(Q,t ) Ψ(Q,t ) ) #i

|ci|2|ψi(Q)|

2 +

#i> j

[cic j *ψi(Q)ψ j *(Q)ei( E j - E i)t /p + c.c.] (2.5a)

!Ψ(t )|Ψ(0)" ) #i

|ci|2e

i E it /p (2.5b)

!V 1-1,V 2|k 1,22Q̂1Q̂22|V 1,V 2-2" $ V 1

1/2[V 2(V 2 - 1)]

1/2(2.6)

Φ°V 1,...,v3 N -6(Q1,...,Q3 N -6) ) %

i)1

3 N -6

φV i(Qi) (2.7)

“|1,0"” ) cos(θ)|1,0" + sin(θ)|0,2" (2.

“|0,2"” ) -sin (θ)|1,0" + cos(θ)|0,2" (2.

∆ E ° ) E °10 - E °02 ) 2∆ (2.

E °V 1V 2) p[ω1(V 1 +

1/2) + ω2(V 2 +

1/2)] (2.9

| E °10 - E V V E °02 - E | ) 0 (2.

E ( ) ([∆2 + V 2]1/2 + E h° (2.

Ψ(0) ) |1,0" ) (1 - R2)1/2“|1,0"” - R“|0,2"” (2.

Ψ(t ) ) (1 - R2)1/2“|1,0"”e-i E +t /p - R“|0,2"”e-i E -t /p (2.

|!Ψ(t )|Ψ(0)"|2≡ P10,10(t ) ) [1 - 2R

2 + 2R4] +

2(1 - R2)R2 cos[( E + - E -)t /p] )

1 - (2R2 - 2R4)[1 - cos ωt ] (2.

P10,10(π /ω) ) 1 - 4(R2 - R4) ) cos2(2θ) (2.

Vibrational Energy Flow in Highly Excited Molecules J. Phys. Chem., Vol. 100, No. 31, 1996 127


4/22

can, of course, be generalized to dynamics in a state spaceconsisting of far more than two levels, where the timedependence is understandably more complicated but predictedby exactly the same formalism.

One particularly useful second limit to consider is that of adense manifold of nearly equally coupled levels, with an averagestate density, F, and root mean square off-diagonal matrixelement, !V 2"1/2. In this limit, the square modulus of theautocorrelation |!Ψ(t )|Ψ(t )0)"|2 decays approximately29 as e-Γt ,

with an exponential rate Γ

given by the Fermi Golden Ruleexpression112

Many authors make distinctions between dynamics in a low-dimension state space (quantum beats, simple anharmonicresonances, restricted IVR) and a high-dimension state space(multiple overlapping resonances, dissipative IVR, quantumchaos); for the purposes of this discussion, we will not makesuch distinctions.

In summary, the simplest way of describing the dynamics of IVR is therefore (i) a short-pulse excitation prepares the systemin a ZOBS, (ii) the nature of the ZOBS is determined by the

nature of the preparation process, and (iii) the dynamics aremost readily seen as motion in state space (periodic or morecomplicated), rather than the 3 N atomic coordinates and 3 N momenta in phase space. (iv) This motion is described byFourier components corresponding to eigenenergy differences[ωij ≡ ( E i - E j )/p] and amplitudes corresponding to productsof mixing coefficients, which in principle can be obtained fromeither frequency- or time-domain studies.

C. Generic Classes of Bright States. For each molecule,an infinite number of initial states, Ψ(0), with nearly the samevalue of ! E " could be prepared, with these initial preparationsexhibiting quantitatively and qualitatively different dynamics.However, the experimentalist either cannot or does not havethe time to look at more than a few of these possible Ψ(0) initial

states; the goal is to learn enough about V (Q) to have apredictably robust theory, i.e., so that consideration of asufficiently similar initial excitation will result in no largesurprises. The choice of Ψ(0) is usually dictated by the natureof the excitation scheme. Historically, these have come in threegeneric categories: (i) direct vibrational excitation, (ii) Franck-Condon pumping via an electronic transition, and (iii) two-steppumping. A wide variety of such schemes exist, and manyexploit supersonic jet cooling and/or double resonance toproduce excitation of a Ψ(0) with a single, rigorously knownvalue of each good quantum number, such as total angularmomentum and rovibronic symmetry.

One-photon direct V ibrational excitation selects a ZOBSwhich has the largest transition probability from the ground state

(i.e., |0") to any of the zero-order states in a specified energyregion. This selectivity is based on vibrational selection rulesfor transitions between basis states which are simple productsof 3 N - 6 normal mode (harmonic) oscillator states: stronginfrared transitions are ∆V i ) (1, fundamentals (and hot bands)for the normal modes (νi) in which the electric dipole moment, µ, varies with the normal coordinate displacement, ∂ µ/∂Qi * 0,and where ∆V j ) 0 for all other modes.113,114 When one allowsfor mechanical anharmonicity (the nonvanishing of third andhigher derivatives of V (Q) with respect to normal coordinates)and electronic anharmonicity (the nonvanishing of second andhigher derivatives of µ with respect to normal coordinates), thesevibrational selection rules relax to become propensity rules. Asa crude rule of thumb for hydride stretches,49,115 the intensities

of vibrational overtone and combination transitions are expo-

nentially decreasing functions of the total change of vibratioquantum number, ∆V ,

where

The drop-off for the first few quanta of excitation may be evsteeper115 by another factor of 10. This means that, in aspectral interval, the strongest vibrational transitions from |0" level will generally correspond to the smallest ∆V and greatest anharmonicity. Historically, the states most expmentally accessible by such direct pumping schemes have bethe highest frequency and most anharmonic modes, typicabuilt on fundamentals or overtones of an R-H stretch. Iworth noting that this essentially experimental constraint hled to a particular focus on IVR dynamics in H-stretching stawhich may or may not be representative of IVR in generalis therefore quite important that multiple resonance and Sschemes are now beginning to provide access to a much wi

region of the potential surface than the R-H stretches aloAnother example of the ZOBS concept is commonly seenweakly bound clusters,116-126 where even a fundamental vibtional excitation of the subunits often lies well above cluster’s dissociation limit. Therefore, the ZOBS is embeddin and coupled to the continuum of “dark” levels associawith the intermolecular bond dissociation coordinate. Hena classic measure of IVR is obtained via Fermi’s Golden R(eq 2.16) from the predissociation line width of the ZOBS afrom the widths of other features (associated with dark stawhere the intermolecular modes are below the dissociatthreshold) that borrow their spectral intensity from the ZOand their width from the intermolecular continuum. This kof experiment provides information about three classes

IVR: bright f dark, bright f continuum, and darkcontinuum. Since one of the key observables in such experiment is the width of features in the frequency-domspectrum or fluorescence decay rates in a time-domain expement, it is essential that each feature contain only a sinrotational transition (i.e., the feature is homogeneously broened). If several rotational transitions are unresolved (i.e., feature is inhomogeneously broadened), the effective line widoes not provide information unambiguously relevant to the IVdynamics. Double-resonance and/or supersonic jet rotatiocooling schemes are often essential to remove these inhomgeneities.

