Intramolecular Vibrational Energy Redistribution in Aromatic Molecules of Type C 6 H 5 X (X ) H, D, F, Cl, CH 3 , CF 3 ) Rebekka S. von Benten, † Yaxing Liu, † and Bernd Abel* ,‡ Institut fu ¨r Physikalische Chemie der UniVersita ¨t Go ¨ttingen, Tammannstrasse 6, D-37077 Go ¨ttingen, Germany, and Wilhelm-Ostwald-Institut fu ¨r Physikalische und Theoretische Chemie, UniVersita ¨t Leipzig, Linne ´-Strasse 2, D-04103 Leipzig, Germany ReceiVed: June 13, 2010; ReVised Manuscript ReceiVed: September 11, 2010 Femtosecond IR pump UV probe spectroscopy was employed in the gas phase to study intramolecular vibrational energy redistribution (IVR) in benzene and five monosubstituted derivatives thereof. After selective excitation of the first overtone of the ring CH-stretch vibration, all molecules showed the same two-step redistribution dynamics characteristic for nonstatistical IVR. The nature of the substituent influences mainly the second, slower IVR component. The presence of an internal rotor does not alter the redistribution rate or pathway compared to that of a monatomic substituent of equal mass. Coupling order model calculations reflect the experimental trends well if the polyatomic substituents are regarded as decoupled from the intra- ring dynamics and modeled as point masses. 1. Introduction Intramolecular vibrational energy redistribution (IVR) is a process that lies at the heart of chemical reactions. In photo- excited reactants, the rate and pathways of IVR govern the rate, pathways and yields of the reaction. 1 On the other hand synthetic chemists are well used to adding certain activating/protective groups to molecules or molecular subunits to influence their reactivity. The question that arises naturally is whether this concept of functional groups is transferable to IVR, i.e., whether systematic chemical substitution can help controlling the outcome of photochemical reactions. To answer this question, it is crucial to understand the influence of certain structural features on the time scales and mechanisms of vibrational energy flow. In the past decade IVR in isolated molecules has been investigated experimentally in the time and frequency domains as well as theoretically with some success, 2–4 and some structural IVR factors for individual classes of molecules have been identified (for a good overview, see ref 5 and literature cited therein). In this article we report a study on benzene and five monosubstituted derivatives thereof, namely benzene-d 1 , fluo- robenzene, chlorobenzene, toluene, and R,R,R-trifluorotoluene, with time-resolved transient absorption spectroscopy. Of these molecules, benzene and toluene have already been subject to many experimental 6–8 and theoretical 9,10 benchmark studies on IVR that can well be tied in with the present investigation. Some of these systems have already been part of a study in our group on the impact of chemical substitution on IVR in the solution phase. 11 Recent results regarding the solvent influence on IVR indicate, however, that certain substitution effects can be masked in a dense liquid environment. 12,13 To elucidate the unperturbed substitution influence, we thus extended the study to the isolated gas phase species. A special focus will lie on the relation between substituent structure (monatomic vs polyatomic), substituent mass and vibrational dynamics of the phenyl ring under conditions of nonstatistical IVR. 2. Experimental Methods The time-resolved measurements were conducted with IR pump UV probe spectroscopy as pioneered by Crim 14,15 et al. Details of the experimental setup have been published elsewhere. 16,11 The principle of the technique is that an IR laser pulse initiates a certain localized, high-frequency, nonstationary vibrational state in the molecule, which in the case of the aromatic molecules described in this paper is the first CH-stretch overtone. This zeroth-order bright state is not Franck-Condon- (FC)-active in the electronic UV transition. As IVR proceeds, the increasing population of low-frequency FC-active vibrations causes an increase in the absorption of the time-delayed UV probe pulse, which is tuned to the long wavelength wing of the first electronic transition. The limited number of FC-active vibrations of the molecules can be identified by UV absorption, resonance Raman, and dispersed fluorescence experiments. 