State-specific studies of internal mixing in a prototypical flexiblebichromophore: Diphenylmethane

Nathan R. Pillsbury,1 Jaime A. Stearns,2 Christian W. Müller,1 David F. Plusquellic,3 andTimothy S. Zwier1,a�

1Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA2Laboratoire Chimie Physique Moléculaire, École Polytechnique Fédérale de Lausanne,CH-1015 Lausanne, Switzerland3Optical Technology Division, National Institute of Standards and Technology, Gaithersburg,Maryland 20899-8441, USA

�Received 16 May 2008; accepted 11 August 2008; published online 16 September 2008�

Laser-induced fluorescence, resonant two-photon ionization, UV-UV hole burning, UV depletion,and single vibronic level fluorescence �SVLF� spectra of jet-cooled diphenylmethane �DPM� havebeen recorded over the 37 300–38 400 cm−1 region that encompasses the S1←S0 and S2←S0

transitions. All transitions in the laser-induced fluorescence excitation spectrum are due to a singleconformational isomer of DPM with C2 symmetry. The S1←S0 origin transition occurs at37 322 cm−1, supporting a short progression in the symmetric torsion T with spacing of 28 cm−1.The S2←S0 origin transition occurs 123 cm−1 above the S1 origin and possesses very weaktorsional structure, observable only under saturating laser power conditions. A combination of SVLFspectroscopy and hot band studies is used to assign the frequencies of the symmetric torsion �T�,antisymmetric torsion �T̄�, and butterfly ��� vibrations in the S0, S1, and S2 states. The emission fromthe S2 origin is composed of two components, a set of sharp transitions ascribable to the S2 state anda dense “clump” of transitions ending in ground-state levels 81, 88, and 93 cm−1 above the S0

zero-point level ascribable to S1�v� emission. Assignment of the transitions in the clump leads to theconclusion that the single vibronic level responsible for the emission has mixed S2 /S1 character. Themixing involves several torsional vibronic levels in the S1 manifold close in energy to the S2 origin,with the correct symmetry to couple the two states. These levels involve significant torsionalexcitation. The close energetic proximity of these levels leads to a breakdown of typical vibroniccoupling selection rules. © 2008 American Institute of Physics. �DOI: 10.1063/1.2977730�

I. INTRODUCTION

From a spectroscopic viewpoint, diphenylmethane�DPM� is an interesting molecule because it contains twoidentical ultraviolet chromophores in very close proximity,linked only by a methylene group. Furthermore, the torsionalcoordinates connecting the two rings to the methylene groupare extremely flexible. Excitonic coupling between the twoaromatic rings will depend on their orientation. In a face-to-face configuration, electronic coupling will be significant,but if the rings are perpendicular, as in benzene dimer1 orspirobifluorene,2 the two � electron systems will be orthogo-nal and interaction will be minimal. Furthermore, the direc-tion of the S0-S1 transition moment of phenyl derivatives isknown to depend sensitively on the nature and conformationof the substituent.3 The combination of excitonic couplingand flexible degrees of freedom is present in many othermolecules, but rarely are both aspects investigated in thesame molecule. Thus, our anticipation is that the first twoexcited states of DPM will be closely intertwined with oneanother in a way that could have fascinating consequencesfor the ultraviolet spectrum of the molecule.

Beyond locating the two excited states and determining

their minimum-energy structures, one can also probe thespectroscopic consequences of their interaction with one an-other. In the time domain, this is the process of internal con-version or electronic energy transfer, but in the frequencydomain, these interactions are more aptly referred to as “in-ternal mixing” since the interactions produce vibronic levelswith mixed electronic character. Internal mixing has been asubject of several previous experimental and theoreticalstudies,4–7 but so far no state-to-state view of internal mixinghas developed.

We have used both vibrationally and rotationally re-solved ultraviolet spectroscopy to study DPM in the unper-turbed environment of the supersonic jet. In the present pa-per, resonant two-photon ionization �R2PI� and singlevibronic level fluorescence �SVLF� spectroscopy are used toexamine the role of torsional motions in the electronic struc-ture of DPM. The origins of S1 and S2 states of DPM areassigned and the vibronic structure of each state is examined.In contrast to molecules such as naphthalene5 and ovalene,4

where the energy separation between S1 and S2 states is sev-eral thousand cm−1, the S1 and S2 origins of DPM are sepa-rated by only 123 cm−1, making it an example of a moleculein the “sparse coupled level structure” limit.7 As we shallsee, SVLF spectra of the S2 origin and S2 vibronic bandsexhibit distinct components that reflect the mixed S2 /S1 char-a�Electronic mail: zwier@purdue.edu.

THE JOURNAL OF CHEMICAL PHYSICS 129, 114301 �2008�

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acter of these levels. We analyze the emission in order todetermine which S1 vibronic levels are mixed, providing astate-to-state perspective on the internal mixing at a level ofdetail not possible in previous studies. The fully deuterated�DPM-d12� isotopomer of DPM has also been studied to helpclarify aspects of the vibronic spectroscopy. The results ofhigh resolution laser-induced fluorescence �LIF� spectros-copy and extensive calculations of the excited state torsionalsurfaces will be discussed elsewhere.8

II. EXPERIMENTAL METHODS

R2PI, LIF, UV-UV hole burning �UVHB�, UV-UVdepletion �UVD�, and SVLF spectroscopies were used to fo-cus on various aspects of the ultraviolet spectrum of DPM.UVHB and UVD are both pump-probe spectroscopies usingtwo ultraviolet lasers, spatially overlapped and separated intime by 200 ns, with the pump laser operating at 10 Hz andthe probe laser at 20 Hz. When the wavelengths of the twolasers are on transitions which share a common ground state,the probe laser signal will be depleted, providing conformer-specific spectra. In UVHB, the pump laser is fixed while theprobe is tuned. Conversely, in UVD, the constant signal fromthe probe laser is monitored while the pump laser is scanned.The former method provides spectra with better signal tonoise while the latter allows detection of transitions that donot appear in the R2PI spectrum due to lack of ionizationefficiency.9