In molecular systems with bound electronic states, FrancCondon pumping followed by either dispersed fluorescence

stimulated emission pumping (SEP) can be used to probe IVin the ground state. For the initial vibronic excitation step, relative intensity pattern is determined by the Franck-Condprinciple. The Franck-Condon-active vibrational normal mo(those in which ∆V i * 0 transitions can be quite strong) those that correspond to large changes in equilibrium geome(∆Qie * 0), frequency (∆ωi * 0), and/or form of the normcoordinate.127 Due to changes in ground vs excited stpotential surface topography, the classes of vibrational staaccessible via Franck-Condon pumping are often quite differfrom those accessible via direct vibrational excitation. Fexample, in the acetylene X̃1Σg+ electronic ground state, infrared-active normal modes are the antisymmetric C-H stre(ν3&&) and the cis-bend (ν5&&); hence, the small-∆V propens

rule weighs heavily in favor of ZOBSs which are odd quan

Γ ) 2π !V 2" F (2.16)

intensity $ 10-∆V (2.1

∆V ≡ #k

|∆V k | (2.17



5/22

overtones or combination bands of ν3&& or ν5&& built on totallysymmetric modes. In contrast, the excited Ã state is trans-bent with a CdC double bond, whereas the X̃ state is linearwith a CtC triple bond; thus, for the Ã 1Au f X1Σg+ electronictransition, the strongly Franck-Condon-active modes are theC-C stretch (ν2&&) and the trans-bend (ν4&&). Consequently, bySEP from different vibrational levels in the intermediate Ã state,one can systematically vary the nature of the X̃ state ZOBS.This extra flexibility can provide new insights into IVR,

especially by separating spectrally overlapping features thatbelong to two different ZOBSs.78

Even greater flexibility in the ZOBS selection process canbe obtained via two-step pumping, based on either sequentialvibrational transition steps or the combination of a directvibrational and Franck-Condon pumping scheme. For ex-ample, in acetylene, if one were first to excite fundamentals orovertones in either the antisymmetric CH stretch (k quanta of ν3&&) or the cis-bend (r quanta of ν5&&), then Franck-Condonpumping would provide access to the large manifold of ZOBSsof the form

for arbitrary n, m. Similarly, in molecules with many nearlydegenerate bond-stretching modes (e.g., CH stretches in hydro-carbons), multiple-step pumping methods can be used to preparequalitatively different distributions of vibrational quanta at nearlythe same total energy. For example, in a molecule with twosuch modes, states with nν1 + mν2 quanta are more readilyaccessed by two-step overtone excitation,

Since the direct anharmonic coupling matrix elements betweenthe two modes, Q1k Q2l, scale as V 1k/2V 2l/2, one might expect theV 1/V 2 coupling effects to be most visible in a |V 1 ) 3, V 2 ) 3"

ZOBS than in either |V 1 ) 6, V 2 ) 0" or |V 1 ) 0, V 2 ) 6". Thiswould provide a particularly rigorous test of the possible stabilityof so-called “extreme motion states”, where the same totalenergy is predominantly localized in a specific bond as opposedto excitation of a mode which involves concerted motion of several nuclei distributed throughout the molecule.56,79-82

D. Choice of Basis Set. Is IVR a real phenomenon or onlya consequence of a poor choice of basis set? Since eigenstatesare stationary, one could argue that IVR disappears whenevera frequency-domain spectrum is recorded with resolutionsufficient to resolve individual eigenstates. However, thisargument is specious because our real-world experience withballs and springs tells us that the underlying dynamics is realand must somehow be reflected in an eigenstate spectrum. To

restrict one’s reality to the fully resolved transition frequenciesand relative intensities is like telling an X-ray crystallographerto stop with the diffraction pattern and not to think about themolecular structure encoded in it!

Ideally, we would know the exact V (Q) , which would providea basis for predicting the dynamics of any conceivable Ψ(0).However, an individual spectrum samples this full potentialenergy surface through a very narrow aperture and a highlydistorting lens. Thus, the study of IVR can be seen as an attemptto extract information about V (Q) by characterizing the dynam-ics of a small number of selectable ZOBSs. In order to do this,we need to choose an orthonormal basis set with which todescribe Ψ(t ). One choice of a basis set is the eigenstates, suchas revealed by a high-resolution experiment. More physically

useful is a basis set typically formed from products of individual

vibrational modes, which are related to the eigenstates byunknown unitary transformation that diagonalizes the molecuHamiltonian. These basis states could range from localibond modes, such as would arise in an internal coordintreatment, to the more delocalized modes from a full normmode analysis; the “optimum” choice for this non-eigenstbasis is dictated by the nature of the excitation process tprepares the ZOBS. Since the oscillator strength for overtoand Franck-Condon pumping physically arises from a localizinitial excitation, and one (in principle if not in fact) excitesthe ZOBS using a short pulse of light, Ψ(t )0) is sometimsimplest to represent in a localized bond mode product baset.128

IVR is frequently described in terms of tiers of these coup

zero-order states (Figure 3). The physical motivation for tis that the spectrum often naturally reveals hierarchistructures.83,84,129-133 At the coarsest level of structure is ZOBS itself. As spectral resolution is increased, the oscillastrength associated with the ZOBS fractionates into finer statsometimes called “feature” or “doorway” states. As oproceeds systematically from lower to higher resolution, oneable to see more and more states coupled to the ZOBS progressively weaker and weaker off-diagonal matrix elemeof the molecular H ˆ (expressed in the imperfectly known complete zero-order basis set).

Sometimes a hierarchical structure is very clear in spectrum. In such cases a tier structure will be very clear in

Typically, each additional tier corresponds to larger values∆V away from the ZOBS. For example, the first tier miinvolve a few strong cubic (∆V ) 3) and quartic (∆V )anharmonic coupling terms. The second tier would thlogically contain states coupled anharmonically to the first tstates (∆V e 8 with respect to the ZOBS) and so on outhigher orders. For J * 0, the tier structure would also haveinclude rotationally induced coupling terms due to Coriolis acentrifugal mixing of the basis states.

One could argue that arranging basis states into tiers isarbitrary and meaningless process. After all, if we do not knexplicitly how to define a basis set, how can we be sure ththe tiers reflect any real physics? The answer is easily stabut provides little guidance as to how to proceed. If

spectrum contains hierarchical structure, the tiers are real, a

Figure 3. Tier model for analysis of IVR. Energy typically sprefrom an initially localized state via strong, low-order anharmointeractions with a few near-degenerate basis states. These states in turn each coupled to a successive tier of near-degenerate basis stavia additional low-order resonances. The net effect is a hierarchcoupling scheme, sequential energy flow, and a progressive set of twith increasing density of states.|V 1&& ) 0, V 2&& ) n, V 3&& ) k , V 4&& ) m, V &&5 ) r"

|0,0"98∆V 1)n

|n,0"98∆V 2)m

|n,m"



6/22

it behooves us to figure out their physical basis. This is not aquestion of arbitrariness of basis sets related by unitarytransformations. The molecule is trying to tell us how todescribe the IVR process as a sequence of expansions into largerand larger regions of energetically and symmetry accessible statespace.

E. IVR Observables in the Frequency and Time Domain.

Frequency Domain. In a typical frequency-domain experiment,one attempts to observe and resolve the features that contribute

to a specific ZOBS. This ZOBS has an overall width, a count-able number of resolved features, an overall intensity, a distri-bution of level spacings, and a distribution of relative intensities.When the excitation energy is above the lowest dissociationlimit, each of the finest features can also have a measurablehomogeneous width. By sampling the ZOBS via severalpreselected J K aK c rotational levels, one can obtain rotationalconstants for the ZOBS, the feature states, and sometimes eventhe subfeature states. These rotational constants often permitassignment of vibrational quantum numbers. In addition, studiesof J K aK c dependence can also identify the coupling mechanismsas anharmonic vs Coriolis (a, b, or c type) vs centrifugal.

The information about IVR in a frequency-domain spectrum

can be reduced to a generic description or a mechanistic model.At the descriptive level one finds overall measures, such as ahierarchy of widths (or couplings) and a comparison of theobserved density of states to various model calculations of thetotal or restricted (e.g., including only a subset of normal modes)density of states of correct symmetry.134-136 One also findsstatistical measures such as level spacings and intensity distribu-tions (e.g., ∆3, Σ2, Brody, ¯ν2) and hierarchical measures (e.g.,parsimonious trees, complexity).137-139 At the mechanistic levelone finds an effective Hamiltonian model that describes all (ormost) of the level splittings and relative intensities associatedwith the ZOBS. This model is expressed in terms of a set of zero-order basis state energies and coupling terms, correspondingrespectively to diagonal and off-diagonal matrix elements of

H ˆ . The parameters that define this model are obtained by aleast-squares fit that minimizes differences between observedand calculated energies and relative intensities. Alternatively,some of these parameters may be obtained from ab initiopotentials or by transfer from similar molecules.

