JOURNAL OF CHEMICAL PHYSICS VOLUME 114, NUMBER 3 15 JANUARY 2001

Electronic continua in time-resolved photoelectron spectroscopy.II. Corresponding ionization correlations

M. Schmitt, S. Lochbrunner,a) J. P. Shaffer, J. J. Larsen,b) M. Z. Zgierski,and Albert Stolowc)

Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa,Ontario K1A 0R6, Canada

~Received 14 June 2000; accepted 20 October 2000!

We investigate further the role of ion electronic continua in time-resolved photoelectronspectroscopic measurements of ultrafast nonadiabatic coupling. In the preceding paper@Blanchet,Zgierski, and Stolow, J. Chem. Phys.114, 1194 ~2000!#, the limiting case of complementaryionization correlations permitted a disentangling of electronic from vibrational dynamics. Here weexamine the other limiting case in which the nonadiabatically coupled sates~e.g., S2 and S1!correlations correspond to the same ionic continua, presumably an unfavorable case. We useultrafast internal conversion in the polyaromatic hydrocarbons phenanthrene and naphthalene asexamples. In this situation, the geometry changes~displacements! upon nonadiabatic crossing andupon ionization will strongly affect the ability to disentangle electronic from vibrational dynamics.Particularly, phenanthrene and naphthalene are both very rigid molecules and have smalldisplacements upon internal conversion and ionization, still allowing for direct monitoring of theS2

state internal conversion rate. ©2001 American Institute of Physics.@DOI: 10.1063/1.1331637#

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I. INTRODUCTION

The nonadiabatic coupling of electronic and vibrationdegrees of freedom is central to much of the photochemiof polyatomic molecules.1 The investigation of nonradiativedecay processes such as internal conversion and intersycrossing has been the subject of intense research over myears.2–9 The inherently rapid mixing of electronic with vibrational degrees of freedom leads to strongly varying trsition moments and complex, often large amplitude nucldynamics. Here we consider the use of time domain teniques in which coherent superpositions of molecular eigstates prepare the essentially zeroth-order states of inter10

The choice of the final state in femtosecond pump–prexperiments is important as it affects the information contand determines the experimental method~e.g., detection ofphotons versus particles!. The particular choice of the molecular ionization continuum as the final state is advangeous11–16 because the ground state of the ion is often wknown, ionization is a universal detection method~no‘‘dark’’ states!, and differential techniques~such as photo-electron spectroscopy! may be employed, increasing the information content.

Femtosecond time-resolved photoelectron spectrosc~for a recent review, see Ref. 17! has been applied to wavpacket dynamics in simple systems,12,13,18–20 nonadiabaticintramolecular11,21–28 and photodissociation23,29 dynamics,spin–orbit coupling dynamics,30,31 intracluster reaction

a!Present address: Institut fu¨r Medizinische Optik, Ludwig-Maximilians-Universitat Munchen, D-80538 Mu¨nchen, Germany.

b!Present address: Institutes of Physics and Astronomy, University of A˚ rhus,DK-8000 Arhus C, Denmark.

c!Author to whom correspondence should be addressed. Electronicalbert.stolow@nrc.ca

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dynamics,32 excited state proton transfer dynamics,33 andmodel molecular switches.34 The outgoing photoelectronmay be differentially analyzed as a function of time not onwith respect to kinetic energy but also with respect to anlar distributions35–40 and spin polarization.41 Additionally,time-resolved photoelectron–photoion coincidence28 andphotoelectron–photoion coincidence-imaging spectrospies29 have been demonstrated.

In this paper, we consider further the role of the ion coelectronic continua in time-resolved photoelectron spectrcopy. In the preceding paper@Blanchet, Zgierski, andStolow42 ~BZS!#, we investigated the limiting case ocomplementary ionization correlations in which the coupelectronic excited states correlate with different ion coelectronic states. The role of correlations upon photoionition was considered in a study of electronic population dnamics during intersystem crossing.30 We demonstrated thathese correlations could be used to disentangle electrfrom vibrational dynamics during nonadiabatprocesses.23,24,26,42This is discussed in detail in BZS.