R2PI, UVHB, and UVD spectroscopies were all carriedout in a supersonic jet time-of-flight mass spectrometerwhich has been described previously.10 LIF and SVLF spec-tra were recorded in a free jet fluorescence detection vacuumchamber which has also been described previously.11 For thepresent work, the fluorescence apparatus described in Ref. 11was modified to accommodate detection with a 2048�512pixel charge coupled device �CCD� camera �Andor seriesDU440BT�. The camera was typically kept at −80 °C viathermoelectric and water cooling. Background subtractionand cosmic ray removal were carried out by the ANDOR soft-ware. Total acquisition times ranged from 20 min to over anhour. The amount of scattered light at the excitation wave-length was determined by adjusting the time the laser fired,so the laser entered the vacuum chamber prior to the gaspulse from the pulsed valve. The signal from scattered lightwas recorded and subtracted from the single vibronic fluo-rescence spectrum, giving quantitative fluorescence intensi-ties at the excitation wavelength. Typical resolution with a50–100 �m entrance slit to the monochromator was6–8 cm−1. The frequency-doubled output of a neodymiumdoped yttrium aluminum garnet �Nd:YAG� pumped dye laserwas used for all ionization and fluorescence experiments.DPM was commercially available �Sigma-Aldrich� and wasused directly with gentle heating �50–70 °C� to achieve avapor pressure of 1 Torr in 2 bars of helium for supersonicexpansion.

DPM-d12 was synthesized in our laboratory based on aFriedel–Crafts alkylation as outlined in a textbook byWade.12 The details of the synthesis are given in Sec. I of the

supplementary information.13 The liquid sample of DPM-d12

was treated in the same manner as DPM-d0 for supersonicexpansion.

III. COMPUTATIONAL METHODS

Electronic structure calculations on DPM were carriedout using GAUSSIAN03.14 Various stationary points in theground state were optimized using density functional theorywith the Becke3LYP functional15 and a 6–31+G� basis set.16

These were followed up with ground-state optimizations us-ing second-order Møller–Plesset perturbation theory17 �MP2�with a 6–311+ +G�� basis set. Vertical excitation energies,not including zero-point energy corrections, were calculatedusing configuration interaction singles18 �CIS�/6–31G, time-dependent density functional theory19 �TDDFT�/6–31+G�,and complete active space self-consistent field20

�CASSCF�/6–31G�, restricting the system to C2 symmetry.The GAMESS computational package21 was used to carry outthe CASSCF calculations. Eight electrons were distributedamong eight orbitals, those � and �� orbitals correspondingto linear combinations of the toluenelike highest occupiedmolecular orbitals and lowest unoccupied molecular orbitalson each ring. The potential energy surfaces of the excitedstates were further investigated using TDDFT. The relaxedground-state potential energy surface was first calculated fora number of ring torsion angles and then single point excitedstate energies were calculated at those geometries.

IV. RESULTS AND ANALYSIS

A. R2PI and LIF excitation spectra

The R2PI spectrum of DPM is shown in Fig. 1�a�. TheS1←S0 origin transition is located at 37 322 cm−1, just155 cm−1 red of the literature value22 for the S1←S0 originof toluene. The low-frequency portion of the spectrum showsa progression with a 28 cm−1 spacing, and additional peaksat 43 and 123 cm−1. Two other prominent peaks appear inthe spectrum, at 562 and 960 cm−1, each with a 28 cm−1

progression built off of them. These higher-frequency vi-bronic transitions have close analogs in the spectrum oftoluene.22

FIG. 1. �a� R2PI spectrum, �b� UVHB spectrum, and �c� UVD spectrum ofDPM. Prominent peaks are labeled with their frequencies in wavenumbersfrom the origin

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Figure 2�a� presents an expanded view of the first160 cm−1 of the LIF excitation spectrum of DPM, recordedunder unsaturated conditions. This spectrum shows low-frequency vibronic transitions involving the inter-ring tor-sional vibrations �symmetric torsion T and antisymmetric

torsion T̄ in C2 symmetry� and inter-ring bending mode �.The assignments for these transitions follow from analysis oftheir SVLF spectra in Sec. IV C, aided by the calculationswhich are described in Sec. II of the supplementarymaterial.13

The 123 cm−1 transition is unusual in the spectra ofFigs. 1�a� and 2�a�, as it is the only transition that does nothave appreciable torsional vibronic structure built off of it.Calculations predict no fundamental vibrations between 64and 180 cm−1. It is unlikely that the 123 cm−1 band is anovertone of the 64 cm−1 vibration ��0

1� because this is a to-tally symmetric vibration and should appear in the funda-mental. Given that this band is not easily assignable as avibration of the S1 state, it seems plausible to explore thepossibility that it is another origin transition, either of a sec-ond conformation or of the S2 state. The assignment of the S2

origin to a band 145 cm−1 above the origin in the crystalspectrum of DPM is consistent with this assignment.23,24 Theexcited state calculations support a low-lying S2 state, withan exciton splitting on the order of hundreds of wavenum-bers �Sec. II, supplementary material�.13

B. UVHB and UVD spectra

UVHB spectroscopy was used to establish whether the+123 cm−1 band was due to a second conformation of DPM.Figure 1�b� shows the UVHB spectrum recorded with thehole-burn laser set to the DPM 00

0 band at 37 322 cm−1.Every peak in the R2PI spectrum, including the transition at123 cm−1, burned out, and must therefore be due to the sameground-state species. On this basis we surmise that only oneconformation of DPM exists in the supersonic expansion. Itis likely, then, that the peak at +123 cm−1 is the origin of thesecond exciton state.

A striking feature of the +123 cm−1 band is that thereare no sizable vibronic bands built off of it, either in the

low-frequency torsional region or in the higher-frequency re-gion of the ring vibrations. One possible explanation for thisis that these bands undergo rapid nonradiative processes thatmake them difficult to detect via R2PI. The technique ofUVD spectroscopy should allow us to see any additionalabsorption transitions in the spectrum. As Fig. 1�c� shows,however, the depletion spectrum contains only those transi-tions present in R2PI within the signal to noise of theexperiment.

C. High resolution UV spectra

Based on exciton theory,2,23–26 our expectation is that thetransition dipole moments of the S0-S1 and S0-S2 origin tran-sitions will be orthogonal to one another. Therefore, one im-portant confirmation of the assignment of the +123 cm−1

transition to the S2 origin would be the changes so producedin the rotational structure of the band. To that end, high res-olution spectra �32 MHz resolution� of the S0-S1 origin and+123 cm−1 transitions have been recorded at NIST and areshown in Figs. 3�a� and 3�b�, respectively. The S0-S1 originhas a strong Q-branch indicative of significant a-character tothe band structure �67% a: 33% c�, while the +123 cm−1

transition shows no central Q-branch, characteristic of a pureb-type band. Detailed analysis of these spectra will be pre-sented elsewhere.8 For the present purposes, we surmise thatthe +123 cm−1 band has a transition dipole moment direc-tion perpendicular to the S0-S1 origin, marking its differentelectronic character.