Time Domain. The ZOBS has a fast (envelope) decay rateand a countable number of quantum beat features, each withits own frequency, amplitude, phase, and decay rate. There isa simple Fourier transform relationship (i.e., a generalizationof eqs 2.8-2.15 for multiple states) between the informationin time- and frequency-domain experiments. However, thereare often technical reasons that make one kind of experimenteasier than another to perform or analyze. For example, a high-resolution spectrum can take a long time to record, and therelative intensities of widely separated features can be illdetermined. Conversely, the dynamic range of intensities in atime-domain experiment can be insufficient to resolve a largenumber of low-amplitude quantum beats. (Note that the numberof features in an N -line spectrum scales simply as N , whereascoherent excitation produces N ( N - 1)/2 quantum beats in thetime domain.) However, the information in a time-domainspectrum can be simplified and systematically examined byrestricting the frequency region of the detected fluorescence orby exploiting phase coherent pump-probe schemes in whichthe frequency, time delay, and optical phase of the probe pulseare all specified.140,141

With this as background, we now turn to a series of examples

of IVR studies that attempt to elucidate the key dynamics

occurring in each of three qualitatively different energy regimon the potential energy surface.

III. Low-Energy Vibrational Excitation: IR Fluorescen

and Direct Absorption Studies

A. Background. A natural starting point in a discussionIVR is near the bottom of the potential well, where in absence of fortuitous resonances between zero-order modes energy level patterns of the zero-order bright states can be wdescribed by harmonic and low-order anharmonic termHowever, the lack of strong coupling with other modes dnot mean that IVR phenomena are not of crucial importancethis regime. Specifically, the density of near-resonant darkbath states, F, grows rapidly with molecular complexity aeven at fundamental excitation energies can exceed mahundreds of states per cm-1. Thus, significant mixing of ZOBS with dark states can occur for average or rms couplmatrix elements as small as 1/Fbath, which, when viewed wsufficient spectral resolution, leads to “fractionation” of single ZOBS transition into spectral clumps of closely spaclines with effective width ∆ω and mean density F. As a reof recent advances in high-resolution IR laser spectroscomethods in jet-cooled beams, this IVR fractionation has bemapped out for several homologous series of molecules wexquisite sensitivity and detail in the frequency domain, whwill be discussed later in this section. This unraveling at hresolution of the so-called true molecular eigenstates is spectral “signature” of IVR in the frequency domain.

Of course, this IVR signature due to fractionation of ZOBS is also apparent in the time domain. For exampcoherent excitation of the entire clump of N lines by definitgenerates the ZOBS, which will evolve according to eq 2.suitably generalized for multiple-state mixing. After an iniperiod (which we may use to characterize an IVR lifetime frτ IVR ) 1/Γ), there will be extensive cancellation of the cohertime-dependent terms (with extremely long recurrence time

The square modulus of the autocorrelation will thereforedominated by the long time average of all N molecueigenstates, which for equivalently coupled dark states woexhibit roughly 1/ N 2 of the original bright state character. Fexample, if the zero-order state were a CH-stretch excitatnear 3000 cm-1, the time-resolved CH-stretch IR fluorescenfrom all N upper states would decay (in roughly 1/Γ) to N1/ N 2 ) 1/ N of the initial value, whereas fluorescence at othfrequencies from zero-order dark states mixed by IVR wogrow in on the same time scale. Of particular relevance, tlong time-average behavior is indistinguishable from an initiaincoherent excitation of the set of molecular eigenstates tcomprises the initial ZOBS and thus samples the IVR-induc“dilution” of oscillator strength into the manifold of dark stat

B. IR Fluorescence Studies in CH-Stretch-Excited Hdrocarbons. In a pioneering series of experiments, McDonand co-workers2,142-145 tested these ideas using a pulsedoptical parametric oscillator (OPO) light source to prepsupersonic jet-cooled hydrocarbons in the V CH ) 1 levels amonitor the IR fluorescence in the CH stretch and other spectregions. Since the IR-detector time resolution (>1 µs) wasslower than any anticipated IVR lifetimes, no explicit tidependence was expected. However, by calibrating agaiknown IR absorption strengths, the “dilution factor” (1/ N ) cobe used to infer N , the effective number of strongly coupstates. Studies on an extensive set of CH-stretch-exci

fundamentals indicated a clear inverse correlation of “dilutfactor” with density of symmetry-selected rovibrational stat

F ) 10-100/cm-1 was interpreted as the “threshold densi



7/22

necessary for promoting efficient IVR (see Figure 4). Corre-sponding IR oV ertone fluorescence studies were also pursuedby Nesbitt and Leone146 for a series of simple alkanes andalkenes in the CH-stretch V ) 2 r 0 region. The results forV CH ) 2 levels proved consistent with the V CH ) 1 studies; i.e.,the observed 1/ N dilution factors dropped off rapidly with bathstate density above 10-100 states/cm-1. If each of these darkstates was equivalently coupled to the bright state, this wouldimply IVR clump structures in the threshold region withcoupling matrix elements on the order of 1/F, i.e., 10-1-10-2

cm-1. This later proved to be in rather remarkable agreementwith direct IR laser absorption studies at Doppler and sub-Doppler spectral resolution, although the implicit suggestion thatIVR rates would scale in proportion to total state density proved

to be untrue. Further efforts by McDonald144

to look at dilutionfactors as a function of jet rotational temperature suggested somerotational enhancement (i.e., Coriolis or centrifugal mixing) of the IVR coupling matrix elements, an observation selectivelysupported by later high-resolution studies.

C. Probing IVR Coupled States: High-Resolution Direct

IR Absorption Studies. The indirect influence of such IVRstate mixing was certainly noted in the early studies of torsionaltunneling splittings in CH stretch excited ethane by Pine andLafferty.147 However, direct observation of the IVR-inducedclump structures in CH-stretch-excited hydrocarbons was firstachieved in a series of high-resolution IR laser measurementsby Perry and co-workers62,63 and McIlroy and Nesbitt.51-53 Theinitial system studied was acetylenic CH stretches in species

such as 1-butyne and measured via direct absorption of single-mode tunable IR lasers under either pinhole (∆ν ) 200 MHz)or slit (∆ν ) 30-50 MHz) supersonic jet conditions. Evenhigher resolution (∆ν ) 10 MHz) studies of CH-stretch-excitedhydrocarbons exploiting skimmed beams and bolometric detec-tion were later implemented by Lehmann, Scoles, and co-workers.3,55-61 As expected, each rovibrational transition (i.e.,accessing a single ZOBS) in 1-butyne was observed to be splitat high resolution into 0.01-0.02 cm-1 broad clumps of closelyspaced transitions (see Figure 5). These splitting patterns wereidentical for P/R-branch transitions to the same upper J K aK c leveland thus unambiguously due to vibrational interactions in theupper state. From the set of observed frequencies ( N ) andrelative intensities ( N - 1), the off-diagonal coupling matrix

elements, uncoupled energies of the zero-order “bright” and

“dark” basis states, and statistics on the number and densityinteracting states could be extracted from a Lawrance and Knideconvolution procedure.21 For the interested reader, Lehmaet al.3 provide an excellent review of these high-resolutionmethods.