17–21 In the same way as IVR increases the absorption, subsequent intermolecular vibrational energy transfer (VET) to surrounding molecules decreases the absorption again. As described in previous reports, 22 change in optical density can be converted into change in internal energy via calibration against high temperature absorption spectra. The laser system is composed of a Hurricane (Spectra- Physics) Ti:sapphire laser pumping two optical parametric amplifiers, namely a TOPAS (Light Conversion) and a home- built two-stage NOPA, with pulse widths of ∼60 fs and a bandwidth of ∼300 cm -1 . The IR-pump pulses and time-delayed UV-probe pulses are focused (f ) 80 mm) and overlapped collinearly in the sample cell, a stainless steel cell with sapphire windows (1 mm) and an optical path length of 20 mm. Both collinear overlap and optical path length are necessary to compensate for the intrinsically low sample concentrations in the probed gas phase volume, even though this lessens the actual time resolution (cross correlation of pump and probe pulses) to only 500 ( 200 fs. The temperature of the sample cell was controlled with electrical heating elements and a thermocouple. * Corresponding author. E-mail: [email protected]. † Universita ¨t Go ¨ttingen. ‡ Universita ¨t Leipzig. J. Phys. Chem. A 2010, 114, 11522–11528 11522 10.1021/jp105417a 2010 American Chemical Society Published on Web 10/08/2010
Transcript
Intramolecular Vibrational Energy Redistribution in Aromatic Molecules of Type C6H5X(X ) H, D, F, Cl, CH3, CF3)
Rebekka S. von Benten,† Yaxing Liu,† and Bernd Abel*,‡
ReceiVed: June 13, 2010; ReVised Manuscript ReceiVed: September 11, 2010
Femtosecond IR pump UV probe spectroscopy was employed in the gas phase to study intramolecularvibrational energy redistribution (IVR) in benzene and five monosubstituted derivatives thereof. After selectiveexcitation of the first overtone of the ring CH-stretch vibration, all molecules showed the same two-stepredistribution dynamics characteristic for nonstatistical IVR. The nature of the substituent influences mainlythe second, slower IVR component. The presence of an internal rotor does not alter the redistribution rate orpathway compared to that of a monatomic substituent of equal mass. Coupling order model calculationsreflect the experimental trends well if the polyatomic substituents are regarded as decoupled from the intra-ring dynamics and modeled as point masses.
1. Introduction
Intramolecular vibrational energy redistribution (IVR) is aprocess that lies at the heart of chemical reactions. In photo-excited reactants, the rate and pathways of IVR govern the rate,pathways and yields of the reaction.1 On the other hand syntheticchemists are well used to adding certain activating/protectivegroups to molecules or molecular subunits to influence theirreactivity. The question that arises naturally is whether thisconcept of functional groups is transferable to IVR, i.e., whethersystematic chemical substitution can help controlling theoutcome of photochemical reactions. To answer this question,it is crucial to understand the influence of certain structuralfeatures on the time scales and mechanisms of vibrational energyflow. In the past decade IVR in isolated molecules has beeninvestigated experimentally in the time and frequency domainsas well as theoretically with some success,2–4 and some structuralIVR factors for individual classes of molecules have beenidentified (for a good overview, see ref 5 and literature citedtherein).
In this article we report a study on benzene and fivemonosubstituted derivatives thereof, namely benzene-d1, fluo-robenzene, chlorobenzene, toluene, and R,R,R-trifluorotoluene,with time-resolved transient absorption spectroscopy. Of thesemolecules, benzene and toluene have already been subject tomany experimental6–8 and theoretical9,10 benchmark studies onIVR that can well be tied in with the present investigation. Someof these systems have already been part of a study in our groupon the impact of chemical substitution on IVR in the solutionphase.11 Recent results regarding the solvent influence on IVRindicate, however, that certain substitution effects can be maskedin a dense liquid environment.12,13 To elucidate the unperturbedsubstitution influence, we thus extended the study to the isolatedgas phase species. A special focus will lie on the relationbetween substituent structure (monatomic vs polyatomic),
substituent mass and vibrational dynamics of the phenyl ringunder conditions of nonstatistical IVR.