D. SVLF spectra

1. S1 origin and torsional vibronic levels

The SVLF spectrum of the S1 origin is shown in Fig.4�a�, with the relative position �in cm−1� of many of the

FIG. 2. �a� Unsaturated and �b� saturated LIF spectra of DPM. Prominentpeaks are labeled with their assignments and frequencies in wavenumbersfrom the origin.

FIG. 3. High resolution UV spectra of the S0−S1 origin �lower trace� and the+123 cm−1 band �upper trace� of DPM.

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higher-frequency peaks labeled. As shown in Table I, most ofthis structure can be interpreted directly in terms of toluene-like vibrations involving in-plane ring distortions. Not sur-prisingly, the spectrum is very similar to that of toluene, withmajor transitions at 554, 622, 822, and 1006 cm−1 ascribableto 6a1

0, 6b10, 11

0, and 1210, respectively. The intensity pattern of

these transitions follows that from toluene’s S1 origin,27 asmight be anticipated.

The first 150 cm−1 of the SVLF spectrum from the DPMorigin are shown in an expanded view in Fig. 5�a�. As withthe R2PI spectrum, there is a significant progression in thesymmetric phenyl ring torsion mode T, with ground-statefrequency of 19 cm−1. Figures 5�b�–5�d� show the SVLFspectra from the T1, T2, and T3 levels. Transitions appear at19 cm−1 intervals up to about 120 cm−1 and are fitted rea-sonably well by a harmonic Franck–Condon �FC� analysiswith displacement parameter D=1.0 �taking into account thefrequency change between the S0 and S1 states�.28 The stickspectra in Figs. 5�a�–5�d� show the results of this analysis.The same structure is built off transitions associated with allthe other ring vibrations present in the origin spectrum.

Two other peaks appear in the SVLF spectrum shown inFig. 5�a�, a shoulder at �31 cm−1, and a peak with torsionalstructure built off of it at 64 cm−1. There are two other cal-culated low-frequency vibrations besides the symmetric phe-nyl ring torsion, which has already been assigned. The peakat 64 cm−1 is assigned to the symmetric butterfly vibrationby virtue of its close match with calculation �Table I� and isdesignated �1

0. Its corresponding transition in the excitationspectrum appears as a shoulder on the high-frequency edgeof the 54 cm−1 transition �Fig. 2�b��. This assignment isclarified and strengthened by results from DPM-d12 �in-cluded in the supplementary material�,13 where the �0

1 tran-sition is well resolved. The peak at �31 cm−1 must therefore

involve the nontotally symmetric �nts� phenyl ring torsion T̄.The SVLF spectrum of the transition 43 cm−1 above the S1

origin �Fig. 5�e�� shows that the upper state vibrational levelat 43 cm−1 is connected with this 31 cm−1 level in S0, whichacts as a false origin for a progression with a 31 cm−1

spacing.The assignment of the 31 cm−1 level in S0 and 43 cm−1

FIG. 4. SVLF spectra from �a� the S1 origin and �b� the +123 cm−1 bands ofDPM. Prominent peaks are labeled by their frequencies from the origin inwavenumbers. Scattered light at the excitation wavelength was subtractedout.

TABLE I. Major peaks in the DPM S1 origin dispersed fluorescence spec-trum.

Expt. freq.a Assignmentb B3LYP/6–31+G� �symm�a Toluenea

0 000

¯ T̄10 19 �B� ¯

19 T10 25 �A� ¯

31 T̄20

38 T20

63 �10 64 �A� ¯

83 �10T1

0

126 �20

146 �20T1

0

223 R10 e 226 �A� ¯

554 6a10 �B� 564 �B� 520c

574 6a10T1

0

610 6a10 �A� 621 �A� 520c

622 6b10 634 �A�, 637 �B� 623c

642 6b10T1

0

739 1110 749 �A,B� 728d

760 1110T1

0

822 110 831�A�, 835�B� 790c

843 110T1

0

1006 1210 1016 �A,B� 1007c

1027 1210T1

0

1035 18a10 1054 �A�, 1055 �B� 1030c

1204 9a10 1217 �A�, 1228 �B� 1215c

1447 19b10 1492�B�, 1493 �A� 1445d

aFrequencies from the ground-state zero-point level in cm−1.bWilson numbering is used for the ring vibrations. See text for othernotation.cReference 27.dReference 29.eSymmetric component of the rotation of the two benzene rings perpendicu-lar to their planes.

FIG. 5. �Color online� SVLF from �a� the S1 origin, ��b�–�d�� the symmetrictorsion progression, and �e� the +43 cm−1 band in DPM. Prominent peaksare labeled by their assignment. The stick spectra correspond to FC simula-tions using ��a�–�d�� D=1 and �e� D=0. Scattered light at the excitationwavelength was subtracted out.

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level in S1 is crucial to our understanding of the geometry of

the S1 state. Frequencies for T̄ of 31 cm−1 in S0 and 43 cm−1

in S1 are roughly twice the predicted values from DFTB3LYP/6–31+G� calculations �19 and 25 cm−1, respec-

tively�, suggesting assignments as T̄20 and T̄0

2. However, theaccuracy with which B3LYP calculations predict these low-frequency torsions is uncertain. If these levels were assigned

as T̄10 and T̄0

1, respectively, their presence would indicate ei-ther a nonzero displacement along the nts torsional coordi-nate or vibronic coupling to another electronic state �presum-ably S2�. The former circumstance would necessarily indicatebreaking of the C2 symmetry in S1. Conversely, if these tran-

sitions are T̄20 and T̄0

2, respectively, the lack of transitions at

half the separation from the origin ascribable to T̄10 and T̄0

1

would provide strong evidence that the S1 state retains the C2

symmetry of the ground state.To distinguish between these possibilities, LIF excitation

and SVLF spectra were taken when exciting closer to thenozzle exit, where the expansion was warmer, thereby creat-ing hot bands and sequence bands which were detected by

LIF. If the +43 cm−1 band is T̄01, then the T̄1

1 sequence bandshould show up at +12 cm−1 �43−31=12� from the origin inthe LIF spectrum. However, if the +43 cm−1 band is actually

T̄02, then the T̄1

1 sequence band should be observed +6 cm−1

�21.5−15.5=6� from the origin transition.Figure 6 shows the cold �Fig. 6�a�� and warm �Fig. 6�b��

LIF spectra of the DPM origin region. A sequence band

clearly appears 5–6 cm−1 above the S1 origin �T̄11�, while no

band is observed at +12 cm−1. This indicates that the

+43 cm−1 band in the R2PI spectrum is actually T̄02, making

the fundamental T̄ frequencies 21.5 cm−1 in S1 and16.5 cm−1 in S0. The hot band at +47 cm−1 is then assigned

to T̄13. A hot band also appears 6 cm−1 above the S2 origin

�129 cm−1 above the S1 origin�, which we shall assign �Sec.