The results of these and other high-resolution IR studiesa series of CH-stretch-excited hydrocarbons allow severigorous tests of different IVR models. For example, splittiin the rotationless ( J & ) 0) upper level are observed, indicat

that purely anharmonic state-mixing effects must be importaThis is confirmed by analysis of matrix elements ( V ij ) extracfrom a Lawrance and Knight deconvolution,21 which, for maCH-stretch-excited hydrocarbons, are of order 10-2 cm-1 aoften depend only weakly on the J and K a states. Howeversimple spectral pattern exists between clump structures successive J values, such as would be predicted for isolacrossings, indicating that the dark states “tune” rapidly throuthe bright state and are only within the spectral coupling windfor at most a few J values. Within experimental uncertaintthe observed densities of the coupled states are equal to total vibrational state density from harmonic and anharmopredictions, indicating that IVR appears to couple the ZOBSthe majority of background vibrational states. Most relev

to prospects of vibrational control of chemical reactions, explicit time-dependent autocorrelation function for these cohently prepared CH-stretch ZOBSs can be obtained directly frthe high-resolution frequency-domain data. These data indicthat IVR relaxation occurs only on the 10-9 s time scale. Tcorresponds to more than 105 vibrations of the CH group, whis a surprisingly long time when contrasted with picosecotime-scale predictions from earlier thermal and chemical actition studies.148,149

D. Structural and/or Density of States Dependence of I

Rates. These frequency-domain studies of 1-butyne raisesimple but intriguing question: Will these CH-stretch Irelaxation rates depend on what group is substituted on the otside of the CC triple bond, or is the IVR rate sensitive primar

to the “local” CCH environment? From a simple but commmisapplication of Fermi’s Golden Rule, one could argue tthe IVR rates should increase with vibrational state densiOn the other hand, drastically increasing total state density adding modes with vanishingly small coupling to the zero-orbright state also decreases the mean square coupling matelement. Mathematically, FN states/cm-1 with a mean squcoupling of !V ij 2", diluted by an additional uncoupled densof FM states cm-1, leads to a lower mean square couplstrength of FN!V ij 2"/(FN + FM), that is, by exactly the same fac(FN + FM)/FN, by which the density is increased. Thus, if IVR dynamics is dominated by purely “local” couplings, corrapplication of Fermi’s Golden Rule predicts little or no chanin IVR lifetimes in a homologous series with increas

molecular complexity.This question was initially addressed52,53 in a high-resolut

study by McIlroy and Nesbitt of CH-stretch-excited (i) propy(R ) methyl), (ii) 1-butyne (R ) ethyl), and (iii) the gauand cis isomers of 1-pentyne (R ) propyl), for which predicted state densities range over 4 orders of magnitude fr0.1 to 2400 states/cm-1. The results (Table 1) indicate IVlifetimes that are remarkably insensitiV e to the nature of substitution group, varying by no more than a factor of 2 more than a 102 increase in state density. These termiacetylene studies have been significantly extended by LehmaScoles, and co-workers3,57-61 at even higher resolution wbolometric methods, probing systems such as (CF3)3C-Cwith state densities as high as 1011 states/cm-1! Again, desp

an enormous range of 107 in state density, the observed IV

Figure 4. Dilution factor for CH-stretch IR fluorescence subsequentto fundamental (V CH ) 1) and overtone (V CH ) 2) excitation, plottedversus the density of vibrational states of appropriate symmetry: circles(V CH ) 1 aliphatic CH stretches); squares (V CH ) 1 acetylenic CHstretches); triangles (V CH ) 2 aliphatic CH stretches). Note theconsiderable decrease in dilution in the vicinity of F ) 10-100 cm-1.Data for V CH ) 1 and V CH ) 2 are taken from refs 142 and 146,respectively.



8/22

rates (see Table 1) are within 1 order of magnitude for allacetylenic systems investigated. From the above discussion, itis apparent that the huge reservoir of state density provided bythe larger substitution groups has essentially little or no couplingwith the zero-order bright CH-stretch state. This is an exceed-ingly important and simplifying result for efforts to model IVRdynamics theoretically and indicates that state mixing in thesesystems is rate limited to a highly restricted region of vibrationalphase space.

It is worth noting that these high-resolution results would atfirst appear to be qualitatively different from the results reported

by Smalley and co-workers16-18 in classic low-resolution

dispersed fluorescence studies of jet-cooled n-alkylbenzenThese earlier studies took advantage of the negligible shiftsFranck-Condon ring mode progressions with length of the al“tail”, which permitted them to systematically vary the densof bath states over many orders of magnitude. The ratiovibrationally relaxed (broad) to resonance (sharp) fluorescenwas observed and used in conjunction with known fluorescenlifetimes to infer an effectiV e IVR rate from the initially exciring vibration. Their results clearly demonstrated a dram

increase of this broad to sharp fluorescence ratio with alkyl chlength and bath state density.

What is the reason for these apparent differences betwering-mode excitation in alkyl-substituted benzenes and termiCH-stretch excitation in substituted acetylenes? Although ipossible that CH stretches and low-frequency aromatic rmodes exhibit qualitatively different behavior or that complitions due to low-lying electronic states may depend on chtail length, a much simpler explanation exists. Essentiallythe excitation pulses are insufficiently fast to prepare the fZOBS coherently, then the laser instead excites a subsetmolecular eigenstates (mostly incoherently) whose subsequfluorescence reflects the long-time behavior correspondinga “prerelaxed” vibrational distribution of bath levels. Thus,

chain-length-dependent alkylbenzene intensity ratios observby Smalley would be more analogous to the dilution factthat McDonald measured for IR fluorescence in CH-stretcexcited hydrocarbons,2,142-145 irrespective of the 10-7

10-2 s radiative lifetimes of the upper state. Indeed, Parmenhas cleverly exploited the inverse of this point in a series“chemical timing” experiments, which use high-pressure quening gases to isolate the fluorescence that occurs exclusively frthe ZOBS on the picosecond time scale even for cw laexcitation. High-resolution studies of low-frequency rvibrational modes in these jet-cooled alkylbenzene systems hnot yet been reported but could prove quite interesting to pursIndeed, from previous IR studies one might speculate that higresolution alkylbenzene spectra would reveal IVR clu

structure in these ring modes, with clump widths consistent wIVR lifetimes largely independent of alkyl tail length and tovibrational state density.

These IVR rates in CH-stretch-excited terminal acetylenindicate localization of vibrational energy on a surprisingly lotime scale, considerably longer than the sub-picosecond lifetimthat had previously been inferred from chemical activatstudies. As an important benchmark for comparison, this 0.1.0 ns localization of the CH-stretch excitation is comparato typical gas kinetic collision times at 1 atm.150 In conjunctwith the very exciting results on vibrationally enhanchemistry in small systems (where IVR is not an issue) suchCl and H atom reactions with H2O/HOD by Crim and

workers,

12,13

this bodes well for extension to significantly larmolecular systems, where IVR had previously been considetoo fast for vibrationally mediated “control” of bimolecureactions in the gas phase.

E. Double-Resonance State Labeling. The sine qua nin these high-resolution studies is to isolate the purely homgeneous IVR-induced structure, uncomplicated by the residinhomogeneous structure due to, for example, different J Krotational states, isomers, isotopes, etc. With the introductof IR/microwave/visible double-resonance techniques, hiresolution spectroscopic studies of IVR mode mixing have berefined to new heights of experimental elegance and flexibiliIn the double-resonance method of Perry, for example, tindependent IR lasers can be both tuned and modulated

different frequencies; if the lasers share any common le

Figure 5. Frequency-domain IVR in the 2ν1 acetylenic CH-stretchexcitation of propyne, as evidenced by the additional spectral “clump”structure observed only at high-resolution (0.0005 cm-1) conditions.The precise repetition of the spectral clump patterns in both R(4) and

P(6) rotational transitions provides unambiguous evidence that the IVRcoupling occurs only in the excited (i.e., J ) 5) state. Note that the K ) 0 level is unperturbed; this suggests that the IVR mixing is mediatedvia Coriolis ( z-axis, i.e., ∆K ) 0) rotational effects, which yield matrixelements proportional to K . Reprinted with permission from ref 55.Copyright 1994 American Institute of Physics.