2. Experimental Methods
The time-resolved measurements were conducted with IRpump UV probe spectroscopy as pioneered by Crim14,15 et al.Details of the experimental setup have been publishedelsewhere.16,11 The principle of the technique is that an IR laserpulse initiates a certain localized, high-frequency, nonstationaryvibrational state in the molecule, which in the case of thearomatic molecules described in this paper is the first CH-stretchovertone. This zeroth-order bright state is not Franck-Condon-(FC)-active in the electronic UV transition. As IVR proceeds,the increasing population of low-frequency FC-active vibrationscauses an increase in the absorption of the time-delayed UVprobe pulse, which is tuned to the long wavelength wing of thefirst electronic transition. The limited number of FC-activevibrations of the molecules can be identified by UV absorption,resonance Raman, and dispersed fluorescence experiments.17–21
In the same way as IVR increases the absorption, subsequentintermolecular vibrational energy transfer (VET) to surroundingmolecules decreases the absorption again. As described inprevious reports,22 change in optical density can be convertedinto change in internal energy via calibration against hightemperature absorption spectra.
The laser system is composed of a Hurricane (Spectra-Physics) Ti:sapphire laser pumping two optical parametricamplifiers, namely a TOPAS (Light Conversion) and a home-built two-stage NOPA, with pulse widths of ∼60 fs and abandwidth of ∼300 cm-1. The IR-pump pulses and time-delayedUV-probe pulses are focused (f ) 80 mm) and overlappedcollinearly in the sample cell, a stainless steel cell with sapphirewindows (1 mm) and an optical path length of 20 mm. Bothcollinear overlap and optical path length are necessary tocompensate for the intrinsically low sample concentrations inthe probed gas phase volume, even though this lessens the actualtime resolution (cross correlation of pump and probe pulses) toonly 500 ( 200 fs. The temperature of the sample cell wascontrolled with electrical heating elements and a thermocouple.
10.1021/jp105417a 2010 American Chemical SocietyPublished on Web 10/08/2010
Experiments with benzene/benzene-d1 were conducted at 473K; for the other measurements the sample temperature was setto 513 K. A pressure gauge directly attached to the samplevolume was used to set a constant pressure of 0.5 bar for allsubstances studied. Transient difference absorptions weremeasured at 0.5 kHz repetition rate for a particular time-delayuntil an acceptable signal-to-noise ratio was reached (∼80 000shots).
To identify the optimal pump wavelength, IR spectra of themolecules were recorded with a Cary 5e spectrometer (Varian).Chemicals were purchased in spectroscopy grade quality andused without further purifications.
3. Results and Discussion
In the present experiments we excited all six molecules inthe two quanta region of the aromatic CH-stretch vibration witha femtosecond laser pulse centered at 1.7 µm. The resultingtransient absorption profiles are shown in Figure 1a-f. Allsignals have the same general form: After excitation (t ) 0),an almost instantaneous rise in absorption is followed by asecond, slower rise until a plateau at maximum change inabsorption is reached. The only exception is toluene (Figure1e) where additionally a slow decay of the signal on a 100 pstime scale is observed. The interpretation of increase anddecrease in transient absorption has been described in detailelsewhere. Briefly, an increase in absorption is caused by IVRfrom the initially excited state into nearly isoenergetic dark bathstates with contribution of FC-active vibrations. The subsequentdecrease of absorption is attributed to energy flow out of thesestates through vibrational energy transfer in collisions (VET).In this case all aromatic molecules under study exhibit at leasttwo intramolecular redistribution steps, which is a clear indica-
tion of nonstatistical IVR. To compare the individual dynamicsquantitatively, the experimental signals were analyzed with amultiexponential model function of the form
to extract time constants τ IVR(1) and τ IVR
(2) and relative IVRamplitudes A. The time resolution of the pump probe experimentwas taken into account by convoluting S(t) with a Gaussianshaped instrument response function of 0.6 ps fwhm. Themodeled signals are included in Figure 1a-f as solid lines. Alsoshown underneath each absorption trace are the residuals of thefits, which leave little uncertainty about the parameter assign-ment. Due to the rather limited time resolution only an upperlimit for the fast IVR component τ IVR