IV D 2� to S2 T̄11 based on its SVLF spectrum.

The SVLF spectra of the +5 and +47 cm−1 hot bandsshown in Figs. 7�b� and 7�c�, respectively, confirm these as-signments, with transitions labeled accordingly. On the basis

of these assignments, combined with the absence of an S1 T̄01

transition, a C2 symmetric structure for the S1 excited state is

deduced. The retention of C2 symmetry in the S1 state is alsoconsistent with the transition dipole orientation observed inthe rotationally resolved study �Fig. 3�a��.8

Before leaving this discussion of the SVLF spectra ofthe S1 torsional levels, we take a final look at the intensitypatterns these levels produce. The assignment of the S0 and

S1 frequencies of T̄ at 15.5 and 21.5 cm−1, respectively,leads to the assignments shown in Fig. 7�a� for the observed

transitions in the emission spectrum of T̄2. In notable contrastto the spectrum from the S1 origin �Fig. 5�a��, the SVLF

spectrum of T̄2 is a nearly pure progression in even quanta of

T̄, with almost no intensity in the symmetric torsion T pro-

gression. Since we know the vibrational frequencies of T̄ inS0 and S1 and have deduced that the molecule retains C2

symmetry in S1, we can predict the FC intensities based on a

harmonic analysis with a displacement along T̄ of zero. Thisprediction, shown in the stick diagram of Fig. 7�a�, substan-tially underestimates the intensity of the �v�0 transitions

involving T̄. Thus, T̄2 emission has more intensity in the T̄progression than expected, at the expense of a near-complete

loss of the progression in T. Finally, the intensity of T̄02 is

much smaller than T̄42, a substantial skewing of the intensity

toward ground-state levels involving large quantum numbers

in T̄. These unique intensity patterns carry over to the T̄3

emission as well.In what follows, we use these unique intensity patterns

as diagnostics of the presence of T̄n excited state character. Itseems likely that these unusual intensity patterns arise fromthe unusual shape of the torsional potential energy surfacesin S0 and S1.

2. S2 origin and torsional vibronic levels

Figure 4�b� shows the SVLF spectrum from the band123 cm−1 above the S1 origin. The same toluenelike vibronicbands appear in this spectrum with a similar relative intensitypattern to those of the DPM S1 origin, shown directly aboveit in Fig. 4�a�. However, these vibronic transitions are sub-stantially more intense relative to the resonance fluorescence

FIG. 6. Cold �a� and warm �b� LIF spectra of the DPM origin region. Thecold bands have been labeled in �a�, while the prominent hot bands havebeen labeled in �b�.

FIG. 7. �Color online� �a� T̄02 SVLF spectrum, �b� T̄1

1 SVLF spectrum, and

�c� T̄13 SVLF spectrum of DPM. FC predictions are shown in red as sticks

beneath the experimental traces. The resonance peaks �0 cm−1� of �b� and�c� contain no information because scattered light from the experiment satu-rated the CCD detector and have been set to zero. The predicted stick in-tensity of the resonance peak in �b� has been divided by 16.

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peak than they are in the S1 00 emission spectrum. Thus, the123 cm−1 band has different FC factors �FCFs� in the ringmodes than the S1 origin, consistent with its assignment tothe S2 origin.

The low-frequency portion of the spectrum in Fig. 4�b�is quite intriguing. The lack of torsional structure built di-rectly off the excitation wavelength is consistent with thelack of such torsional structure built off the 123 cm−1 bandin the R2PI spectrum, indicating little change in geometryalong the torsional or butterfly modes upon electronic exci-tation. More interesting is the closely spaced clump of tran-sitions starting about 80 cm−1 to the red of the excitationwavelength. Careful checks were carried out to ensure thatthese peaks were not the result of collisional cooling occur-ring on the timescale of the fluorescence.

Despite the lack of sizable transitions built off of the+123 cm−1 band, there were a couple of minor transitions inthe LIF excitation spectrum just above the 123 cm−1 bandthat deserved further investigation. In order to enhance theintensities of these transitions, a LIF spectrum was recordedwith sufficient UV laser power to saturate the strong transi-tions in the spectrum. Figure 2 compares the unsaturated�Fig. 2�a�� and saturated �Fig. 2�b�� LIF spectra. In particular,the saturated spectrum clearly shows a couple of small tran-sitions just to the blue of the +123 cm−1 band at +136 and+145 cm−1.

The SVLF spectra of the +136 and +145 cm−1 cold vi-bronic bands and the +129 cm−1 hot band are compared tothe emission from the S2 origin in Figs. 8�a�–8�d�. The emis-sion from the +136, +145, and +129 cm−1 bands shows acombination of “sharp” transitions with no torsional sidebands and a “clump” of transitions shifted from the reso-nance fluorescence by an amount comparable to that ob-served in the S2 origin emission �Fig. 8�a��.

The SVLF spectrum of the +136 cm−1 band �Fig. 8�b��shows a false origin shifted from the excitation wavelengthby 20 cm−1, consistent with emission to the v�=1 level ofthe symmetric torsion T. The sharp vibronic transitions builtoff this false origin look nearly identical to the sharp transi-tions in the S2 origin spectrum, apart from being shifted by

20 cm−1. On this basis, the +136 cm−1 band is assigned tothe S0-S2 T0

1 transition. This makes its frequency 13 cm−1 inS2 and demonstrates that an A symmetry S2 vibronic levelemits to a ground-state vibrational levels.