TABLE 1: IVR Lifetimesa for WCH ) 1 CH-StretchExcitation in R-CtC-H Terminal Acetylenes

molecule τ IVR (ps) Fbath (states/cm-1)

prop-2-yn-1-ol 500 201-butyne 270 22(CH3)C-CtCH 200 4901-pentyne (trans) 440 24001-pentyne (gauche) 240 2400(CD3)3C-CtCH 40 2800(CF3)3C-CtCH 60 1.0 × 1011

a References 52, 57, 58, and 59.



9/22

(upper or lower) and one laser is partially saturating thetransition, the modulation of the saturating laser will be writtenonto the transmission of the other. Alternatively, with the EROS(electric resonance optothermal spectroscopy) scheme of Fraser,Pate, and co-workers,69-71 optical lasers have been combinedwith classic radio-frequency/microwave electric resonancemethods to probe transitions between states via deflection towardor away from a bolometer.

The significance of these double-resonance methods is theachievement of maximal rotational ( J K aK c) state selection andlabeling, as well as excitation into even higher oV ertone andcombination vibrational levels. This overtone capability has

permitted Lehmann, Scoles, and co-workers47-61 to study thedependence of acetylenic CH-stretch IVR rates on the numberof vibrational quanta (Table 2). For the terminal CH acetylenicsystems investigated thus far, the dependence of IVR lifetimeson V CH is remarkably small, often less than a factor of 2, and insome special cases even slowing with increasing quantumnumber. Even though there are interesting structure and moiety-specific trends to be discovered (discussed in section VI), allspectroscopically measured IVR rates in the acetylenic V CH )1, 2, and 3 CH-stretch manifold have proven to be (i)surprisingly slow ((20-0.2) × 109 s-1), (ii) within a relatively“narrow” window (less than 2 orders of magnitude), and (iii)remarkably insensitiV e to total state density. This last pointdeserves particular emphasis, since a common conclusion fromlower-resolution studies has been that total state density is akey parameter controlling IVR rates.

F. Probing the Nature of Bath States. This discussion of multiple-resonance methods highlights an important point.From the high-resolution distribution of absorption frequenciesand intensities within a spectral clump illustrated by a givenZOBS, one can therefore predict |!Ψ(t )|Ψ(0)"|2 without any

further knowledge of the nature of the molecular eigenstates!This sounds like good news, but the corresponding disadvantageis that even though you know how fast the energy leaves theoriginal ZOBS, you do not know where or how fast thevibrational energy subsequently flows! This situation changesqualitatively for multiple-resonance methods, which can inde-

pendently interrogate other spectral properties of the moleculareigenstates. Stated simply, double-resonance capabilities allowa glimpse of the eigenfunction composition of an IVR featurestate by projecting it onto a different ZOBS with a secondphoton. This is, of course, true of any two-color pump-probeexperiment, in either time or frequency domain. For example,in the V CH ) 1 IR fluorescence studies of McDonald and co-workers,2,142-145 the CH-stretch ZOBS gets to “choose” at whatcharacteristic frequencies (e.g., CH stretch, CH bend, etc.) toreemit the initial laser excitation. Thus, the dispersed IRfluorescence spectrum can elucidate the nature (after an initialtransient) of the bath states that are coupled with the zero-orderbright state.

In order to sample the character of the excited-state eigen-

functions, this second probe field need not be provided by

another photon. A beautiful example of this has been reporby Fraser et al.,69-71 who measured the electric field-inducStark shifts of IVR mixed energy levels in OH-stretch-exciethanol. In the absence of any IVR state mixing, one woanticipate a strong dipole moment for the OH-stretch-excistate. Thus, a coherently prepared ZOBS should tune rapiwith E-field, and therefore it should be possible to deflmolecules by a force proportional to the electric field gradieSpecifically, all eigenstates can be separated into those that fo

or defocus in a quadrupole field, and thus resonances detected when a transition converts a molecule from a focusto a defocusing state. Indeed, such Stark-induced forces precisely what makes the EROS method work for many othmolecular applications. What Fraser et al. observe, howeverthe complete lack of any measurable deflection for strongly IVmixed levels in the OH-stretching state; the individual eigestates in vibrationally OH-stretch-excited ethanol exhibit apparent dipole moment, even though the coherently prepaZOBS certainly must.70,71

The resolution of this apparent paradox provides importinsights into IVR phenomena. There is a dense manifoldenergy-level-avoided crossings as the molecular eigenstaattempt to tune in the E-field. Due to off-diagonal terms in

Hamiltonian, however, the levels do not actually cross, instead the dominant zero-order character switches as the fitunes the eigenstates through the crossing region. Due to tdense “traffic jam” of avoided crossings, no individual eigenstsucceeds in tuning V ery far in energy, even though a coherenexcited ZOBS would exhibit a clear second-order Stark shConsequently, the aV erage slope of energy versus E-field the eigenstates vanishes and thus the molecules are not deflecby the external E-field gradient.

IV. Intermediate Vibrational Excitation on the Potentia

Surface: High-Overtone Studies of IVR

A. IVR in CH-Stretch-Excited Benzene Overtones: R

of Nonlinear Resonances. Even though arguably the mdetailed spectroscopic information on IVR phenomena near potential surface minimum has been obtained via the higresolution methods described above, the associated excitatenergies in those studies are typically only a small fracti(j10%) of a typical covalent chemical bond strength. Conquently, there has been considerable interest in developinsimilarly detailed understanding of IVR dynamics at “chemicasignificant” energies, accessing regions of the potential surfwhere large-amplitude, anharmonic coupling effects beginbe quite dramatic and which may even sample high-barriunimolecular chemical transformations such as isomerizatiOne approach to this energy regime, pursued by several grouhas been high-overtone excitation of high-frequency stretch

modes,32-50

with particular emphasis on near-IR/visible/Uovertone absorption spectroscopy in the CH-stretch manifo

Of the numerous studies of CH-stretch-excited hydrocarbothere has been a special focus on the benzene molecule, whhas historically been the “hydrogen atom” of high-overtospectroscopic studies of IVR. This was stimulated by development of sensitive intracavity dye laser photoacousmethods, which Berry, Bray, and Hall49,50 used in pioneerstudies to measure CH/CD-stretch-overtone spectra in rotemperature benzene vapor up to as high as V CH ) 9 rAlthough the initial interpretations of the data were somewflawed, these studies raised some very important questions abIVR in CH-stretch-excited hydrocarbons and in turn stimulaan enormous amount of subsequent theoretical and experimen

effort.

TABLE 2: IVR Lifetimes for WCH ) 1 and 2 QuantaCH-Stretch Excitation (Experimenta and Theoryb)

τ IVRv)1 (ps) τ IVRv)2 (ps)

molecule exp theory exp theory

(CH3)3C-CtCH 200 260 110 90(CD3)3C-CtCH 40 35 5.2 × 104 4000 1300(CD3)3Si-CtCH 830 260 140 170(CH3)3Sn-CtCH 6000 >1000

a References 57 and 58. b Reference 85.



10/22

Specifically, the benzene spectra reveal a clear CH-stretch-overtone progression, with a Birge-Sponer anharmonicityanalysis characteristic of localized CH-stretch excitation. Fur-thermore, despite the fact that the low-overtone spectra containsignificant contributions from inhomogeneous broadening atroom temperature, the spectroscopically observed line widthsfor the higher overtones are quite broad (30-110 cm-1), whichwas interpreted to imply rapid IVR on the subpicosecond timescale. However, these line widths depend in a surprisingly

nonmonotonic way on the number of vibrational quanta excited,increasing for V CH ) 4 r 0 to V CH ) 7 r 0 and then eventuallydecreasing for V CH ) 8 r 0 and V CH ) 9 r 0. Furthermore,this nonmonotonic trend is sensitive to H/D isotopic substitution,suggesting the presence of low-order vibrational resonancesbetween CH/CD stretches and other modes in benzene. Asinterpreted in elegant detail by Sibert et al.,86-88 these theoreticalstudies identified the source of IVR line width as a nonlinear2:1 Fermi resonance between the CH-stretch and CCH-“bend”manifolds. This vibrational state mixing tunes in and out of resonance due to the anharmonicity of the CH stretch. Theremarkable success of this analysis is that experimentallyobserved IVR line widths in a complicated molecule, as wellas the isotopic dependence thereof, could be qualitatively

reproduced from relatively simple model calculations on a trialforce field. A particularly important result of this study is thatthe time scale for fast IVR dynamics in benzene could bepredicted by analysis of local stretch-bend interactions on thesame functional group. It is precisely this sort of moiety-specificdescription of IVR, developed from detailed analysis of a finitenumber of test molecules, that would ideally permit extrapolationof IVR time scales, tier structures, and energy flow paths tomore general molecular systems.