Here, we study the other limiting case, that of corrsponding ionization correlations in which the coupled eletronic states~e.g.,S2 andS1! correlate upon photoionizationwith the same electronic state of the ion~e.g., the groundstateD0!. We expect such correlations to be unfavorabledisentangling electronic from vibrational dynamics. Nevetheless, nonadiabatic processes convert electronic to vitional energy and the change in the latter could still beparent in the photoelectron spectra. However, our abilitymonitor the vibrational dynamics in each of the coupled eltronic states depends strongly and specifically on the geetry changes~displacements! between the nonadiabaticallcoupled states and that of the ion state. In order to provexamples with corresponding ionization correlations andil:

6 © 2001 American Institute of Physics

1207J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Electronic continua. II

TABLE I. Molecular orbital configuration in phenanthrene.

Electronicstate

Molecular orbital occupancy

WeightCorrelatedion statea2 a2 b1 a2 b1 b1

NeutralS0

1A1 2 2 2 0 0 0 100% D02B1

S11A1 2 2 1 0 1 0 50% D0

2B1

2 1 2 1 0 0 50% D12A2

S21B2 2 2 1 1 0 0 75% D0

2B1

2 1 2 0 1 0 25% D12A2

CationD0

2B1 2 2 1 0 0 0 100%D1

2A2 2 1 2 0 0 0 100%D2

2A2 1 2 2 0 0 0 100%

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illustrate the effects discussed previously, we have chosestudy ultrafast internal conversion in the polyaromatic hydcarbon phenanthrene and compare this behavior with thanaphthalene.

In Table I the molecular orbital configuration and aproximate weights are shown for the electronic statesphenananthrene which are important in the internal consion process. These were obtained with the QCFF/Cmethod.43,44 The groundS0 state is a single configuratiowhile the S1 and theS2 states consist of two configuratiowith a 1:1 and 3:1 weight, respectively. Within the Koomans picture, ionic states are populated by single-phosingle active electron ionization. The result of this appromation is shown in the last column of Table I, which givthe ionic states formed upon adiabatic removal of the oumost electron. It can be seen that in the case of phenanthboth theS2 and theS1 states correlate with the ground staof the cation as well as the first excited state of the catiThis is the limiting case of corresponding ionization corretions and is to be contrasted with the limiting casecomplementary ionization correlations discussed in BZSthis paper, we show that even in this unfavorable case, tiresolved photoelectron spectroscopy can be applied in oto directly monitor theS2 to S1 internal conversion processThe ability to do this depends upon geometry changes inmolecule of interest. The results obtained on phenanthrwill be compared with those of naphthalene, which shothe same Koopmans-type correlations as phenanthrene.main difference in the electronic level structure betwephenanthrene and naphthalene is the energy gap betweeS2 and theS1 states. Phenanthrene, which has a fairly laenergy gap, belongs to the statistical limit case whernaphthalene, with a smaller energy gap, corresponds tointermediate coupling case.45–53These differences are furthediscussed in the following.

The optical transition prepares a zeroth-order electrostate ~e.g., S2! that is selected by its respective oscillatstrength from the ground or initial state.2,5,6,54,55Isoenergeticwith the optically bright state is a dense manifold of vibronlevels which belong to some lower zeroth-order electrostate~e.g.,S1!. It is assumed that optical transitions betwethe initial state and this vibronic manifold are forbidden. Tnonadiabatic coupling of the bright electronic state with

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dense manifold of zeroth-orderS1 vibronic levels leads tothe nonradiative ‘‘decay’’~dephasing! of the zeroth-orderS2

wave packet. If the energy gap between these two excstates is big, the density ofS1 vibronic levels is extremelylarge and the dark state forms an apparently smooth qucontinuum. Such a situation is known as the statistical limfor the radiationless transition problem. The very small aunequal level spacings mean that the revival time of thetially prepared state is very long compared to other tiscales and therefore the dephasing of the initially prepazeroth-order state appears irreversible. By contrast, ifelectronic energy gap is comparable to the vibronic enespacing, theS1 vibronic states often form a highly structuremanifold which is known as the intermediate case. The stistical limit is phenomenologically characterized bLorentzian-type absorption bands where the apparent hogeneous widthG is related to the ‘lifetime’ of the brightstate,t5\/G. In the intermediate case, a complex structurabsorption spectrum with a broad energy spread obtainsdue to the larger level spacings in this case, very fast~usuallynonexponential! nonradiative decay of the initialS1 /S2 mix-ture is observed.

In the following, we describe our experimental methand then present our TRPES studies of internal converfor the case of corresponding ionization correlationsphenanthrene and naphthalene.