The +145 cm−1 band �Fig. 8�c�� also shows a series ofsharp transitions nearly identical to those in Figs. 8�a� and8�b�, but in this case the sharp transitions are built off a falseorigin which is shifted 15 cm−1 from the excitation fre-

quency, an amount equivalent to one quantum of T̄ in S0. The

+145 cm−1 band is therefore assigned to S2 T̄01 and the false

origin emission to T̄11, appearing by virtue of strong �v=0

FCFs involving T̄ in the S2→S0 emission. This assignment

makes the frequency of T̄ in S2 22 cm−1. This transitionaccesses an upper state with A�b=B vibronic symmetry,which is the same symmetry established for the S1 origin

from the observed rotational structure.8 Therefore, the S2 T̄01

transition must be gaining intensity from the S1 state viavibronic coupling.

If the assignment of the +145 cm−1 band to S0-S2 T̄01 is

correct, it predicts the presence of the S0-S2 T̄11 sequence

band 6 cm−1 above the S0-S2 origin, at 145−16.5=+129 cm−1. A hot band at that position is indeed observed�Fig. 6�b��, with a SVLF spectrum �Fig. 8�d�� identical to the+145 cm−1 transition �Fig. 8�c�� in absolute wavelength, in-dicating that the two transitions share the same excited state

level S2 T̄1.Based on the R2PI and SVLF spectra, we have assigned

the symmetric and antisymmetric torsional levels in the S0,S1, and S2 electronic states. Table II summarizes the frequen-

cies of T, T̄, and � in S0, S1, and S2 for both DPM-d0 and-d12. The most dramatic difference between these vibrationsin the three electronic states is in the symmetric torsion T,which drops in frequency by more than a factor of 2 in S2

�13 cm−1� relative to S1 �28 cm−1�.The spectra in Fig. 8 provide evidence that the combina-

tion of sharp toluenelike vibronic transitions and the clumpof closely spaced transitions shifted to the lower wavenum-ber side of them are characteristic signatures of the S2 vi-bronic bands. The shape of the clump of bands is similar in

the three examples available �S2 00, T1, and T̄1�, but notidentical, with peak positions shifted from their respectivefalse origins that are similar. What does change from oneband to the next is the intensity of the clump transitionsrelative to the sharp bands. In particular, the +136 cm−1 tran-

FIG. 8. SVLF spectra of �a� the +123 cm−1 cold band, �b� the +136 cm−1

“saturated” band, �c� the +145 cm−1 “saturated” band, and �d� the+129 cm−1 hot band of DPM-d0. The unusual structure near the resonancefrequency in �b�–�d� is due to saturation of the CCD by scattered light.

TABLE II. Experimental frequencies of the lowest vibrational frequenciesin S0, S1, and S2 for both isotopomers of DPM.

Isotopomer State T �cm−1� T̄ �cm−1� � �cm−1�

DPM-d0 S0 19 16.5 64S1 29 21.5 �56 a

S2 13 22 ¯

DPM-d12 S0 18 15 60S1 25 20 54

aThis value is approximate since the transition was not completely resolved.

114301-6 Pillsbury et al. J. Chem. Phys. 129, 114301 �2008�

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sition �now assigned as S2 T01� has a relative integrated inten-

sity of the clump transitions which is significantly greater

than from the S2 00 or S2 T̄1 level.Most importantly, as the tie lines and brackets in Fig.

8�a� show, the intensity of the first clump of transitions builtoff the resonance fluorescence or false origin is significantlygreater than the corresponding intensity of the clump emis-sion built off of higher vibronic bands. Therefore, the clumpemission has more nearly �v=0 FCFs in the toluenelike vi-bronic bands, with relative intensities similar to those foundin the S1 SVLF spectra �Fig. 4�a��. This is a confirming pieceof evidence that the closely spaced clump emission reflectsthe S1 character of the upper state�s�.

In order to test this hypothesis further, analogous scanswere recorded for the fully deuterated isotopomer, DPM-d12.Indeed, similar characteristic features of the S1 and S2 vi-bronic levels are found in DPM-d12. The resulting assign-

ments for T and T̄ in d12 are included in Table II. The pre-sentation and analysis of these spectra are included in thesupplementary material.13

E. Analysis of the mixed character of the S2 levels

Up to this point, the analysis of the emission from the S2

vibronic bands has shown that the S2 origin and S2 vibronicbands in DPM-d0 and -d12 are of mixed character, with partof the emission ascribable to the S2 character �the sharpbands lacking torsional activity� and part due to the S1 vi-bronic levels which are coupled to the S2 level �the clumpemission�. In this section, an attempt is made to assign thetransitions in the S1 vibronic emission in order to extractfurther information about the nature of the vibronic couplinginvolved under the present circumstance of near-degenerateelectronic states.

1. The S2 origin of DPM-d0 „S2 000, S1+123 cm−1

…

Figure 9 presents another view of the low-frequency re-gion of the SVLF spectra of the S2 origin transition ofDPM-d0. In order to better resolve the clump emission, thisspectrum was taken with higher laser power and slightly im-

proved resolution over the spectrum in Figs. 4 and 8. In thisexpanded view, the clump of transitions ascribable to the S1

vibronic character of the band is displayed in significant de-tail. One striking aspect of the emission in DPM-d0 is thesharp onset in intensity at 81 cm−1.

The clump emission in Fig. 9 is dominated by two setsof three transitions, with the first triad at 81, 88, and93 cm−1, followed by a second set at 112, 118, and125 cm−1. The separation between these sets of transitions is

thus 31 cm−1, an amount equal to two quanta of T̄. This

nearly pure progression in even quanta of T̄ built off each of

these false origins is reminiscent of the nearly pure T̄ pro-

gression that appears in the emission from S1 T̄2 �Fig. 7�a��and T̄3 �Fig. 7�c��. Recall that in these spectra, a clear pro-

gression in T̄ is accompanied by a near-complete lack ofintensity in transitions involving T �which would have aspacing of 19 cm−1� and a skewing of the �v�0 intensity

toward T̄n+2n rather than T̄n−2

n . This suggests that the upper

states responsible for these transitions have considerable T̄excitation, with the set of transitions at 81, 88, and 93 cm−1

possessing �v=0 FCFs from the upper states responsible forthem. The tie lines and quantum number designations in Fig.9 provide proposed assignments for the six transitions that

dominate the clump emission. These have odd quanta of T̄,as required for vibronic coupling with the S2 origin.

The energy level diagrams in Fig. 10 show the experi-mentally determined or extrapolated values for a subset ofthe low-lying torsional energy levels in the S0 and S1 statesof DPM-d0. While Fig. 10 shows only a subset of the levels,Tables S4 and S5 of the supplementary material13 give all ofthe energy levels up to 150 cm−1. The vibrational levels inFig. 10 are separated by symmetry, with a/b symmetry levelson the left/right. The �mnp� labels on the energy levels indi-

cate the level’s vibrational quantum numbers �v�T�, v�T̄�,and v����.