B. Stretch:Bend Fermi Resonances in Isolated CH-

Stretch Chromophores. The relevance of such 2:1 stretch:bend Fermi resonances in CH overtone spectra has beenbeautifully elucidated in a series of studies by Quack and co-workers41-45 of substituted methanes such as CHX3 (X) D, F,Cl, Br, CF3). Specifically, by making the CH stretch chemicallyunique, they were able to study the stretch-bend coupling inisolation. As a result of this 2:1 Fermi resonance (i.e., υbend ≈1500 cm-1, υstretch ≈ 3000 cm-1), there exists a set of near-resonant stretch-bend states in the vicinity of the ZOBS thatsatisfies the expression

and forms a vibrational polyad of order N + 1. By applyingthe scaling rules of section II.C and eq 2.6, the associated tierstructure becomes quite simple; the ZOBS is |V stretch,0", the firsttier consists exclusively of |V stretch -1,2", the second tier,

|V stretch -2,4", etc. The Hamiltonian matrix is therefore blockdiagonal, with adjacent off-diagonal elements determinedanalytically by cubic terms (i.e., QstretchQbend2) in the potential.Due to the sequential nature of the coupling, the bright statecharacter of the overtone is mixed into each of the N + 1molecular eigenstates, but with a magnitude that drops rapidlywith decreasing overtone character. Results for the secondovertone spectrum ( N ) 3 polyad) of HCF3 are displayed inFigure 6, which shows the anticipated cluster of N + 1 ) 4bands of monotonically decreasing intensity. From analysis of the series of polyad overtone spectra, both the intensity patternsand vibrational band origins can be quantitatively fit to low-order quadratic and cubic terms in the potential.

Due to a combination of strong coupling and detuning of these

zero-order stretch-bend vibrations, the spacing of the resulting

molecular eigenstates is now so large (≈

1000 cm-1

) thawould require extremely fast IR pulses (j15 fs) to prepare original ZOBS coherently. In principle, however, suchcoherent excitation would lead to sequential IVR flow of initial ZOBS overtone state |V stretch,0" into the dark states w|V stretch-1,2", |V stretch-2,4", etc., on a time scale given bmultistate generalization of eq 2.14. However, due to multiple tier level participation in the IVR mixing, populattransfer is by no means as simple or complete as in a two-lesystem. For example, in this simple case of IVR with ofour coupled states, there would be partial recurrences in autocorrelation function characteristic of “quantum beaThere would also be much smaller amplitude recurrencesthe cross-correlation or “probability transfer” functions cor

sponding to each of the dark states in the polyad.44,45

Thianalogous to the quantum beat time-domain structures observin electronically excited state fluorescence studies by FelkZewail, Field, Zare, and others22-26,110,111 and has been chacterized as “restricted IVR” due to the relatively small numof strongly coupled bright and dark states. This example anicely stresses the utility of the IVR tier structure concewhereby a polyad pattern of sequential mode couplings takon a physical reality as a sequential flow of vibrational enerwith a nested sequence of time scales and decreasing amplitudSimilar tier analyses of more complicated multiple Feresonance behavior in systems such as NH3151,152 aHCCF153,154 have also been successfully performed.

C. CH-Stretch Overtones in Jet-Cooled Benzene: Co

parison of Theory and Experiment. Based on the abodiscussion, high-resolution overtone spectra of benzene mibe anticipated to reveal additional structure correspondingCH stretch-bend Fermi resonance mixing, in addition to evfiner structures that would identify the IVR relaxation pathwrelevant at even longer time scales. However, this is observable in the room temperature benzene photoacouspectra, due to inhomogeneous broadening from rotational bacontours and sequence congestion from low-frequency vibtional hot bands. In order to eliminate such thermal effethese benzene overtone experiments have been performed unsupersonic jet conditions by (i) Page et al. using IR + Udouble-resonance methods155 and (ii) Scotoni et al. usoptothermal bolometric methods.156 The results from b

groups indicate considerable narrowing of the V CH ) 3 r

Figure 6. Moderate-resolution FTIR N ) 3 overtone polyad of CH stretch in 13CHF3. Note the clear evidence of N + 1 ) 4 Cstretch bands, due to successive mixing of the initial ZOBS (|V stretch,V bend" ) |3,0") with near-resonant |2,2", |1,4", and |0,6" tiers2:1 Fermi resonant bend-stretch coupling. The relative intensities shifts provide quantitative support for such a near-resonant tier modReprinted with permission from ref 43. Copyright 1985 AmeriInstitute of Physics.

N ) V stretch + 0.5V bend (4.1)



11/22

overtone spectrum with supersonic rotational cooling, revealinga rich, albeit complicated, spectral substructure with featuresas narrow as 5 cm-1 and clearly showing that the photoacousticline widths for the lower V CH levels are substantially broaderthan the homogeneous width. Though the size of benzenemakes this quite challenging, considerable progress toward aninterpretation of this spectral structure has been made by Wyattand co-workers93-97 and Marcus and co-workers.157,158 Thesequantum vibrational calculations require including many more

degrees of freedom than in the Sibert et al. study86-88

and arecomputationally extremely intensive. Though all 30 degreesof freedom in benzene cannot yet be treated, converged resultshave been obtained that include all 21 in-plane vibrationalmodes.93-97 Nevertheless, semiquantitative agreement has beenachieved between experiment and theoretical predictions, interms of both line widths and detailed spectral structure. Thecalculations also directly confirm the central importance of CHstretch-bend Fermi resonances in the early time IVR processes.

D. Vibrationally Mediated Photolysis. As noted in sectionII, any sufficiently high-resolution one-photon absorptionspectrum can predict completely the magnitude of the time-dependent autocorrelation of Ψ(t ) with the original ZOBS, i.e.,Ψ(0). However, it tells us frustratingly little about where the

energy eventually goes, i.e., what comprises the dark statemanifold. Although in principle one can glean this informationfrom dispersing the IR emission spectra of the resultingmolecular eigenstates, an even more useful strategy has beento probe the resulting absorption spectra. This has beenattempted for low CH-stretch levels (V CH ) 2) via high-resolution double-resonance studies (V CH ) 2 r 1, 1 r 0) interminal acetylenes by Perry and co-workers66,67 and Lehmannand co-workers.60,61 Though at considerably reduced resolution,a very useful alternative method has been pursued by Rizzoand co-workers32-36 in a classic series of studies of OH-stretch-excited species. This method takes advantage of vibrationallymediated photodissociation schemes of Crim and Andresen toprepare a molecule above the dissociation threshold to generateOH, followed by LIF detection of the radical. For example, apulsed dye laser is used to excite the V OH ) 4 r 0 overtoneregion in nitric acid (HNO3), which lies just below the energeticthreshold, to form OH + NO2 fragments. Since any furtherexcitation of OH-stretch vibrational quanta energetically leadsto predissociative formation of OH radicals, a second IR pulsedlaser can then “map” out the resulting absorption/actionspectrum of the V OH ) 4 overtone-excited nitric acid molecules.The large anharmonicity for OH-stretch excitation in nitric acidallows the effective vibrational quantum number to be estimatedfrom the center frequencies of features in the absorption profiles.Specifically, if there is only weak IVR mixing of high OH-stretch overtones with the bath, the ∆V ) +1 absorption

spectrum for the second laser would resemble that of a singleV OH ) 5 r 4 band, whereas in the limit of strong mixing, thecorresponding ∆V ) +1 spectrum would be sequentially blue-shifted by OH-stretch anharmonicity into the V OH ) 4 r 3,3 r 2, 2 r 1, 1 r 0 regions. Indeed, the absorption/actionspectrum for the second laser reveals precisely such a sequenceof bands, the relative intensities of which correspond well tothe predicted total densities of vibrational states for a given V OHat the total vibrational energy of the initial excitation (see Figure7). Thus, the results indicate essentially complete mixing of all vibrational states of nitric acid in the V OH ) 4 and V OH ) 5regions. This is consistent with both the earlier IR fluorescencestudies of V CH ) 1 and 2 stretch excited hydrocarbons and thedark state densities inferred from high-resolution IR laser

absorption studies of terminal acetylenes.