II. EXPERIMENT

The experimental apparatus, described in deelsewhere,56,57 relies on a amplified femtosecond laser sytem to generate independently tunable UV pump and prpulses and a high intensity molecular beam version of a mnetic bottle photoelectron spectrometer.

Briefly, for these experiments, the laser system consisof a Ti:sapphire oscillator~830 nm, 75 fs! pumped by adiode-pumped based YLF laser. These pulses seeded a 1regenerative amplifier, resulting in 1.1 mJ pulses of 80duration. The amplified 830 nm output was split into twwith a 30:70 ratio. Fourth-harmonic generation of the weabeam by two successive BBO crystals provided UV propulses at 207.5 nm. The stronger beam was used to pumfour-pass optical parametric amplifier, the output of whi

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1208 J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Schmitt et al.

was mixed with residual pump light at 830 nm to produtunable pulses in the visible region~500–600 nm!. Thesewere frequency doubled in a thin BBO crystal to produceUV pump pulses. Both the pump and probe pulses werecompressed in a double-prism configuration. The pump pwas sent through a computer controlled optical delay lirecombined collinearly with the probe pulse, and focuseda 500 mm focal length mirror into the ionization regionthe magnetic bottle time-of-flight spectrometer. Typical eergies at the entrance to the chamber are 550 nJ in the pbeam and up to 2.0mJ in the pump beam. Intensities wekept below 131011W/cm2 and therefore ponderomotivbroadening of the spectra was neglible.58 The absolutepump–probeDt50 and laser cross-correlation width wedetermined by difference frequency mixing of the pump aprobe pulses in a BBO crystal directly in front of the chaber and byin situ nonresonant ionization of a simple ga~e.g., Xe!. The cross-correlation signal between pump aprobe laser was determined to be;170 fs full width at halfmaximum ~FWHM!. In these experiments, both phenathrene and naphthalene were each prepared by a fs ppulse to be at the vibrationless electronic origin of theirspectiveS2 states.

The large, main high throughput source chamber~pump-ing speed 10 000 l/s, base pressure 231027 Torr! is sepa-rated by two skimmers~0.3 and 1.0 mm diameter! from theultrahigh vacuum magnetic bottle chamber~base pressure 2310210Torr!. A schematic sketch of the spectrometershown in Fig. 1. It is basically composed of a 1 T electro-magnet, a solenoidal magnetic guiding field~10 G! along thedrift tube, and a detector. The electrons initially emitted inthe upper half-plane are parallelized by the highly divergstrong magnetic field at the interaction point, leading to apsolid angle collection.59 The simple time-of-flight~TOF!measurement permitted each laser shot to be rapidly trferred to a computer for dynamic background subtractireal-time data normalization, and active laser pulse ene

FIG. 1. Schematic sketch of the magnetic bottle photoelectron spectromA skimmed molecular beam enters the interaction region of the magnbottle. The strongly divergent 1 T magnetic field parallelizes electron trajectories in the upper-half plane. These are guided in a 10 G field towadetector. In a typical experiment, photoelectron kinetic energy spectrarecorded as a function of time delay.

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filtering. The photoelectron energy calibration was obtainvia two-photon ionization of nitric oxide. Due to the cylindrical symmetry about the laser propagation direction, thmeasurements are angle integrated.

Phenanthrene~or naphthalene! molecules were seeded iHe ~200 Torr! and introduced through a 0.5 mm continuomolecular beam nozzle. The phenanthrene sample cellheated to 80 °C, the gas line and the nozzle to 120130 °C, respectively, to prevent plugging. The naphthalesample reservoir was kept at a temperature of 60 °C, wthe gas line and nozzle temperatures were 70 and 80respectively. The naphthalene and phenanthrene werechased from Aldrich and used without further purification