Based on Fig. 10, we assign the emission to levels 81,88, and 93 cm−1 to transitions ending in the ground-state�050�, �230�, and �410� levels �in red in Fig. 10�a��, whichare predicted to be 83, 89, and 97 cm−1 above the S0 zero-

point level based on harmonic extrapolation of the T and T̄S0 frequencies. The corresponding levels in S1 have esti-mated energies of 109, 120, and 129 cm−1 above the S1 ori-

gin based on the known experimental frequencies for T and T̄in S1, placing them in close proximity to the S2 origin�123 cm−1�. These three S1 vibronic levels are three of thefour closest-energy levels of the right symmetry to couple tothe S2 origin. Furthermore, the fourth close-lying b symme-try level in S1, �031�, has predicted energies of 121 cm−1 inS1 and 114 cm−1 in S0. Thus, the S1 �031� level may also beinvolved in the mixing, contributing to the intensity of thetransition at 112 cm−1 in the clump emission �Fig. 9�. Basedon what we know about the emission spectrum from �1, wecan rule out the possibility that the �011� band at 78 cm−1 inS1 �81 cm−1 in S0� may also contribute to the 81 cm−1 bandin the SVLF spectrum because if it did, the �1

1T10 combina-

tion band should also be visible at 100 cm−1 �directly be-tween the two maxima of the clump�, which it is not.

FIG. 9. Close view of the clump emission in the SVLF of the S2 origin�+123 cm−1 band� in DPM. This spectrum was taken with higher laserpower and slightly better resolution than the spectrum in Figs. 4 and 8 inorder to better resolve the closely spaced set of transitions. Prominent peaksare labeled with their frequency from the excitation wavelength in wave-numbers and with their corresponding assignments of the ground-state levelsinvolved.

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In summary, these postulated assignments indicate thatthe clump of bands observed in emission from the �nomi-nally� S2 origin have imprinted in their unusual closelyspaced pattern the vibronic character of the S1 levels that aremixed with the S2 zero-point level to produce an upper stateof mixed character,

��+ 123 cm−1� = c2000�S2,000� + c1050�S1,050�

+ c1230�S1,230� + c1410�S1,410�

+ c1031�S1,031� . �1�

2. The S2 T01 transition „S2+13 cm−1, S1+136 cm−1

…

As Fig. 8�b� shows, the clump emission in the SVLFspectrum of the S2 T0

1 transition at +136 cm−1 is less re-solved, but has two transitions at 117 and 145 cm−1 thatdominate the spectrum. Applying the same arguments usedto assign the clump emission from the S2 origin, we look forb symmetry S1 vibrational levels in close energetic proximityto the S2 T1 level at 136 cm−1 and use �v=0 FCFs to predictthe position of the dominant band�s� in emission. In thiscase, the b-symmetry �012� and �211� levels are closest inenergy �Fig. 10�, with corresponding levels in S0 at 145 and120 cm−1, precisely as observed. Other levels may also beinvolved in the mixing, but are unresolved in the weak emis-sion from this band. The close proximity of these coupledstates may be responsible for the larger intensity of theclump emission relative to the sharp transitions due to S2 T1,reflecting a greater S1 character to the emitting mixed excitedstate level.

3. The S2 T̄01 transition „S2+22 cm−1, S1+145 cm−1

…

If the S2 state retains the C2 symmetry of S0, then the

S2←S0 T̄01 transition would gain oscillator strength from a

symmetry vibrational levels in S1. In this case �Fig. 8�c��,transitions in the clump region are unresolved, giving riseonly to the same general shape as the S2 00 clump emission,but shifted from the corresponding maxima in the S2 00 emis-

sion by one quantum of T̄ �17 cm−1�. Since the frequencies

of the antisymmetric torsion T̄ are 22 cm−1 in S2 and21 cm−1 in S1, the likely S1 vibronic levels involved in themixing are the same ones involved in the S2 origin emission,

but with one additional quantum of T̄; that is, �S1 ,060�,�S1 ,240�, �S1 ,420�, and �S1 ,041�.

V. DISCUSSION AND CONCLUSIONS

A. Excitonic splitting in DPM

A primary goal of the present investigation is to under-stand the excitonic coupling in DPM and its dependence on

the two low-frequency torsional coordinates �T and T̄� alongwhich the molecule can so easily distort. A first level ofanalysis is simply to identify the S1 and S2 origins, and hencedetermine the excitonic splitting in DPM in the region nearthe ground-state geometry. We have presented several piecesof experimental evidence that the S2 origin is located123 cm−1 above the S1 origin. By comparison, CASSCF cal-culations predict a splitting of 136 cm−1, in fortuitous agree-ment. McClure23 observed a similar S1-S2 splitting in theabsorption spectrum of crystalline DPM, although the as-

FIG. 10. �Color online� Experimentally determined or extrapolated values for the energy levels of the S0 and S1 states of DPM-d0. The a and b symmetrylevels have been separated for convenience. Each energy level is designated with a set of quantum numbers and a position �in wavenumbers� as shown inbottom right corner. The dotted lines indicate levels that are coupled.

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signment of the symmetries of the states contained in thatwork differs from that determined by our high resolutiondata �Fig. 3�a��.8 An excitonic splitting of 123 cm−1 indi-cates that the electronic coupling matrix element at theground-state geometry is half this size, H12=61.5 cm−1.

An excitonic splitting of 123 cm−1 is small compared towhat is found in many other bichromophores �e.g., biphenylor spirobifluorene, �1000 cm−1�. On the other hand, theflexible nature of DPM produces very low-frequency tor-sional vibrations ��20 cm−1�, placing DPM in the strongcoupling limit of excitonic theory.24,26,30

B. Internal mixing between the excitonic states

The present data set, particularly the SVLF spectra, hasprovided a detailed look at the mixed electronic state char-acter of the low-lying S2 vibronic levels due to internal mix-ing with near-degenerate S1 vibronic levels. The close prox-imity of the two electronic states gives rise to a situation inwhich the density of S1 vibrational levels is still quite sparsein the region of the S2 origin, as shown in Fig. 10. As aresult, we are afforded state-specific insight to the process ofinternal mixing in the isolated molecule. Under nanosecondlaser excitation, the upper states responsible for the emissionare single vibronic levels of mixed S1 /S2 character, with notime dependence in the nanosecond experiment we have car-ried out.