E. Franck-Condon Pumping/SEP Studies of AcetyleThus far in the discussion, there has been a clear emphasishigh-overtone studies involving CH-, OH-, or NH-streexcitations. This is due both to the relatively large quantumvibration (∼3000 cm-1) and to the unusually large mechaniand electronic anharmonicity of hydride-stretching motiowhich makes overtone excitation at chemically signific

energies possible. With Franck-Condon pumping/SEP schemas an alternative, however, a much broader range of vibratiolevels can be accessed in favorable molecules. One system thas received extensive attention with SEP methods is acetyleThis is arguably the simplest possible molecule in whichfeatures relevant to vibrational dynamics in larger polyatomare qualitatively represented and therefore provides an excellpedagogical example of what analysis of IVR can hopeachieve.

The special characteristic of acetylene that makes this possiis that its vibrational density of states grows relatively slowwith energy; thus, fully resolved spectra can be recordedto chemically interesting levels of vibrational excitati

E VIB e 20 000 cm-1 ) 57 kcal/mol, which is well above

barrier to a bond-breaking isomerization between acetylene a

Figure 7. An IR double-resonance ∆V ) +1 absorption spectrumHNO3 originating from the V OH ) 4 level. The arrows identify origins of the various ∆V ) +1 bands. If this upper state w

completely free of IVR mixing, the subsequent∆

V ) +1 IR absorpwould occur at the substantially red-shifted V OH ) 5r 4 region. Insteabsorption bands clearly corresponding to V OH ) 3 r 2, 2 r 1, anr 0 are observed. A quantitative analysis of these band intensitieconsistent with a statistically mixed nature of the V OH ) 4 level inear-resonant bath states. Reprinted with permission from ref Copyright 1991 American Institute of Physics.



12/22

vinylidene.

As demonstrated below, this SEP access to a wide range of electronic ground state vibrations permits (i) characterizationof all resonances that control IVR at low E VIB, (ii) a test of scaling predictions as E

VIB is increased systematically along

families of ZOBSs, (iii) the development of statistical proceduresfor extracting structural and dynamical information fromincompletely assigned spectra, and (iv) the use of the breakdownof scaling predictions as a pattern-recognition scheme forcharacterizing chemically important topographic features of thepotential energy surface.

1. Characterization of Resonances at Low EVIB. Eversince the first high-resolution infrared and Raman spectra of acetylene were recorded, it was clear that most of the lowest-lying vibrational levels exhibited spectroscopic perturbations(i.e., level shifts, extra lines, anomalous molecular constants)due to several different anharmonic resonance terms in the V (Q).Among these are a 2:2 stretch Darling-Dennison, a 2:2 bend

Darling-Dennison, and several 1:1+1+1 quartic interactionswhere one quantum of a CH stretch (ν1&& or ν3&&) is exchangedfor one quantum of the CC stretch (ν2&&) plus two quanta of thebends (trans-bend ν4&&; cis-bend ν5&&). Each of these low-ordervibrational resonances can be investigated at low E VIB by high-resolution IR, Raman, or SEP spectroscopies and characterizedby an effective Hamiltonian matrix (i.e., H ˆ eff ) in a product basisof zero-order vibrational states. The vibrational resonanceappears in H ˆ eff as off-diagonal matrix elements, each expressedas a coupling strength (one for each resonance) times an a prioriknown function of normal mode quantum numbers (e.g., eq 2.6).The simplified matrix elements of H ˆ eff are therefore based onharmonic oscillator selection (Q̂in f ∆V i ) n) and couplingmatrix element scaling rules (e.g., Q̂in f V in/2), with a small

number of resonance coupling strengths that have been least-squares fit to match energy eigenvalues and intensities withexperiment at low E VIB. Thus, the model H ˆ eff matrix is largeand may appear to be complicated, but each resonance isrepresented by only one coupling strength parameter.

2. Block Diagonalization of H ˆ eff : Polyads and PolyadQuantum Numbers. As a linear four-atom molecule, acetylenehas seven vibrational quantum numbers (V 1, V 2, V 3, V 4, l4, V 5, l5),where l4 and l5 reflect the vibrational angular momentaassociated with the doubly degenerate V 4 and V 5 bending modes.Naively, one might expect that each resonance would destroyat least one vibrational quantum number. Since more than sevenstrong resonances are known in HCCH, one might expect thatthere would be no useful (i.e., approximately good) quantum

number labels for the molecular eigenstates. This would bebad news for characterizing IVR mechanisms in acetylene,because assigning quantum number names to eigenstates orfeature states is the first step in determining “where” (as opposedmerely to “how fast”) the energy flows.

But condolences are premature! These resonances are notall linearly independent. This can be seen by representing eachresonance by a 7-D vector in quantum number space, wherethe components express the harmonic oscillator selection rulefor nonzero off-diagonal matrix elements. For example, thestretch Darling-Dennison, k 1133Q̂12Q̂32, and the “3,245” reso-nance, k 3,245Q̂3Q̂2Q̂4Q̂5, correspond respectively to resonancevectors (∆V 1,∆V 2,∆V 3,∆V 4,∆l4,∆V 5,∆l5) ) (2,0,-2,0,0,0,0) and(0,1,-1,1,0,1,0). By representing each important resonance by

a vector in quantum number space, it then becomes a standard

problem in linear algebra to find a set of mutually orthogovectors that are also orthogonal to all of the resonance vectoPhysically, these vectors represent the generalized vibratioquantum numbers that are not destroyed by the set of knoresonances.

In the case of HCCH, the surviving quantum numbers

In the above expression for nres, the integers can be tracedthe approximate 5:3:5:1:1 ratios of the normal-mode frequenciwith E VIB ≈ nres‚(650 cm-1). Similarly, ns reflects the tonumber of quanta in stretching vibrations, and l is the tovibrational angular momentum. These three (approximateconserved quantities [nres, ns, l] serve to (approximately) blodiagonalize H ˆ eff . Each block of H ˆ eff is called a polyad andlabeled by the three polyad quantum numbers [nres, ns, l].

3. Dispersed-Fluorescence Spectra: Scaling of Early Ti

IVR. The resonances characterized by a least-squares analy

of the low- E VIB levels of acetylene certainly include all of strongest and most important anharmonic interactions. Hoever, there are, of course, weaker resonances neglected in ttreatment that will partially degrade the polyad quantnumbers, in essence by introducing off-diagonal matrix elemebetween members of different polyads. Thus, IVR in the tidomain will consist of relatively fast, well understood trapolyad dynamics plus slower, mechanistically less wcharacterized interpolyad dynamics. This description is inmately related to the concept of IVR tiers, but where we ignoi.e., truncate, the tier structure beyond a certain limit. By Foutransforms, we can use this ignorance of the IVR dynambeyond some time limit to particularly clever advantaSpecifically, if we observe spectra in the high- E VIB region

reduced spectral resolution, the data contain information oabout the early time dynamics, which corresponds to intrapolyvibrational energy flow from a preselected ZOBS. Since ionly this early time behavior that we seek to characterizeleast at first!), dispersed fluorescence (DF) methods at ∼5 cmresolution with only one excitation laser provide an experimtally much more convenient way of obtaining this informatthan via SEP methods at ∼0.05 cm-1 resolution, which requmultiple PUMP and DUMP lasers.