(1) is given. In the case ofbenzene and toluene the collisional energy transfer parametersof Toselli et al.23,24 were used to calculate fixed VET timeconstants, so that only the IVR parameters remained to be fitted.Such energy transfer data have unfortunately not yet beenreported for the other four molecules under study; here τVET
was chosen to be at least 3 orders of magnitude larger thanτ IVR
(2) to reproduce the plateaus in absorption seen in Figure 1.The IVR time constants are not affected by collisions becauseof the large difference in time scales. Therefore, although theparameter τVET is included in the model function it is omittedin the further discussion. The energy transfer parametersobtained from the fits are summarized in Table 1. The existence
Figure 1. Normalized transient absorption profiles (b) of pure gaseous benzene (a), benzene-d1 (b), fluorobenzene (c), chlorobenzene (d), toluene(e), and R,R,R-trifluorotoluene (f). λpump/λprobe were set to 1678/270, 1670/270, 1658/280, 1663/283, 1678/280, and 1660/275 nm, respectively. Alsoshown are fits using the model of eq 1 and residuals.
S(t) ∝ exp(- tτVET
) - [A · exp(- t
τIVR(1) ) +
(1 - A) exp(- t
τIVR(2) )] (1)
Vibrational Energy Redistribution in Aromatic Molecules J. Phys. Chem. A, Vol. 114, No. 43, 2010 11523
of further intramolecular redistribution steps cannot be fullyexcluded, but since the analysis with the two step IVR kineticmodel gives already very satisfactory results, we will regardthis model as sufficient to describe the IVR dynamics.
Before IVR in individual molecules is discussed, a fewgeneral remarks on the experimental results are appropriate. Themechanism most appropriate to describe sequential IVR as seenhere is the well accepted tier mechanism (see Figure 2).25 It isbased on a sorting of the density of dark bath states into subsets(tiers) according to their coupling strength to the initially excitedzeroth-order bright state. When this model is applied to ourresults, the fact that the overall signal compositions, especiallythe fast IVR component, are similar in all six molecules pointsto similar relaxation channels in the early stages and thus tosimilar first tiers in these systems. A likely explanation is thecommon chromophore for excitation in these molecules, i.e.,the first CH-stretch overtone. It is a vibrational state withneglectable substituent contribution, as can be seen from thesimilarity in the stationary IR absorption spectra in Figure 3(gray: region of excitation). It appears plausible that the Fermiresonance between aromatic CH-stretch and CH-bend vibrationsthat dominates the first redistribution step observed in benzene7,26
also facilitates the early IVR dynamics in benzene derivatives.We will come back to this aspect later in the discussion. Thedifference in the relative amplitudes A most likely originates inmolecule-specific FC-factors of the otherwise nearly identicalFC-active normal modes. The influence of chemical substitutionis most clearly seen on the second, slow time scale of IVR,represented by τ IVR
(2) , where we note a variation of at least 1order of magnitude. The fastest IVR(2) is observed in R,R,R-trifluorotoluene (τ IVR
(2) ) 3.8 ( 0.5 ps); the slowest, in benzene(τ IVR
(2) ) 48 ( 5 ps). It should, however, be mentioned that amongthe six aromatic molecules in this study benzene presents aspecial case since it belongs to a higher symmetry class (D6h),while the monosubstituted species can all be classified as C2V.[The barrier for internal rotation is 4.88 cm-1 in toluene27 and3.57 cm-1 in R,R,R-trifluorotoluene.28] To exclude any additionalinfluence of symmetry on the acceleration of IVR(2) upon
substitution, we will therefore in the following limit thediscussion mainly to the five monosubstituted benzene deriva-tives. A detailed investigation by our group of the symmetryeffect on IVR in benzene will be presented in a separate paper.29
For the benzene derivatives of this study one can distinguishbetween monatomic and polyatomic substituents. The compari-son of these systems therefore gives direct insight into theinfluence of the substituent’s structure on the IVR process.
TABLE 1: Energy Flow Parameters for C6H5X Obtained with Eq 1 and Total Density of States
a Obtained with Beyer-Swinehardt direct counting algorithm41 for X ) H, D, F, and Cl. For X ) CH3, CF3 a modified algorithm of Lenzeret al. was used to incorporate the substituent rotational states.42 b Calculated from collisional energy transfer data in ref 23. c Calculated fromcollisional energy transfer data in ref 24.
Figure 2. Stationary absorption spectra of the six aromatic modelsystems. The gray area marks the two quanta region of the aromaticCH-stretch vibration.
Figure 3. Schematic representation of the tier mechanism for IVR:dark states are sorted into tiers by their coupling strength to the zerothorder bright state |B⟩. IVR proceeds as population redistribution fromleft to right.
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Naturally, the size (number of atoms) of a substituent group isclosely related to the total density of states. Since we couldshow that IVR proceeds in a nonstatistical fashion in thesearomatic systems (vide infra), testing for a correlation betweendensity of states, substituent structure, and IVR rate will beespecially interesting. Ideally suited for this comparison is themodel system fluorobenzene (F)/toluene (CH3). Besides the samesymmetry, these two molecules have the same molar mass andthus differ only in the number of vibrational degrees of freedom(F, 30; CH3, 38 + torsion). Furthermore, the methyl groupconstitutes an internal rotor, a structural factor of high interestfor IVR acceleration. Substitution of the fluorine atom with amethyl group leads to an increase in total state density in theregion of excitation (∼6000 cm-1) from 7 × 103 (F) to 5 × 104
(CH3) states per cm-1. Thirty percent of the increase is attributedto additional vibrational states, to which the internal rotationadds a multitude of isoenergetic rovibrational states. Even ifthe selection rules for coupling between internal rotational andvibrational states are taken into account and the effective“accessible” total density of states is thus slightly reduced,30
one would still expect to see some effect on the intramoleculardynamics. Instead, fluorobenzene and toluene exhibit nearlyidentical IVR time constants (see Table 1). Consequently, thequestion to ask is to what degree the additional methyl groupstate density actually contributes to the redistribution process.As mentioned above in our experimental approach, the methylstate density is not directly populated, since the IR excitationpulse is selectively tuned to the phenyl CH-stretch vibrations.Also the observation of the dynamics takes place via FC-activevibrations that belong to the aromatic chromophore. Under theassumption that no efficient relaxation channels between theexcited bright state and the methyl rotational and vibrationalstates exist, one can imagine the substituent to have no activeparticipation in the energy redistribution and rather act as a“spectator group”. The main relaxation dynamics would thenbe limited to the phenyl ring. For that matter theoreticalinvestigations of toluene have been reported that actually predicta partial decoupling of the methyl substituent from the vibra-tional dynamics of the phenyl ring. Martens and Reinhardtconducted classical simulations of S1 p-fluorotoluene thatshowed a separation of the full dimensional vibrational statespace into two subsystems.31 Besides the methyl rotor, the firstsubsystem also holds the lowest frequency vibrations of thephenyl ring, which mix strongly and chaotically with the rotor.Within this part of phase space the authors predict rapid andefficient energy redistribution. The second subsystem is incontrast composed of the remaining high frequency phenylvibrations including the CH-stretching modes. Since these modescouple only indirectly to the methyl rotor, a comparativelyslower relaxation out of this part of the phase space is expected.In another study, Guan and Thompson simulated the vibrationaldynamics of toluene with classical trajectory calculations onan ab initio potential energy surface.32 Through a comparisonof intramolecular relaxation channels after excitation of methyl-and aryl-CH-stretch vibrations, two elementary different IVRmechanisms were identified: From the methyl CH-stretchvibration the excitation energy is first redistributed into themethyl CH-bending modes and from there into CC-stretchingand bending vibrations of the ring. The phenyl CH-stretchingexcitation on the opposite relaxes directly into other ringvibrations, indicating a comparatively inefficient coupling to themethyl group degrees of freedom.