In DPM, the S2 �000�, �100�, and �010� levels all showdual emission, with sharp vibronic bands ascribable to the S2

character of the excited state level and clump emission fromthe S1 character. In Sec. IV.F we analyzed the S1 clump emis-sion and deduced that the S2 origin is, in fact, of mixed S2 /S1

character, with the S1 character arising from several levels ofthe right symmetry within about 10 cm−1 of the S2 upperlevel of interest. In fact, as Fig. 10 shows in pictorial fashion,the four identified S1 vibronic levels mixed with �S2 ,000� arethe four closest-energy b symmetry vibrational states in theS1 manifold.

When two electronic states well separated from one an-other are vibronically coupled, the perturbative treatmentlaid out in standard Herzberg–Teller theory leads to �v�Qk�= �1 selection rules in the coupled vibration Qk. However,in DPM and DPM-d12, the two excitonic states of differentsymmetries �A and B� are in close proximity to one another,where the closely related theories of internal conversion�time-dependent picture� or internal mixing �stationary-statepicture�31 are more appropriate. In this case the standard per-turbative treatment begins with adiabatic Born–Oppenheimerstates, in which the perturbative operator inducing internalconversion is the nuclear kinetic-energy operator.32,33

Using the treatment of internal mixing from Sharf etal.,34 we have developed an expression13 for the vibroniccoupling matrix element V applied to the case at hand inwhich the two vibronic states differ only in their vibrationalquantum numbers in a single non-totally symmetric promot-

ing mode �T̄� and a single totally symmetric accepting mode�T�,

V � �1 −�

S2 − �S1

ES2�Q0� − ES1

�Q0���

T̄�

S2�QT̄��

T̄�

S1�QT̄��

T�S2��

T�S1�QT

� �j�T̄�T

3N−6

���S2���

S1�Qj. �2�

Here � is the electronic coupling matrix element,

� = ��S2�q;Q0�� �U�q,Q�

�QT̄�

Q0

��S1�q;Q0��q, �3�

�vSn�Q� is the one-dimensional harmonic oscillator wave

function with energy Sn for mode Q in vibrational level v

and electronic state Sn. Thus, the coupling matrix element Vbetween two vibronic adiabatic Born–Oppenheimer stateswith unperturbed energies �

S1 and �S2 is a product of several

terms: �i� the electronic coupling matrix element �, �ii� anenergy-dependent term that is maximized when the differ-ence in vibronic energies is much smaller than the differencebetween the electronic state energies �ES2�Q0�−ES1�Q0�=123 cm−1�, �iii� an integral in T̄ that yields the usual �v= �1 propensity rule for the coupling coordinate QT̄ induc-ing the radiationless transition,33 �iv� a vibrational overlapintegral in T, and �v� the product of all other vibrationaloverlap integrals.

The levels in DPM which are measurably mixed with�S2 ,000� are �S1 ,050�, �S1 ,230�, �S1 ,410�, and �S1 ,031�.These levels involve total quantum number changes of�vtot=5, 5, 5, and 4, respectively. The relevant quantumnumber change for vibronic coupling between S1�B� and

S2�A� is that involving T̄, the lowest-frequency vibration of b

symmetry, with �v�T̄�=5,3 ,1, and 3 for the four S1 vibroniclevels involved in the mixing, in apparent violation of the

�v�T̄�= �1 selection rule. Thus, in order for the �050�,�230�, and �031� levels of S1 to couple to the S2 origin, third-order and fifth-order terms in the electronic HamiltonianTaylor series expansion would be required, terms discardedin the perturbative treatment just described.34,35 Thesehigher-order terms are anticipated to drop off steeply with

increasing �v�T̄�, likely by about an order of magnitude witheach integer increase in �v.35

At the same time, the quantum number changes in thesymmetric torsion T for these same levels are �v�T�=0, 2, 4,and 0, respectively. Since the geometry change between S1

and S2 in T is small, the overlap integrals strongly favor�v�T�=0 and will also fall off rapidly as �v�T� increases.

As Table III summarizes, the �v�T̄�, �v�T�, and �E con-tributions to the fractional mixing given in Eq. �5� counter-balance one another in the levels in close proximity to�S2 ,000�. Given the similar relative intensities of the clumpemission transitions ascribable to four S1 vibronic levels�Fig. 9�, it appears that all four close-lying levels have com-parable fractional mixing with the S2 origin. The energy lev-els involved are within about 10 cm−1 of �S2 ,000�, so thatvibronic coupling reaches across a very small energy gap,with coupling matrix element V�5 cm−1.

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In principle, the integrated intensity of each componentof the dual emission can be used to determine the extent ofmixing present in the upper state giving rise to the emission.As described in greater detail in the supplementarymaterial,13 we estimate based on our spectra that the frac-tional S1�050� character in the S2 �000� level is

�CS1,050�2

�CS2,000�2� � 0.08. �4�

This estimate indicates that the mixing of any one of the S1

vibronic levels into the S2 zero-point level is less than 10%,but its effect on the SVLF spectrum of S2 �000� in the first200 cm−1 of the spectrum is amplified by the greater oscil-lator strength of the S1→S0 emission and more nearly �v=0 FCFs in the ring modes. Combining this result with thetwo-level energy formula �see supplementary material13�leads to estimates for the internal mixing coupling matrixelements V in the 0.8–3.7 cm−1 range.

These estimates explain our inability to clearly pick outthe coupled levels directly in the R2PI �Fig. 1� or LIF exci-tation spectrum �Fig. 2�. The S1 �050�, �231�, �410�, and�031� levels are dark from the S0 zero-point level, but gainoscillator strength from the S2 origin. However, since each S1

vibronic level is anticipated to have less than 10% S2 origincharacter, their intensities are anticipated to be at least tentimes smaller than the S2 origin.