Acetylene offers some special advantages that make our jeasier; by an accidental combination of Franck-Condon activand resonance structure, each acetylene [nres, ns, l] polyfortuitously contains only one ZOBS! Therefore, by observdispersed fluorescence from different intermediate vibratio

levels in the Ã-state, one can systematically change the relatFranck-Condon intensities of different polyads (e.g., by chaing the number of quanta in the Ã-state trans-bend), whallows spectrally overlapping polyads to be “unzipped” freach other. Alternatively, one can illuminate a different bristate in each polyad, e.g., by IR-UV double-resonance exction of an Ã-state vibrational level that is a Franck-Conddark mode, such as a C-H stretch, a torsion, or an antisymetric in-plane bend. This second trick allows systemasampling of the short-time IVR dynamics as a functionadditional quanta away from the usual Franck-Condon-allowZOBS, which permits one to probe new members of the polythat may be more strongly coupled to, for example, unimolecular isomerization path between acetylene and vin

idene.

Cb

HaCc

Hd

CcHdHaCb Cc –HaHd –Cb (4.2)

nres ) 5V 1 + 3V 2 + 5V 3 + V 4 + V 5 (4.

ns ) V 1 + V 2 + V 3 (4.l ) l4 + l5 (4.



13/22

By way of example, Figure 8a shows the result of such an

“unzipping” procedure in the DF spectra of acetylene. Each

row contains a progression of polyads ( E VIB increases lef

right) accessed via consecutive excitation in the trans-bend (V

(a)

(b)

Figure 8. IVR sampled by dispersed fluoresence (DF) spectra of acetylene. By recording DF spectra that originate from two different uppintermediate levels, overlapping features can be “unzipped” from each other. (a, top) Unzipped spectra, shown as progressions in even quantatrans-bend (V 4&&) at constant CC stretch (V 2&&). The width and number of resolved subfeatures in each unzipped clump provide sensitive tests oscalable polyad model for IVR. In this system, IVR (i.e., spectral fragmentation) clearly increases more rapidly with increasing V 2&&. (b, bottoIntrapolyad dynamics in state space resulting from t ) 0 excitation of a bright state, B, within the ( ns, n res, l) ) (1,11,0) polyad. The four pandescribe the dynamics when B ) (0,1,0,80,00)0, the initial Franck-Condon ZOBS in the polyad. The upper left shows the “survival probabili(square modulus of the autocorrelation function) of the ZOBS, whereas the other three panels show time-dependent probability of transfer to ftier [(0,1,0,6+2,2-2) and (0,1,0,60,2)0] and second tier [(0,0,5+1,2-1)0] levels. Reprinted with permission from ref 77. Copyright 1995 VCH.



14/22

for a constant number of quanta in C-C stretch (V 2&&). Eachcolumn shows a progression of polyads ( E VIB increases bottomto top) accessed via consecutive excitation in the C-C stretch,for constant excitation of the trans-bend. The plot clearly showsthat spectral fractionation symptomatic of IVR increasesmonotonically as excitation in the trans-bend increases, butdecreases as excitation in the C-C stretches increases! Re-markably, these initially nonintuitive trends in IVR rates canbe completely explained in terms of the simple scaling relation-

ships for the coupling matrix elements, energy differences inthe zero-order states, and a single (least-squares-fitted) parameterfor each low-order resonance. From the time-frequency Fouriertransform, the polyad model not only successfully accounts forV 2&&,V 4&&-dependent trends in IVR fractionation but also explicitlypredicts the intrapolyad vibrational energy flow subsequent toexcitation of any ZOBS. For example, Figure 8b demonstratesthe time-dependent probability of finding the system in each of four different zero-order states following coherent preparationof a specific ZOBS {i.e., (0,1,0,80,00)0} at t ) 0.

The frequency- and time-domain patterns presented respec-tively in Figure 8a,b appear complicated , but they are in factwell predicted from a small number of well determinedspectroscopic (ωi, xij ) and anharmonic resonance (k ijkl) param-

eters. The polyad model is the basis for a powerful pattern-recognition scheme that may prove useful in systematicallyrefining ab initio surfaces against experimental data or detectingthe abrupt change of resonance structure that occurs nearchemically important topographic features of a potential energysurface.

V. IVR at “High” Energies: Vibrational Dynamics above

Potential Barriers to Unimolecular Bond Breaking and/or

Molecular Rearrangement

The analysis of the acetylene spectra described in the previoussection provides a clear example of the power of SEP and DFmethods for selecting a specific ZOBS, as well as the spectro-

scopic tools for decoding the IVR dynamics encoded in such avibrationally energized initial state. An even richer set of dynamical IVR phenomena becomes experimentally accessiblewhen the initial vibrational excitation lies at an energy aboV ethe ground state barrier to dissociation. In this regime, couplingof the zero-order dark states to the translational continuum canalso be important, which introduces an additional “clock,” thatof dissociation (or predissociation), into the IVR analysis. Thetime scale for dissociation vs the initial IVR loss of coherenceof the ZOBS, for example, can control whether the bond-breaking process is “direct” (ZOBS f fragments) or “sequen-tial” (ZOBSf relaxed distributionf fragments). Furthermore,for polyatomic molecules, there can be significant modespecificity in both the dissociation rates as well as IVR, which

can lead to a dependence of the actual dissociation mechanismon the choice of ZOBS.

A. Direct Mode-Specific Photofragmentation. A particu-larly instructive polyatomic system for detailed investigationof these mixed IVR/dissociation phenomena is HFCO. Specif-ically, HFCO f HF + CO dissociation rates have beenmeasured by Choi and Moore79-82 from highly excited vibra-tional levels of the X̃1A& electronic ground state, using a varietyof fluorescence-dip-detected SEP-related techniques that exploitvibrational levels of the Ã1A&& excited state as intermediates(see Figure 9). Similar to the case in the well-studied H2COf H2 + CO system,31 there is a large barrier (∼17 200 cm-1)to nearly thermoneutral HFCO f HF + CO dissociation onthe S0 surface. Dispersed fluorescence spectra of HFCO include

long progressions extending to E VIB ≈ 22 000 cm-1 in the two

Franck-Condon-active modes, ν2 (CO stretch) and ν6 (out-plane bend). Thus, SEP permits double-resonance accessregions of vibrational phase space on the ground electromanifold both below and aboV e the barrier to dissociation, wboth ZOBS and rotational ( J K aK c) initial state selectivity.

Three types of SEP experiments have been performed: moderately high-resolution (0.05 cm-1) SEP, which determithe S0 rotation-vibration energy levels, and dissociation rafrom spectroscopic line widths for the states which dissoci

fast enough; (ii) SEP-delay-LIF, a PUMP-DUMP-PROscheme which measures the lifetimes of HFCO rotatiovibration levels that are too long-lived to broaden the SEP libeyond the 0.05 cm-1 resolution limit; and (iii) SEP phofragment fluorescence excitation based spectral measuremof the vibration, rotation, and translational distributions of CO photofragments.

The SEP studies of HFCO sample rotation-vibration levin the 13 000


15/22

additional stability due to extreme versus distributed vibrationalmotion. Though not yet analyzed at the same level of detail,the decoupling of the out-of-plane ν6 motion from the stronglycoupled in-plane modes in HFCO is almost certainly a conse-quence of the weakness of low-order anharmonic resonancesinvolving the V 6 mode combined with the rapid growth inanharmonic couplings with successive V 6 vibrational quanta,similar to effects observed previously at lower levels of vibrational excitation in both benzene and acetylene.

Documents

Nesbitt JPhysChem1996