Experimentally, a similar scenario is found in studies byLehmann et al., where the IVR lifetime of the CH-chromophore
in acetylenes was hardly influenced by the chemical nature ofthe substituent.3 Even with a 107-fold increase in total statedensity the observed IVR rates changed no more than 1 orderof magnitude. Here also the large reservoir of bath states offeredby the substituent group remains unused in the relaxationbecause it does not directly couple to the excited chromophore.
With this mechanistic ansatz of a spectator methyl group intoluene, the apparent disagreement of our results with thepioneering study of Parmenter and Stone on the influence ofan internal rotor on IVR33 can also be set aside. In the lateeighties the authors investigated the dynamics of S1 p-difluo-robenzene and p-fluorotoluene with chemically timed fluores-cence experiments and reported an increase in IVR rate uponmethyl substitution by 2 orders of magnitudesan immense effectin contrast to our results on the analogous system fluorobenzene/toluene! A closer look at the mode of excitation reveals,however, that in the fluorescence study excess energies averagedto less than 2000 cm-1, so that the intramolecular redistributionwas mainly initiated in low frequency ring vibrations. Withouttaking up the still ongoing discussion on the nature of the rotoreffect on IVR, we note that all mechanistic models proposed inthis context, i.e., the already mentioned separation of vibrationalphase space,31 the change in vibrational anharmonicity throughvan der Waals interactions between methylic and ortho-ringhydrogen atoms (“intramolecular collisions”),30 and the defor-mation of the phenyl ring through periodic hyperconjugationwith the rotating methyl group,34 have one aspect in common:They predict an intensive coupling between low frequency ringvibrations and the internal rotor. Consequently, they agree wellwith the results of Parmenter and Stone but by no means excludea possible spectator role of the methyl group in the case ofaromatic CH-stretch overtone relaxation.
The structure of R,R,R-trifluorotoluene is isomorphic totoluene, so that this molecule represents a second model systemto study the influence of substituent structure and internalrotation on IVR. Compared to that for toluene (and fluoroben-zene), an acceleration of the second IVR step by a factor 2 isobserved (see table 1). Several explanations can be discussedfor this finding. First, new relaxation channels in the fluorinatedderivate could be opened up by [1:1] resonances between CFand low frequency ring vibrations. Second, the fluorine atomhas a 1.2 times larger van der Waals radius than the hydrogenatom. From the perspective of perturbation by intramolecularcollisions proposed by Parmenter et al. the interactions of thefluorinated methyl rotor with ortho-hydrogen atoms on the ringshould be more pronounced than in toluene. However, thesetwo mechanisms are again best suited to describe the acceleratedrelaxation of low frequency vibrations in contrast to the actuallyprepared overtone bright state. Therefore, a further aspect,namely the strong increase in rovibrational isoenergetic bathstates through the lower CF bond force constant, has to beconsidered. Interestingly, the 2-fold increase in IVR(2) rate againstands in no (linear) relation to the 35-fold increase in totaldensity of states upon methyl fluorination. This suggests thatalso in R,R,R-trifluorotoluene the additional rovibrational densityof states is not fully contributing to IVR. Considering that therotation of the fluoromethyl group is classified as free (unhin-dered), a partial decoupling of the substituent from thevibrational dynamic initiated and probed in the aromatic ringappears highly likely. As a first conclusion from the experimentson fluorobenzene, toluene, and R,R,R-trifluorotoluene, we thusnote that, after 2νCH excitation in the phenyl ring, the substituentstructure plays only a minor role in intramolecular vibrationalenergy redistribution. The total density of states is obviously
Vibrational Energy Redistribution in Aromatic Molecules J. Phys. Chem. A, Vol. 114, No. 43, 2010 11525
inappropriate to predict any IVR acceleration even qualitatively,which becomes quite clear when τ IVR
(2) in, for instance, tolueneand chlorobenzene are compared (see Table 1), the latter ofwhich exhibits the faster relaxation in spite of the lower statedensity.
In view of the fact that all five monosubstituted derivativesdisplay the same two step dynamics as the unsubstituted benzenemolecule, one should turn the attention to the structuralcomponent that is common to all six systems: the phenylfragment C6H5. Two indications that the excitation energybecomes primarily delocalized within the phenyl ring have beenmentioned above: the selection of ring chromophors for thepump and probe processes and the neglectability of internalrotational states/additional intrasubstituent oscillators. Then,from the perspective of the C6H5 fragment, polyatomic substit-uents could be regarded as simple point masses. The effect ofdifferent substituents on IVR(2) would then have to be primarilyattributed to specific variations of those C6H5 fundamentalvibrational frequencies that have high substituent contribution.Two observations support this interpretation: the trend ofdecreasing τ IVR
(2) with increasing substituent mass (compare Table1), and the similarity in the dynamics of fluorobenzene andtoluene. The actual shifts in phenyl ring fundamental frequenciesfor all six aromatic molecules are shown schematically in Figure4 (black bars). The seemingly low number of benzene frequen-cies is due to the double degeneracy of ten normal modes inthe D6h point group. For toluene and R,R,R-trifluorotoluene theeight additional (perfluoro)methyl group oscillations are listedseparately (gray bars). Two effects of increasing substituent masson the C6H5 frequencies become visible. First, the number oflow frequency vibrations increases, and second, the vibrationsappear less grouped. Furthermore the energy levels of tolueneand fluorobenzene show a strong resemblance of each other.
At this point it is helpful to consider the vibrational statespaces of these molecules. Plausibly, differences in vibrationalfrequencies of molecules (here: molecular fragments) shouldbe reflected in different state space structures. An increasednumber of low frequency vibrations increases the state densityper energy volume and leads to a more isotropic distribution ofstates, as does the removal of frequency grouping in energyspace. Consequently, for molecular fragments with similarfundamental frequencies, e.g., toluene and fluorobenzene, similarstate space structures would be expected. The simplest and mostperspicious visualization of a vibrational state space is the so-called quantum number space (QNS), a concept introduced byGruebele and co-workers.35–38 For a molecule with N atoms itsQNS is the state space spanned by its s ) 3N - 6 vibrationaldegrees of freedom, and each Cartesian lattice point resemblesa distinct vibrational state. In the context of the symmetry effectinvestigation on benzene/benzene-d1, we employed a simplifiedmodel of IVR as population diffusion in QNS and could showthat the change in normal-mode frequencies upon monodeu-teration shown in Figure 4 is sufficient to explain the observedchange in IVR(2) rate in this model system.29 Unfortunately, thevibrational state density of the other four benzene derivativesis too large to allow an analogous full scale QNS investigation.It is, however, possible to at least assess the nature of the statespaces of these molecules by sorting their total vibrationaldensity of states by the order of the coupling to the excitedbright state, an approach that results in an approximate tierscheme for each system. The coupling order ∆n is defined asthe total number of vibrational quanta n exchanged betweentwo coupled states i and j.
The concept has been employed already for gaseous acetylenes39
and alkyl iodides in weakly interacting solvent environments1
where the experimentally observed IVR lifetimes could beexplained via correlation with the number of low ordercouplings. To imitate the experimental conditions in this study,we chose the first overtone of the asymmetric CH-stretchvibration (∼6000 cm-1) as the starting state for all moleculesand considered only states within an energy interval of (100cm-1 of the initial excitation. Assuming spectator substituentstoluene and R,R,R-trifluorotoluene were simulated as 30-mode-molecules by neglecting the eight substituent vibrations and thetorsion mode. The resulting number of couplings of third, fourth,fifth, and higher than fifth order to the bright state are listed inTable 2. For the sake of completeness, the results for benzeneare also included despite the difference in symmetry. Thecalculations reveal a striking similarity in the number of loworder couplings (∆n ) 3, 4) for all six molecules, slightdifferences in the number of intermediate order couplings (∆n) 5) and significant differences in the number of high ordercouplings (∆n > 5). Since low order couplings most likelymediate the energy flow from the bright state to the first tier(s),the similarity in early dynamics of the aromatic molecules can
Figure 4. Fundamental vibrational frequencies of C6H5X type mol-ecules: black, vibrations of the phenyl ring; gray, intrasubstituentvibrations.
∆n ) ∑ |n(νs)i - n(νs)j| (2)
11526 J. Phys. Chem. A, Vol. 114, No. 43, 2010 Benten et al.
be explained with these results. One can conclude that in theimmediate vicinity of the initially excited state, the state spacestructures for all systems are nearly identical and resemble thestate space of the unperturbed C6H5 fragment, dominated bythe aforementioned Fermi resonance between CH-stretch andCH-bend vibrations. The presence of the substituent becomesnoticeable only in later tiers composed of states that are lesswell coupled to the bright state, corresponding to ∆n g 5 inTable 2 and the second IVR step represented by τ IVR
(2) . Interest-ingly, the trend in IVR(2) rate correlates well with the numberof high order couplings (∆n > 5), as shown in Figure 5. Thecorrelation is not linear (logarithmic scale for F(∆n)), indicatingthat the vast density of these dark background states indirectly,i.e., via couplings to states in early tiers, influences thedepopulation of the bright state. Mechanistically, all theseobservations correspond well with a tier model of IVR wherethe overall redistribution process happens in a nonstatisticalfashion while individual redistribution steps between tiers couldstill be described statistically.
4. Conclusions
In summary, we studied IVR in six monosubstituted benzenederivatives after selective overtone excitation of the phenyl CH-stretch vibration with ∼6000 cm-1. All systems exhibit the samenature of vibrational dynamics, namely a nonstatistical, two-step energy redistribution. The substituents influence primarilythe second, slower IVR time scale. A comparison of fluoroben-zene and toluene proves that with this excitation mode aninternal rotor does not accelerate the IVR and acts rather as a
spectator group.40 The results on R,R,R-trifluorotoluene furtherconfirm that the density of states contributed by a polyatomicsubstituent is hardly accessed during the primary stages ofnonstatistical IVR. From the perspective of the initially excitedphenyl ring, polyatomic substituents can therefore be regardedas point masses. Coupling order modelings based on 30-modemolecules indeed indicate phenyl dominated state space struc-tures in the vicinity of the excited state, which are reflected inthe similar early dynamics seen in the experiments. Thesubstituent influence becomes noticeable only in the numberof high order couplings, which correlates with the rate of thesecond IVR step. We thus conclude that for aromatic moleculesof type C6H5X a possibility to control IVR is given through themass of the substituent, if high frequency ring vibrations serveas chromophore of excitation. It would be interesting to see ifthis concept also holds for other substituted rigid ring systemslike, for instance, azulene or naphthalene.
Acknowledgment. We thank the Deutsche Forschungsge-meinschaft for financial support through the Graduiertenkolleg782 “Spectroscopy and Dynamics of Molecular Aggregates,Chains and Coils”. Help with the experimental setup by O. Linkis also gratefully acknowledged.
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TABLE 2: Density of States for C6H5X,a Sorted byCoupling Order to the Bright State
a within (100 cm-1 of the bright state (first overtone ofasymmetric CH-stretch-vibration (∼6000 cm-1)). b 30-mode-calculation.
Figure 5. Correlation between number of states with coupling order∆n within an interval of (100 cm-1 around the first overtone of thephenyl CH-stretch vibration (left-hand y-axis) and second IVR rateconstant (right-hand y-axis) for C6H5X type molecules.
Vibrational Energy Redistribution in Aromatic Molecules J. Phys. Chem. A, Vol. 114, No. 43, 2010 11527
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