III. RESULTS AND DISCUSSION

Considerable spectroscopic information is availaabout the energies and symmetries of the phenanthreneecule and its cation, as summarized in Fig. 2~a! ~see alsoTable I!.60 We excited jet-cooled phenanthrene from tS0(1A1) ground state to the origin of theS2(1B2) state witha 282 nm~4.39 eV! fs pump pulse. The excited moleculeare then ionized after a time delayDt using a 207.5 nm~5.98eV! probe photon. TheS2(1B2) state is known to rapidlyinternally convert to the lower lyingS1(1A1) state at 3.64eV, transforming electronic into vibrational energy~dashedline!. The Koopmans-type correlations expected for sinphoton, single active electron ionization, as given in Tableare shown by the downwards arrows. It can be seen thatthe S2(1B2) and S1(1A1) states can correlate with thD0(2B1) ion ground state, producing thee1 and e4 photo-electron bands. They can also each correlate withD1(2A2) ion excited state, producing the electron bandse2

ande5 .In Fig. 2~b! we show time-resolved photoelectron spe

tra for phenanthrene as a function of time delay betwepump and probe pulses. The pump and the probe laserlarizations were parallel to the electron TOF axis. The phtoelectron spectra reveal a rapidly decaying but energeticnarrow peak ate1'2.5 eV @see Fig. 2~b!#. This peak is dueto photoionization of the vibrationlessS2(1B2) state into theionic ground stateD0(2B1), as expected based on Table I.order to monitor the zeroth-order electronic population dein theS2 state, i.e., to obtain its lifetime, this time-dependepeak in the photoelectron spectra was integrated and thetegral plotted as a function of pump–probe delay time,shown in Fig. 3. The solid line shown in Fig. 3 is a convlution of the pump–probe cross correlation of 170 fs~CC,dashed line! and a monoexponential decay. The fit resultsa decay time constant of 522616 fs. The population flow outof the S2 state is due to the population of high vibrationlevels of the S1(1A1) state which are nonadiabaticallcoupled to theS2 state~internal conversion!.

The broad band, centered at about 1.5 eV, in these ptoelectron spectra is partially due to ionization of vibrtionally hot molecules in theS1 state formed by theS2–S1

internal conversion. Normally one would expect this 1.5band to grow as a function of time due to population flointo theS1 state, as was demonstrated for the case of deeraene internal conversion24,42 in BZS. This simple picture is

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1209J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Electronic continua. II

not observed in our measurement because our probe lasesufficient energy~5.98 eV! to project the intermediate statnonadiabatic wave packet produced by the pump laserseveral cation electronic states. Figure 2~a! shows that up tofour photoionization bands (e2–e5) can in principle contrib-ute to this 1.5 eV feature, although ionization out of theS2

state into the second excited ionic stateD1(e3) should beless favorable because of the Koopmans propensity rules~seeTable I!. The broad component of the photoelectron specwe observe around 1.5 eV is therefore, at short times, aperposition of both decaying (e2 ,e3) and growing (e4 ,e5)photoelectron bands. Generally one can expect that thetoelectron bands arising from ionization out of theS1 stateshould be broader than those arising from the electronicgin of the S2 state because of the ongoing intramolecuvibrational energy redistribution~IVR! in the vibrationallyhot molecule on theS1 potential energy surface. At timest

FIG. 2. Time-resolved vibrational and electronic dynamics during interconversion for phenanthrene.~a! Energy level scheme for phenanthrenSymmetry labels for the neutral and ionic states relevant to the tiresolved photoelectron spectra are given. As suggested in Table I, thS2

state correlates electronically with theD0 andD1 producing the photoelec-tron bandse1 and e2 . The S1 state formed by internal conversion alscorrelates electronically with theD0 andD1 , here producing the photoelectron bandse4 ande5 . The dashed lines represent the vibrational energythese states after internal conversion.~b! Time-resolved photoelectron spectra of phenanthrene for parallel pump and probe laser polarizations~lpump

5282 nm, lprobe5207 nm!. The disappearance of the peak ate152.5 eVrepresents a direct measure of theS2–S1 internal conversion time. Thebandse4 ande5 are due to photoionization ofS1 into D0 andD1 , respec-tively. For a discussion, see the text.

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.1500 fs or so~i.e., after internal conversion!, the 1.5 eVband is comprised almost exclusively of signals due toS1

ionization ~e4 ande5!. As can be seen, theS1 state itself islong lived on the time scale of our experiment.61

As discussed in Sec. I, phenanthrene presents anample of the~unfavorable! limiting case of correspondingionization correlations because both theS2 andS1 states cancorrelate electronically to the same ion electronic states~e.g.,D0!. Despite this fact, we still see a dramatic shift in tphotoelectron spectrum as a function of time, allowing usdirectly monitor the electronic population flow. This is duto the fact that phenanthrene is a very rigid molecule andS2 , S1 , andD0 states all have roughly similar geometrieThe photoionization probabilities are therefore expectedbe dominated by smallDv transitions. This is illustrated bythe calculated~QCFF/PI! Franck–Condon structures for thS1,2→D0 andS1,2→D1 transitions, shown in Figs. 4~a! and4~b!, respectively. The results are convoluted with a 75 minstrumental width in order to match the experimental eneresolution, as in BZS. We can see that similar, short FranCondon progressions occur inS2→D0 @Fig. 4~a!, solid line#,S1→D0 @Fig. 4~b! dashed line#, andS2→D1 @Fig. 4~b!, solidline# transitions. Only theS1→D1 @Fig. 4~b!, dashed line#transition is expected to show a somewhat longer progsion, although even in this case, the 0–0 transition playsimportant role in the spectrum. Hence, the 0.75 eV vibtional energy in theS1 state would be roughly conserveupon ionization into theD0 ionic state. That is to say, wewould expect the edge of thee4 band to be shifted to loweenergies by about 0.75 eV as compared with thee1 band.Indeed this is what is observed in Fig. 2~b!. Therefore, forthe particular case of phenanthrene, small geometry chafavor conservation of vibrational energy upon ionization athereby permit the direct observation of the excited stelectronic population dynamics via a photoelectron kineenergy analysis. More generally, larger geometry chanupon internal conversion and ionization would mean tbands such ase1 ande4 would overlap, as was observed fo

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FIG. 3. Energy integration of the peak ate152.5 eV shown in Fig. 2~b!,plotted as a function of time. The solid line is a fit to a convolution ofmonoexponential decay of time constant 522616 fs with a Gaussian crosscorrelation function~CC, dashed line! of width 170 fs FWHM. This deter-mines theS2 lifetime to be 522616 fs.

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1210 J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Schmitt et al.

the case ofS1–S0 internal conversion in hexatriene.21 Insuch cases, a clear disentangling of electronic from vibtional dynamics is more challenging and requires a coneration of even more differential measurements, such asergy resolved photoelectron angular distributions.

Photoelectron spectra measured at perpendicular puprobe polarizations can show different ionization cross stions than those measured with parallel pump–probe poizations due to an aligned intermediate state. Figure 5 shthe photoelectron spectra obtained with perpendicular poization between pump and probe laser. These photoelecspectra are essentially identical to those obtained with palel polarization@see Fig. 2~b!#. These observations indicatthat the experimental measurements are insensitive tointermediate state alignment and rotational dephasing effeRotational dephasing would otherwise be unexpected ontime scale of these measurements. In Fig. 5~inset!, we showthe integratede1'2.5 eV peak~due toS2 ionization into theD0 continuum! as a function of time. The fit yields a decatime constant of 52068 fs. This agrees with the results fromFig. 3 within our experimental error bars and confirms taccuracy and reproducibility of these measurements.

The energy gap between the electronic origins of theS2

and S1 states is 0.75 eV. This value is sufficiently largeensure that electronic ‘‘relaxation’’ from theS2 state occursin the statistical limit. The absorption and the fluorescenexcitation spectra for theS0→S2 transition measured in asupersonic free jet revealed a Lorentzian-type spectralshape.52,53In the statistical limit, the line shape is expectedappear Lorentzian with a homogeneous width related direto the electronic dephasing time scale. From the obserlinewidth the homogeneous width was estimated by decvoluting the rotational broadening contribution. The latwas obtained from the inhomogeneously broadenedS0→S1

origin by assuming that the rotational broadening is the sa

FIG. 4. Calculated QCFF/PI Franck-Condon structures for theS1,2→D0 ~a!and theS1,2→D1 transition ~b! in phenanthrene. TheS2→D0 @~a!, solidline# S1→D0 @~a!, dashed line#, and S2→D1 @~b!, solid line# transitionsshow similar structure. Only theS1→D1 @~b!, dashed line# transition showsa somewhat longer progression, although still showing a strong 0–0 tration ~vertical solid line!. The calculations have been convoluted with ameV instrument function in order to match the experimental kinetic eneresolution.

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for both transitions. This estimated homogeneous widthphenanthrene was found to be 11.1 cm21 and leads to aninferred internal conversion rate for the vibrationless levelthe S2 state in isolated phenanthrene molecules of;500 fs.This estimate based on linewidth measurement and rotatideconvolution can now be confirmed by the more accurvalues we measured directly~Figs. 3 and 5!. As discussedpreviously, the time-resolved photoelectron spectra@Figs.2~b! and 5# directly reveal theS2–S1 internal conversiontime scale via the decay of the peak ate1'2.5 eV. We notethat linewidth measurements can give a good estimate ofelectronic dephasing time scale but do not provide muinformation about the underlying nuclear dynamics. Athough not apparent in phenanthrene due to the high denof states, time-resolved photoelectron spectroscopy canveal the underlying vibrational dynamics which promotand tunes the nonadiabatic crossing as well as the IVR whoccurs on the ‘‘dark’’ potential energy surface,24 as dis-cussed in BZS.

While phenathrene shows narrow Lorentzian-typesorption or fluorescence excitation bands, naphthalenecontrast has a complicated, irregularly structured absorpspectrum above theS2 threshold.45,46,49The structure cannobe assigned to a conventional vibrational progression andbeen interpreted in terms of strong mixing of the zeroorder vibronic states in theS2 manifold with a sparse set ozeroth-order vibronicS1 states.45,46,48–50,62In such cases, themixing of zeroth-orderS2 with zeroth-orderS1 states de-pends on accidental degeneracies. The character of theselecular eigenstates can therefore fluctuate between thoseare essentiallyS2 , those that are essentiallyS1 , and statesthat are on average an equal combination of both. These

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FIG. 5. Time-resolved photoelectron spectra of phenanthrene for perdicular pump and probe laser polarizations~lpump5282 nm, lprobe

5207 nm!. The disappearance of the peak ate152.5 eV again representsdirect measure of theS2–S1 internal conversion time and confirms the acuracy of the results shown in Fig. 2. The bandse4 and e5 are due tophotoionization ofS1 into D0 andD1 , respectively.~Inset! Energy integra-tion of the peak ate152.5 eV plotted as a function of time. The solid linea fit to a convolution of a monoexponential decay of time constant 568 fs with a Gaussian cross-correlation function~CC, dashed line! of width170 fs FWHM. This determines theS2 lifetime to be 52068 fs, confirmingthe accuracy of the results shown in Fig. 3.

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1211J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Electronic continua. II

typical characteristics of the intermediate level structure cwhich is found in molecules with smallS2–S1 energy gapssuch as naphthalene@DE(S2–S1)50.48 eV#. If the vibroniclevel density in theS1 state is low in the region of the electronic resonance, the spectrum is not broadened as instatistical limit case but rather appears as a highly compset of sharp lines. In this case the complete vibronic mixof theS2 state with the lower lyingS1 state leads to the losof the identity of theS2 state in the Born–Oppenheimesense. The estimated degree of the zeroth-order vibrationS2 character in the region near theS2 origin is only10%–20%.46,49 Vibrationally resolved photoelectron spectof jet-cooled naphthalene, obtained via ionization from vaous vibronic levels of theS1 and S2 states, was previouslyreported.51 Among other things addressed was the quesof which electronic state the photoelectrons were ejecfrom in the case of the excitation to theS2 origin. It wasobserved that the electronic dephasing rate is much fathan the ionization rate from the optically prepared zeorder S2 state and that many vibrationally excitedS1 statesare produced. The estimatedS2–S1 dephasing rate was fastethan 1011s21.

Naphthalene has the same limiting case Koopmans-correlations as phenanthrene. An interesting question isthe intermediate caseS2–S1 coupling in naphthalene manfests itself in time-resolved photoelectron measurementsorder to investigate this, we prepared theS2 electronic originwith a fs pump pulse at 278 nm@see Fig. 6~a!#. As in phenan-threne, bothS2 and S1 can ionize intoD0 producing thephotoelectron bandse1 and e3 , both S2 and S1 can ionizeinto D1 producing the photoelectron bandse2 ande4 . Thesedynamics lead to the time-resolved photoelectron speshown in Fig. 6~b!. The spectra show a peak ate152.3 eV,which is due to ionization of theS2(1B2u) state into theD0(2Au) ground electronic state of the ion. Figure 7 shothe integrated 2.3 eV photoelectron peak~circles! from Fig.6~b! as well as the laser cross-correlation signal~CC, dashedlines! measured by difference frequency mixing in a BBcrystal. It can be seen that thisS2 signal does not differappreciably from the cross-correlation signal~for positivetimes!. This observation means theS2–S1 internal conver-sion time must be considerably faster than 100 fs, aspected. These spectra also show an energetic band ae3

51.8 eV arising from photoionization of vibrationally hotS1

molecules into theD0(2Au) ionic ground state of the ionThe signal between 1.2 and 1.7 eV corresponds to ionizaof theS2 state into theD1(2B1u) excited state of the ion. Fotime delays outside the cross correlation we find a conssignal between 0.6 and 1.8 eV which is due to ionizationthe S1 state~e3 ande4!. Photoelectrons arising from ionization out of theS2 state into theD1 excited state of the ionhaving an energy ofe2'1.60 eV do not contribute to thisbroad band because, as we see from the peake1 which fol-lows the cross-correlation signal, theS2–S1 internal conver-sion occurs within the cross-correlation time. This showsnonoverlapping lasers that, only theS1 state is populatedFor negative delay times~i.e., pumping at 207.5 nm!, decaydynamics of an unassigned higher lying state can be seeFig. 7.

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TheS2 origin of naphthalene, which is a typical exampof an intermediate coupling case, shows a much fasterS2–S1

internal conversion than phenanthrene. The rate of inteconversion depends not only on the gap between theinteracting states but also on the vibronic coupling of the tstates by promoting modes ofb2 symmetry for phenanthrenandb1g symmetry for naphthalene. We have calculated thparameters previously for naphthalene using the compneglect of differential overlap/S method using QCFF/normal modes.63 Calculations done for phenanthrenethe same way reveal that the largest coupling, for1375 cm21C–C b2 stretching mode, is 30 cm21. This is afactor of 2 smaller than the value of the largestS2–S1 cou-pling in naphthalene.63 Therefore, the slower internal convesion in phenanthrene as compared with naphthalene is duboth a larger electronic energy gap and a smaller vibrocoupling strength between the two electronic states.

The characterization of nonradiative processes like innal conversion is described as a dephasing of molec

FIG. 6. Time-resolved vibrational and electronic dynamics during interconversion for naphthalene.~a! Energy level scheme for naphthalene. Symmetry labels for the neutral and ionic states relevant to the time-resophotoelectron spectra are given. As suggested in Table I for phenanththe S2 state correlates electronically with theD0 and D1 producing thephotoelectron bandse1 ande2 . TheS1 state formed by internal conversiocorrelates electronically withD0 andD1 producing the photoelectron bande3 ande4 . The dashed lines represent the vibrational energy in these safter internal conversion.~b! Time-resolved photoelectron spectra of napthalene for parallel pump and probe laser polarizations~lpump5278 nm;lprobe5207 nm!. The peak ate152.3 eV is due to photoionization ofS2 intoD0 . The bandse3 ande4 are due to photoionization of theS1 state intoD0

andD1 , respectively. The internal conversion time scale in this intermedcoupling case is faster than our time resolution.

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1212 J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Schmitt et al.

eigenstates.5,54,55The pump pulse coherently excites a wapacket, in the impulsive limit, withS2 character. Immedi-ately after the laser pulse, the phases of all eigenstates inwave packet interfere constructively so as to augmentS2

character and interfere destructively with respect toS1 char-acter. This means that the photoelectron spectrum at theof excitation shows a signal dominated by photoionizationthe zeroth-orderS2 state. For longer delay times, dephasiof all the molecular eigenstates occurs, leading to a loss oS2

character. If these states contain bothS2 and S1 character,and theS1 character dominates, then the dephasing processentially converts a zero-orderS2 state into a zero-orderS1

state. The time required for this process is on the order ofreciprocal energy width over which theS2 character is dis-tributed. Our laser pulses were not short enough~i.e., did nothave sufficient bandwidthDv! to excite all eigenstates withS2 contribution in naphthalene. This means that, in contrto phenanthrene, the excitation does not in fact preparezeroth-order Born–OppenheimerS2 state and therefore wobserve a dephasing time which is just;Dv21, the inverselaser bandwidth.~Due to the irregular level spacings in thproblem, the revival of the zeroth-orderS2 state would takequite some time!. Nevertheless, the molecular ionizatiocontinuum is still quite a useful template for projecting ozeroth-order electronic configurations, as can be seen fFig. 6~b!.

IV. CONCLUSION

In this paper, we investigated the role of different iocore electronic continua upon time-resolved photoelectspectroscopy measurements. We have identified two limicases of photoionization correlations in such experimeSpecifically, in contrast to the preceding paper~BZS! wherecomplementary ionization correlations permitted a disentgling of electronic from vibrational dynamics, here we cosidered the other limiting case of corresponding correlatiwhere the nonadiabatically coupled excited states corre

FIG. 7. Energy integration of the peak ate152.3 eV shown in Fig. 6~b!,plotted as a function of time. It can be seen that, for positive times,signal follows the cross-correlation signal~CC, dashed line! indicating thatthe internal conversion time scale is much less than 100 fs. For negtime delays, the excited state dynamics of a higher lying state can beFor a discussion, see the text.

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with the same ion electronic states. In these situations, gmetrical effects~displacements! become important for ob-serving the electronic population flow. To this end, we hachosen the presumably unfavorable case of polyaromaticdrocarbons where both the initial (S2) and final (S1) statescorrelate to the same electronic states of the ion~e.g.,D0!.We investigated theS2–S1 internal conversion process iphenanthrene and, for comparison, in naphthalene.phenanthrene, the electronic population flow out of theS2

state, forming a vibrationally hotS1 state, was directly ob-served with a time constant of 521 fs, confirming previoestimates based upon deconvoluted linewidth measuremPhenanthrene is a rigid molecule with small displacemeupon transitions. The direct observation of electron popution flow was favored by the small geometry changes upionization ~small Dv!.

The S2–S1 internal conversion process in naphthalenby contrast, occurred within the cross correlation of our lapulses. The different dephasing times of phenanthrenenaphthalene can be understood in terms of the differS2–S1 energy gaps and coupling strengths in these two mecules. In phenanthrene the energy gap is 0.75 eV so thS1

state forms an apparently smooth quasicontinuum, the sttical limit. In this case, the initially preparedS2 statedephases irreversibly into this quasicontinuum with a rconstant given by the well-known Fermi golden rule raexpression. Naphthalene has a smallerS2–S1 energy gap~0.48 eV! and a vibronic coupling strength roughly doubthat of phenanthrene. In this case theS1 state forms a highlystructured ‘‘quasicontinuum,’’ known as the intermediacoupling case. Here theS2 state is diluted among a manifolof spectroscopically distinct molecular eigenstates whichformed by the coupling. The mixing ofS2 with S1 statesleads to a very fastS2–S1 internal conversion process. Inaphthalene, the bandwidth of our pump laser pulse is nrower than the spectral spread of molecular eigenstatestaining S2 character. In such cases, the observed electrodephasing time is simply the inverse pump laser bandwid

In the most general case, neither the electronic corrtions nor the geometry changes may be favorable. Asexample, consider a case where the two coupled statesrelate to the same ion states~e.g., D0! and the geometrychanges upon internal conversion and ionization are sigcant, leading to long, overlapping vibrational progressioIn this situation, photoelectron kinetic energy analysis alowill likely fail to disentangle electronic from vibrational dynamics. However, the other component of the ionization ctinuum, the free electron wave function, remains availafor analysis. The free electron partial wave compositiontermines the photoelectron angular distribution~PAD!. Thesymmetry of the PAD is determined by the electronic symetry changes upon ionization and therefore it is expecthat photoelectron angular distribution measurements rethe evolution of excited state electronic symmetry durinonadiabatic processes. A general nonperturbative formafor the calculation of time-resolved PADs has bedeveloped.36,39,40In forthcoming paper,64 we apply this for-malism to several examples of excited state nonadiabaticnamics and discuss the new opportunities which eme

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1213J. Chem. Phys., Vol. 114, No. 3, 15 January 2001 Electronic continua. II

from these considerations. We expect time-resolved phelectron spectroscopy to be of potential use whenevercited state nuclear dynamics leads to changes in the chdistribution of the molecule. As discussed in BZS, such pcesses include internal conversion, intersystem crossing,ton transfer, electron transfer, and molecular scale electrswitching. We anticipate seeing many new studies of ssystems.

ACKNOWLEDGMENTS

The authors thank Professor C. A. de Lange, ProfesW. J. Buma, and Professor V. Blanchet for helpful discsions on magnetic bottle photoelectron spectroscopy. Mand S.L. acknowledge the Deutsche Forschungsgemeinsfor the receipt of a Postdoktoranden Stipendium. J.J.L.knowledges the Danish government for financial support

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