Before leaving this section, it is worth returning to oneaspect of the LIF spectra of DPM �Fig. 2� that we are onlynow prepared to discuss. Given the close proximity of the S1

and S2 states, one might have thought that the S1 T̄01 transition

should be visible in the spectrum �21.5 cm−1 above the S1

origin� due to vibronic coupling with the S2 origin, which isonly 101.5 cm−1 above it in energy. The S1�010� and S2�000�states have �v�T̄�=−1, �v�T�=0, and �v���=0, fulfillingthe propensity rules for vibronic coupling, which oftenreaches over energy separations of thousands of inverse cen-timeters to produce measurable intensity in ultravioletspectra.36 From our experimental spectrum, we can place an

upper bound on the intensity of the S1 T̄01 transition of 0.3%

of the S2 origin, from which it would gain intensity. Thus, thefractional internal mixing of S2 �000� into S1 �010� must beless than 0.3%. Solving as before leads to an upper bound forthe coupling matrix element V between these two levels of

5 cm−1. Note that V /�=0.05 so that these two levels are inthe weak coupling limit in which V /� can be equated withthe mixing coefficient. This value for V /� is six times lessthan for the near-resonant levels, consistent with its weakintensity. When compared to the 0.8–3.7 cm−1 estimate for

V in the cases where �v�T̄� 1 and/or �v�T� 1, we see thatour upper bound for the fully vibronically allowed S1�010�level is in the same range, while we would have expected itto be much greater based on Table III. Whether this arisesfrom the large-amplitude character of the torsion or a break-down of the perturbative treatment leading to Eq. �2� is anopen question worthy of further investigation.

It will be important to study other bichromophores inwhich the energy separation between S1 and S2 is variedsystematically in order to see how the state-specific internalmixing evolves with changes in the energy separation anddensities of states. This we are currently pursuing.

C. The lack of vibronic bands built off the S2 origin

A final, particularly intriguing aspect of the vibronicspectroscopy of the S2 state of DPM-d0 and -d12 is the near-complete lack of vibronic structure built off the S2 origin.The lack of torsional structure built off the S2 origin is asimple consequence of a small change in geometry along the

torsional coordinate�s�, leading to �v�T , T̄�=0 FCFs. This isborne out by the lack of torsional structure in the sharp S2

vibronic emission �Fig. 4�b��. However, the strong toluene-like vibronic bands observed in emission argue for strongvibronic coupling and/or significant geometry changes alonga few of the ring modes, analogous to those in toluene. Onthis basis, we should anticipate strong vibronic bands in theR2PI spectrum, appearing about 123 cm−1 above the analo-gous levels in the S1 state. As shown in greater detail in thesupplementary material,13 these transitions are not identifi-able in the spectrum.

One possible solution is simply that the S2 vibronicbands are so strongly coupled to the dense manifold of S1

vibrational levels at these energies, that the oscillatorstrength is spread over a wide energy range that makes thebroadened bands difficult to observe. In this scenario, theS1 /S2 coupling favors internal conversion from S2 to S1 vi-bronic levels by virtue of the higher density of S1 states at agiven excitation energy due to the fact that the S2 state zero-point level is 123 cm−1 above that for S1.

An alternative is that the S2 “origin” could be one ofonly a few bound levels supported by a shallow “dimple” inthe S2 surface near the S0 minimum geometry. Figure 11supports the notion that the S2 state surface is quite differentin shape than that due to S1. The figure portrays a cut alongthe C2 diagonal on the two-dimensional �2D� torsional sur-face of S1 and S2, calculated at the TDDFT B3LYP/6–31+G� level of theory. Along this diagonal, the two excitedstates necessarily retain their delocalized character. Note thatthe state designated as S2 at the S0 geometry crosses the S1

state to form a minimum below that state near �1=�2=90°.The unusual shape of the torsional surface of the S2 statemay be reflected in the sharp drop in frequency of the sym-metric torsion T, which is 29 cm−1 in S1, but only 13 cm−1

TABLE III. Quantum number changes and contributions to the magnitudeof the mixing coefficient between the S2 origin and the indicated S1 vibroniclevels of DPM-d0.

S1 level �v�T� �v�T̄� �v��� �E�cm−1� a

�050� 0, large 5, small 0, large −14, medium�230� 2, med 3, med 0, large −3, small�410� 4, small 1, large 0, large +6, medium�031� 0, large 3, med 1, small −2, small

�010� b 0, large 1, large 0, large −100, very large

a�E=experimentally observed energy difference between the S1 levels andthe S2 origin.b�010� does not contribute significantly to the mixing with the S2 origin. Seetext for further discussion.

114301-10 Pillsbury et al. J. Chem. Phys. 129, 114301 �2008�

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in S2. This indicates a substantial softening of the potentialalong the C2 diagonal. On this basis, even in a harmonicdescription of the two states along coordinate T, the S1 andS2 states would cross not too far above the S2 minimum.

In order to resolve these issues, it would be helpful tostudy other deuterated isotopomers of DPM that vary thedegree of asymmetry between the two rings. Such a study iscurrently being pursued.37 On the theoretical side, the close-lying entangled nature of the S1 and S2 states will present aparticular challenge that requires methods that extend be-yond CIS or TDDFT to correctly describe the excited statesof DPM. Ultimately, accurate calculations of the full 2D tor-sional surface for the S1 and S2 states would be of great use,in which the energy separation, degree of electronic localiza-tion, and torsional energy levels/wave functions are mappedout over the entire surface.

ACKNOWLEDGMENTS

This work was supported by the Department of EnergyBasic Energy Sciences, Division of Chemical Sciences underGrant No. DE-FG02-96ER14656. The authors gratefully ac-knowledge Aloke Das and Talitha M. Selby for their contri-butions to the preliminary calculations and R2PI spectra.J.A.S. gratefully acknowledges NASA for a Graduate Stu-dent Research Fellowship and Purdue University for a Dis-sertation Year Fellowship. C.W.M. would like to thank the“Deutsche Akademie der Naturforscher Leopoldina” for apostdoctoral scholarship �Grant No. BMBF-LPD 9901/8-159of the “Bundesministerium für Bildung und Forschung”�.N.R.P. acknowledges Purdue University and the Andrewsfamily for the Frederick N. Andrews Fellowship. This workwas also supported in part by a fellowship from Merck Re-search Laboratories. The authors thank John R. Cable foruseful discussions and for sharing his data on DPM isoto-pomers prior to publication.

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FIG. 11. Calculated relaxed potential energy curves of DPM at C2 symmetryusing TDDFT/B3LYP/6–31+G�. The lower curve �circles� is the ground-state potential. The excited state of B symmetry, which is the S1 state at theminimum-energy geometry of the ground state, is the upper solid curve�triangles�. The upper dashed curve �squares� is the excited state of A sym-metry or the S2 state at the geometry of the ground state. The markersrepresent the calculated points.

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114301-12 Pillsbury et al. J. Chem. Phys. 129, 114301 �2008�

Downloaded 14 Oct 2008 to 128.210.142.201. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp