Electronic spectra of 2- and 3-tolunitrile in the gas phase. II. Geometry changes fromFranck-Condon fits of fluorescence emission spectraFelix Gmerek, Benjamin Stuhlmann, Leonardo Álvarez-Valtierra, David W. Pratt, and Michael Schmitt Citation: The Journal of Chemical Physics 144, 084304 (2016); doi: 10.1063/1.4941924 View online: http://dx.doi.org/10.1063/1.4941924 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/144/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Full dimensional Franck-Condon factors for the acetylene A 1 A u — X Σ g + 1 transition. II. Vibrationaloverlap factors for levels involving excitation in ungerade modes J. Chem. Phys. 141, 134305 (2014); 10.1063/1.4896533 Franck–Condon analysis of laser-induced fluorescence excitation spectrum of anthranilic acid: Evaluation ofgeometry change upon S 0 → S 1 excitation J. Chem. Phys. 130, 054307 (2009); 10.1063/1.3043818 Determination of the excited-state structure of 7-azaindole-water cluster using a Franck-Condon analysis J. Chem. Phys. 123, 224311 (2005); 10.1063/1.2136868 Geometry change of simple aromatics upon electronic excitation obtained from Franck-Condon fits ofdispersed fluorescence spectra J. Chem. Phys. 121, 2598 (2004); 10.1063/1.1767517 Rigorous Franck–Condon absorption and emission spectra of conjugated oligomers from quantum chemistry J. Chem. Phys. 113, 11372 (2000); 10.1063/1.1328067

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THE JOURNAL OF CHEMICAL PHYSICS 144, 084304 (2016)

Electronic spectra of 2- and 3-tolunitrile in the gas phase. II. Geometrychanges from Franck-Condon fits of fluorescence emission spectra

Felix Gmerek,1 Benjamin Stuhlmann,1 Leonardo Álvarez-Valtierra,2 David W. Pratt,3and Michael Schmitt1,a)1Heinrich-Heine-Universität, Institut für Physikalische Chemie I, D-40225 Düsseldorf, Germany2División de Ciencias e Ingenierías, Universidad de Guanajuato, León, Guanajuato 37150, Mexico3Department of Chemistry, University of Vermont, Burlington, Vermont 05405, USA

(Received 14 November 2015; accepted 26 January 2016; published online 24 February 2016)

We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowestexcited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescenceemission spectra and of the rotational constant changes upon excitation. These structural changescan be connected to the altered electron distribution in the molecules and are compared to theresults of ab initio calculations. We show how the torsional barriers of the methyl groups in bothcomponents are used as probe of the molecular changes upon electronic excitation. C 2016 AIPPublishing LLC. [http://dx.doi.org/10.1063/1.4941924]

I. INTRODUCTION

Electronic excitation of aromatic molecules alters avariety of molecular parameters, which can be determinedby different spectroscopic techniques. Among the photophys-ically interesting properties that are strongly altered are thenuclear structure (what is called the geometry of the moleculein the individual electronic state), the electron density andhence the permanent dipole moment of each state and thetransition dipole moment, and the barriers to internal motions,which determine the state density of the molecules at a certainenergy above the zero-point vibrational level.

2- and 3-tolunitrile (2-TN and 3-TN) have beenstudied using rotationally resolved laser induced fluorescencespectroscopy in order to investigate the torsional barriersin both electronic states, as reported in Paper I.1 In thepresent publication, we will use the combined informationfrom the changes of the rotational constants upon electronicexcitation and the vibronic intensities in absorption andemission through various absorption bands for a combinedFranck-Condon/inertial parameter fit of the geometry changeupon electronic excitation.

S1 ← S0 fluorescence excitation spectra and S0 ← S1fluorescence emission spectra of 2-, 3-, and 4-tolunitrilewere reported by Fujii et al.2 They determined the torsionalbarriers of ground and lowest excited singlet states from thelow frequency torsional bands in the S0 and the S1 states,respectively. The ground state internal rotational parametersof 2-TN have been determined from microwave spectroscopyin the frequency ranges of 22.0-26.0 GHz and 32.0-37.0 GHz3

and from millimeter wave spectroscopy in the frequencyrange 50.0–75.0 GHz.4 Nakai and Kawai studied the torsionalpotential of various substituted toluenes, among them 2-and 3-TN.5 They showed how a π∗σ∗ hyperconjugation

a)Author to whom correspondence should be addressed. Electronic mail:mschmitt@uni-duesseldorf.de. Tel.: 49 0211 81 12100. Fax: 49 2118115195.

mechanism can be used to explain their different barriersin different electronic states. Later, Park et al. measuredthe vibronic emission spectra of the jet-cooled 2-tolunitrile6

and 3-tolunitrile7 in a corona-excited supersonic expansion.From a density functional theory (DFT) based analysis ofthe spectrum, several vibrational modes were assigned inthe emission spectrum. The cationic ground state D0 hasbeen studied using pulsed field ionization zero kinetic energyelectron (ZEKE) spectroscopy by Suzuki et al.8

Nagao et al.9 investigated oriented 2-, 3-, and 4-tolunitrileas guests in α, β, and γ-cyclodextrin (CD) using FTIRspectroscopy. They found that the charge distribution of thetolunitriles determines the orientations and depths of inclusionin the CD cavity. Nagabalasubramanian et al.10 calculated thevibrational spectrum of 2-TN using ab initio and densityfunctional theory and compared their computational results toFTIR and Raman spectra.

In the present contribution, geometry changes of 2-TNand 3-TN are determined from Franck-Condon (FC) fits ofthe vibronic band intensities in several fluorescence emissionspectra and the changes of the rotational constants uponexcitation, which are determined in Paper I of this series.1

II. EXPERIMENTAL AND COMPUTATIONAL DETAILS

A. Experiment

The experimental setup for the dispersed fluorescence(DF) spectroscopy has been described in detail elsewhere.11,12

In brief, 2- and 3-tolunitrile were evaporated at 293 K andco-expanded through a pulsed nozzle (kept at 328 K toavoid condensation) with a 500 µm orifice (General Valve)into the vacuum chamber using helium as carrier gas. Theoutput of a Nd:YAG (SpectraPhysics INDI) pumped dyelaser (Lambda-Physik, FL3002) was frequency doubled andcrossed at right angles with the molecular beam. The resultingfluorescence was imaged on the entrance slit of a f = 1 m

0021-9606/2016/144(8)/084304/8/$30.00 144, 084304-1 © 2016 AIP Publishing LLC

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084304-2 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

monochromator (Jobin Yvon, grating 2400 lines/mm blazedat 400 nm in first order). The dispersed fluorescence spectrumwas recorded using a gated image intensified UV sensitiveCCD camera (Flamestar II, LaVision). One image on theCCD chip spectrally covers approximately 600 cm−1. Sincethe whole spectrum is taken on a shot-to-shot basis, the relativeintensities in the DF spectra do not vary with the laser power.The relative intensities were afterwards normalized to thestrongest band in the spectrum, not including the resonancefluorescence band, which also contains the stray light and istherefore excluded from the FC analysis.

B. Ab initio calculations

Structure optimizations were performed employingDunning’s correlation consistent polarized valence triplezeta basis set (cc-pVTZ) from the T library.13,14

The equilibrium geometries of the electronic ground andthe lowest excited singlet states were optimized using theapproximate coupled cluster singles and doubles model(CC2) employing the resolution-of-the-identity approximation(RI).15–17 The Hessians and harmonic vibrational frequenciesfor both electronic states, which are utilized in the FCfit, have been obtained from numerical second derivativesusing the NumForce script18 implemented in the Tprogram suite.19 A natural population analysis (NPA)20 hasbeen performed at the CC2 optimized geometries using thewavefunctions from the CC2 calculations as implemented inthe T package.19

C. Franck-Condon fit of the structural change uponelectronic excitation

The change of a molecular geometry upon electronicexcitation can be determined from the intensities of absorptionor emission bands using the FC principle. According to thisprinciple, the relative intensity of a vibronic band depends onthe overlap integral of the vibrational wave functions of bothelectronic states. The transition dipole moment for a transitionbetween an initial electronic state |m, v⟩ and a final electronicstate |n, w⟩ is defined as

Mvw = ⟨v |µmn(Q)|w⟩ (1)

with the electronic transition dipole moment µmn(Q),µmn(Q) = ⟨Ψm|µ|Ψn⟩ , µ =

g

erg , (2)

where rg is the position vector of the gth electron. Thedependence of the electronic transition dipole moment µmn

on the nuclear coordinates can be approximated by expandingµmn in a Taylor series about the equilibrium position at Q0. Theseries is truncated after the first term in the FC approximation.

The fit has been performed using the program FCF,which has been developed in our group and described indetail before.21,22 The program computes the FC integrals ofmultidimensional, harmonic oscillators mainly based on therecursion formula given in the papers of Doktorov, Malkin,and Man’ko23,24 and fits the geometry (in linear combinationsof selected normal modes) to the experimentally determined

intensities. This is simultaneously done for all emissionspectra, which are obtained via pumping through differentS1 vibronic modes.

The vibrational modes of the electronically excited statecan be expressed in terms of the ground state modes usingthe following linear orthogonal transformation, first given byDuschinsky:25

Q′ = SQ′′ + d. (3)

Here, Q′ and Q′′ are the N-dimensional vectors of the normalmodes of excited and ground state, respectively. S is anN × N rotation matrix (the Duschinsky matrix) and d is an N-dimensional vector which describes the linear displacementsof the normal coordinates.

The fit of the geometry to the intensities in the vibronicspectra can be greatly improved if independent informationabout the geometry changes upon electronic excitation isavailable. This additional information is provided by thechange of the rotational constants upon electronic excitation,which can be obtained from rotationally resolved electronicspectroscopy. While geometry fits to the rotational constantsare routinely performed using non-linear fits in internalcoordinates, the combination of rotational constant changesand vibronic intensities allows for determination of manymore geometric parameters.

III. RESULTS

A. Ab initio calculations

The structures of 2- and 3-TN in their ground and lowestexcited singlet states have been determined from optimizationsat the CC2 level of theory using the cc-pVTZ basis set. Theatomic numbering used throughout this publication is shownin Figure 1. The Cartesian coordinates of the optimizedstructures of 2-TN and 3-TN in their S0 and S1-states aregiven in Tables S1–S4 of the supplementary material.26

2- and 3-TN belong to the Cs symmetry point group inboth electronic states, in agreement with experimental inertialdefects of−2.87 amu Å2 (−0.02 amu Å2) in 2-TN (3-TN) in theelectronic ground state and of −3.14 amu Å2 (−0.81 amu Å2)in 2-TN (3-TN) in the lowest excited state.1 The inertial defectof 2-TN is approximately the same as a static value of twoout-of-plane hydrogens due to the high barrier hindering thetorsional motion of the methyl group. For 3-TN, much smallervalues are reported due to vibrational averaging at the onsetof nearly free internal rotation.

Of the 42 normal modes, 27 are symmetric with respect tothe mirror plane and 15 are antisymmetric and they transformlike Γvib = 27A′ + 15A′′. Since both the ground state, as well asthe electronically excited state have electronic A′-symmetry,all vibronic transitions are allowed in absorption and emission.The relevant details about these states are compiled in Table Iand are compared to the results of the experiments.

The numbering of the 42 normal modes of 2- and 3-TN,their symmetries, and their wavenumbers in the electronicground and excited states are compiled in Tables S4 andS5 of the supplementary material.26 The last columns ofthese tables show the largest elements of the Duschinsky

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084304-3 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

FIG. 1. Structure and atomic numbering of o- and m-tolunitrile.

TABLE I. Rotational constants A, B, and C are given in MHz, components of the dipole moments µa, µb, andµc in Debye, the angle of the transition dipole moment θ in degrees, vertical (∆νvert.) and adiabatic excitationenergies (∆νadiab.) in cm−1, and oscillator strengths f are dimensionless. The last four rows give the leadingcontributions to the transition.

2-TN 3-TN

S0 S1 S0 (expt.) S1 (expt.) S0 S1 S0 (expt.) S1 (expt.)

A 2944 2 917 2892.6 2 853.4 3322 3 246 3331.8 3 256.0B 1505 1 459 1500.4 1 460.2 1209 1 184 1203.0 1 177.8C 1002 978 993.5 971.7 891 873 883.9 866.1µa −3.710 −4.194 . . . . . . −2.69 −2.89 . . . . . .µb 1.632 1.700 . . . . . . 3.82 4.16 . . . . . .µc 0.000 0.000 . . . . . . 0.00 0.00 . . . . . .θ . . . −73 . . . ±71.3 −71 . . . −71∆νemission

vert. . . . 37 272 . . . . . . . . . 37 473 . . . . . .∆ν

absorptionvert. . . . 40 332 . . . . . . . . . 40 420 . . . . . .

∆νadiab. . . . 37 603 . . . 35 768.95 . . . 37 726 . . . 35 815.53f . . . 0.019 . . . . . . . . . 0.012 . . . . . .HOMO → LUMO . . . 0.68 . . . . . . . . . 0.71 . . . . . .HOMO-1 → LUMO+1 . . . 0.40 . . . . . . . . . 0.47 . . . . . .HOMO-1 → LUMO . . . −0.47 . . . . . . . . . 0.38 . . . . . .HOMO → LUMO+1 . . . 0.36 . . . . . . . . . 0.32 . . . . . .

matrix, which were calculated from the respective Hessiansat the equilibrium positions and facilitates the assignments ofground state modes to excited state vibrations. Most of theS1-state vibrational modes can be described by a single groundstate vibration (diagonal elements of the Duschinsky matrix)and only very few modes are heavily mixed.

B. Experimental results

1. The fluorescence excitation spectrum of 2-TN

The laser induced fluorescence (LIF) spectrum of 2-TNis shown Figure 2. It is similar to spectra already shownin the literature.2 Nevertheless, we present it here alongwith a Franck-Condon simulation of the absorption spectrum(lower trace), since some of the features and assignmentsin this spectrum are still not fully understood. Furthermore,the vibronic S1 state assignments are crucial for the Franck-

Condon fit of the emission spectra. The inset in the uppertrace shows a zoomed part of the spectrum in the region ofthe torsional transitions that are due to the hindered internalrotation of the methyl group.

The agreement between the experimental spectrum andthe simulation, calculated using the CC2/cc-pVTZ optimizedstructures and the Hessians calculated at the stationary pointsof both electronic states, is fair. In general, deviations betweenFranck-Condon simulations and absorption spectra are largerthan for emission spectra. The main reason is the largercontributions of Herzberg-Teller effects to the absorptionspectra, since the perturbing higher electronic states areenergetically closer to the excited state than to the groundstate, thus perturbing the absorption spectra more than theemission. Other reasons for deviations between experimentand simulations are common for both types of spectra. Theseare mainly the non-consideration of anharmonicity in ourmodel, resulting in frequency deviations and the neglect

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084304-4 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

FIG. 2. Fluorescence excitation spec-trum of 2-TN along with a Franck-Condon simulation of the absorptionspectrum using the ab initio parameters.

of Fermi or Darling-Dennison resonances, resulting both infrequency and intensity deviations. Most of the differencesbetween simulation and experiment can be attributed to oneof these effects.

The most striking difference, the large intensity of theovertone of the out-of-plane vibration Q36 can be attributed to aFermi resonance with vibration Q23, shifting Q2

36 down and Q23up in energy. In the harmonic approximation, Q2

36 is expectedat 662 cm−1, right in the middle of the experimental spectrumbetween the bands at 658 cm−1 (Q2

36) and 677 cm−1 (Q23). Butfrequency arguments using only the S1 state would be a weakbasis for reasoning about Fermi resonances in molecules withsuch a great number of allowed vibrational transitions. Wetherefore report here a result from the fluorescence emissionspectra, which will be presented in detail in Section III B 2.The emission spectra taken through the vibronic bands at 658and 677 cm−1 are very similar, showing the strongly mixedcharacter of the underlying excited modes. The strongestemission takes place to the Q23 ground state level, withconsiderable intensity also in the Q2

36 overtone.This Fermi doublet of Q2

36 and Q23 is separated by19 cm−1 and has an intensity ratio of 1:2, cf. Figure 2.Careful experiments showed that neither of the transitions wassaturated. Using standard perturbation theory,27 we adaptedthe energy distance of unperturbed levels δ = E0

Q23− E0

Q236

,

and the perturbation matrix element WQ23Q236

to the measuredenergy distance of the perturbed levels EQ23 − EQ2

36and

to the experimentally observed intensity ratio of 1:2,simultaneously. The energy difference of the perturbed levelscan be obtained from E = Eni ±

4|Wni |2 + δ2, where Eni

is the mean of the unperturbed levels. The ratio of theintensities can be adapted through the coefficients of the

zero order wave functions: a =(√

4|Wni |2+δ2+δ/2√

4|Wni |2+δ2) 1

2

and b =(√

4|Wni |2+δ2−δ/2√

4|Wni |2+δ2) 1

2 , with the intensity ratio

given by In/Ii = a2/b2. The resulting two mixed wavefunctionsare best described by the linear combinations

ψQ23 = 0.817ψ0Q23− 0.576ψ0

Q236, (4)

ψQ236= 0.576ψ0

Q23+ 0.817ψ0

Q236

(5)

using the zero approximation wavefunctions ψ0n and ψ0

i .The distance of the unperturbed levels δ = E0

Q23− E0

Q236

was

determined to be 6.5 cm−1, the perturbation matrix elementWQ23Q

236

to be 9.1 cm−1.The large number of quite weak transitions around

100 cm−1 can be traced back to torsional transitions, whichof course cannot be described properly in the harmonicapproximation. These torsional transitions in the fluorescenceabsorption spectrum of 2-TN are very weak. This wasattributed before to the weak Franck-Condon factors of thetorsional transitions, due to the similar potentials in the S0 andS1 states of 2-TN.2 Table II shows the torsional levels of 2-TN

TABLE II. Torsional levels of 2-TN and 3-TN in their electronic groundand lowest excited singlet states, obtained from the LIF and SVLF spectraof this study. Since a and e levels are not linked via allowed transitions, thelowest level (0a1 and 1e) serve as origins for the torsional ladder within eachsymmetry.

2-TN 3-TN

Level S0 S1 S0 S1

0a1 0 0 0 01e 0 0 0 02e 17 223a1 130 139 51 584e 152 157 80 825e 2026a1 188 183

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084304-5 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

and 3-TN in their S0 and S1 states that were determined in thepresent study.

The bands at 331 cm−1 (Q36), 405 cm−1 (Q26), 494 cm−1

(Q25), and 677 cm−1 (Q23) have been excited in order toobtain the single vibronic level fluorescence (SVLF) spectra,described in Section III B 2. The assignments of vibronicwavenumber to vibrational modes in the excited state havebeen performed in an iterative manner. First, based on theresult of the ab initio calculated vibrational wavenumber,a preliminary assignment was made. This was checked ina second step, through calculation of the Franck-Condonemission spectrum via excitation through this band, whichwas then compared to the experimental SVLF spectrum. Ifthe agreement was reasonable, the band was included in thelist of assignments for the Franck-Condon fit.

Imperfect geometries for one or both states involvedin the transition cause errors in the intensities. These canbe eliminated by displacing the geometry of one of theelectronic states along a selected set of ab initio calculatednormal modes, in order to better match the geometrychanges upon electronic excitation. All emission intensitiesfrom the SVLF spectra that were used in the FC fit arecompiled in Table S7 of the supplementary material.26 In thefollowing paragraphs we describe the fit of the 2-TN SVLFspectra.

2. Single vibronic level fluorescence of 2-TN

We recorded SVLF spectra through the electronic origin0,0 at 35 769 cm−1 (Figure 3) and through five vibronic bandsat 0,0 + 331, 0,0 + 405, 0,0 + 494, 0,0 + 656, and 0,0 + 677cm−1, which are shown in the supplementary Figures S1–S4.26

Each experimental spectrum is shown along with a Franck-Condon simulation using the ab initio geometries, and aFranck-Condon fit, with the excited state geometry displacedalong selected normal coordinates, given in supplementary

Table S10.26 The assignments of the modes shown in Figure 3refer to the mode numbering in supplementary Table S5.26

Below 300 cm−1, only very weak vibrational activity can beobserved. The weak bands that are shown in the zoomedinset of Figure 3 can be assigned to torsional transitions ofthe methyl group and are included in Table II. The spectrumis dominated by modes Q26, Q20, and Q16, which appear asfundamentals, overtones, and in combination with numerousother vibronic bands.

3. The fluorescence excitation spectrum of 3-TN

Figure 4 shows the LIF spectrum of 3-TN, along with aFranck-Condon simulation of the absorption spectrum usingthe ab initio parameters. As in the case of 2-TN, the partsof the spectrum with non-harmonic contributions cannot bedescribed by our program, which takes into account only theharmonic Hessians of both states. Therefore, the torsionaltransitions of the methyl group internal rotation are missing.The inset in Figure 4 (shown in the simulation trace with anintensity offset of 0.1) gives a simulation of the torsional bands,using the Hamiltonian described in Section IV. Compared to2-TN, the torsional bands of 3-TN below 200 cm−1 have aconsiderably higher intensity due to larger Franck-Condonfactors. Most of the torsional transitions have been observedbefore,2 with the exception of the 6a′1 ← 0a′′1 transition, cf.Table II.

The strongest vibronic transitions in the investigatedrange that are not due to torsional motions are observed at409 cm−1 and at 667 cm−1. They are assigned to the vibrationalmodes Q26 and Q34, respectively. Their intensities are wellreproduced by the Franck-Condon simulation, shown in thelower trace of Figure 4. The vibronic bands at the electronicorigin 0,0, at 0,0 + 79, 0,0 + 409 and at 0,0 + 667 cm−1 havebeen excited in order to obtain SVLF spectra. They will bediscussed in Section III B 4.

FIG. 3. SVLF spectrum of the elec-tronic origin of 2-TN, along with a sim-ulation of the emission spectrum usingthe ab initio parameters and a FC fit.

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084304-6 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

FIG. 4. Fluorescence excitation spec-trum of 3-TN along with a Franck-Condon simulation of the absorptionspectrum using the ab initio parameters.The spectrum between 0 and 200 cm−1

is additionally fit using the torsionalHamiltonian, described in Section IVand displayed in the lower trace with anintensity offset of 0.1.

4. Single vibronic level fluorescence of 3-TN

The SVLF spectrum obtained via excitation of thevibrationless origin of 3-TN is shown in Figure 5. It isdominated by emission to Q26, Q20, their overtones and theircombination bands.

Also here, the overall FC fit of the vibronic intensityshows better results than the FC simulation using the ab ini-tio geometries for both states. The same holds for the otheranalyzed bands at 79, 409, and 667 cm−1, shown in the sup-plementary Figures S5–S7.26 The very good agreement of FCfit and experimental spectrum for the vibration at 79 cm−1 (see

supplementary Figure S526) is at first sight surprising, sincethis band is assigned to the torsional transition 4e′ ← 1e′′.Assignment of this band to the third overtone of the modeQ42, which is the torsion on harmonic approximation leads toa nearly perfect FC fit. Obviously, this band in the S1 stateis sufficiently close to the top of the barrier to be treated inthe harmonic approximation. As expected from the assignmentof the excited band at 409 cm−1 to mode Q26, the strongestband in emission is found at 457 cm−1 (Q26) in the electronicground state (supplementary Figure S626). Excitation of Q34in the excited state at 667 cm−1 results in strongest emission toQ35 in the ground state at 714 cm−1 (Figure S726).

FIG. 5. SVLF spectrum of the elec-tronic origin of 3-TN along with a simu-lation using the ab initio parameters anda FC fit.

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084304-7 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

IV. DISCUSSION

From the combined Franck-Condon/rotational constantsfits, the displacements of the excited state geometry withrespect to the ground state geometry were determined. Thebasis for the displacements are the selected normal coordinatesfor each of the conformer from the ab initio calculated Hessian.The fit results for the geometry changes of 2-TN and 3-TNupon electronic excitation are depicted in Figure 6. All five(four) SVLF spectra of 2-TN (3-TN) along with the changesof the rotational constants, determined in the second paper ofthis series, have been used for the fit of the geometry changes.In total, 82 vibronic intensities (Table S7 of the supplementarymaterial26) and 3 rotational constants changes (supplemen-tary Table S926) were utilized in a fit along twelve normalcoordinates for 2-TN and along ten normal coordinates for 3-TN, shown in supplementary Table S10.26 The reason for thevery good agreement between the fitted and the experimentalfluorescence emission spectra is indeed the simultaneous useof vibronic band intensities and inertial parameters from thehigh resolution study. Since the FC analysis is based on theharmonic approximation, distortion in negative and positivedirection along a selected normal mode would lead to the sameFranck-Condon factor. While this indeterminacy is partiallyremoved by the use of 3N-6 dimensional FC integrals, a muchmore reliable way to the sign of the distortion is the change ofthe rotational constants, which are correctly reproduced onlywith the correct sign of the distortions.

In both conformers, the CC bonds between the chromo-phore and the cyano group, and between the chromophore andthe methyl group, decrease upon electronic excitation, whilethe CN distance of the cyano group increases. The aromaticring expands upon electronic excitation. In general, these struc-tural changes can be understood in terms of electron densityshifts upon electronic excitation. Excitation from bonding toantibonding orbitals is accompanied by an electron shift fromthe cyano group to the aromatic ring. The resulting resonancestructures are shown in Figure 7. Excitation into antibondingorbitals leads to the observed overall expansion of the aromaticring, while the bond order of the CN bond decreases, and theCC bond order between the chromophore and the cyano groupincreases. All these trends are clearly visible in the resonancestructures of Figure 7. At the same time, the CC bond lengthbetween the chromophore and the methyl group decreases.This effect is considerably larger in 2-TN (−3.1 Å), comparedto 3-TN (−1.5 Å). The reason for this different behavior canbe rationalized by the resonance structure in the last row of

FIG. 6. Geometry changes of 2-TN and 3-TN upon electronic excitation fromthe FC fits.

FIG. 7. Resonance structures of 2-TN.

Figure 7. Only substituents in the ortho (or para) positionwith respect to the cyano group can stabilize the negativecharge at the ring C-atom. This stabilization takes place viathree equivalent resonance structures, arising from the threeequivalent H-atoms, as shown in Figure 7. Thus, this effect ismuch larger in 2-TN, compared to 3-TN, since in the meta-substituted conformer, only inductive effects can take place.These changes in electronic structure have been quantified bystudies of the 14N quadrupole couplings in benzonitrile andselected molecules.28

A more subtle view on the geometry changes upon elec-tronic excitation can be made on the basis of a natural popula-tion analysis (NPA). The atomic numbering used in the follow-ing refers to the numbering of 2-TN in Figure 1. The same argu-ments hold for structural changes of 3-TN. The main structuraleffects in the cyano group can be traced back to lone pair (LP)interactions of the nitrogen atom. The interaction between thenitrogen atom lone pair (in a sp0.83 hybrid) and the unoccupiedRydberg orbital at the neighboring C(15) atom is stronglydecreased upon electronic excitation. The resulting bond orderreduction of the C(15)N(16) bond leads to the observed bondlength increase. LP(N) interaction with the antibonding π bondorbital C(4)C(15)* also decreases by more than a factor of 2.Thus, less electron density is shifted to the antibonding orbitalupon electronic excitation, leading to a net increase of bondorder and a resulting decrease of the C(4)C(15) bond length.The bond length decrease of the C(3)C(11) bond between thearomatic ring and the methyl group is mainly due to decreasedinteractions between the bonding π orbital between C(3) andC(11) and the antibonding π orbitals C(3)C(4)*, C(4)C(5)*,C(1)C(2)*, and C(1)C(3)* in the aromatic ring, since theiroccupancy is increased by ππ∗ excitation.

Not only do the geometries of the conformers change in amanner that reflects effects of the electronic excitation, but thebarriers to methyl torsion change as well. In a one-dimensionalmodel, the torsional motion of the rotating methyl group canbe described by the Hamiltonian

HT = Fp2 +12

n

Vn(1 − cos nα), (6)

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084304-8 Gmerek et al. J. Chem. Phys. 144, 084304 (2016)

TABLE III. Experimental and fitted wavenumber of methyl torsional tran-sitions in absorption and emission. The values for the torsional parametersfrom the fit of 2-TN (3(TN) are F′′= 5.57(6) cm−1 (5.61(3) cm−1), V ′′3= 180.6(39) cm−1 (20.7(12) cm−1), V ′′6 =−1.9(164) cm−1 (−11.5(41) cm−1),F′= 5.18(15) cm−1 (4.95(6) cm−1), V ′3= 202.2(53) cm−1 (43.3(11)), V ′6=−17.6(171) cm−1 (−25.6(22) cm−1).

2-TN 3-TN

Transition Expt. Fit Transition Expt. Fit

0a′1← 0a′′1 0 0 0a′1← 0a′′1 0 01e′← 1e′′ −0.098 −0.098 1e′← 1e′′ −1.457 −1.4572e′← 1e′′ . . . 97 2e′← 1e′′ 22 21.93a′1← 0a′′1 139 139 3a′1← 0a′′1 58 58.24e′← 1e′′ 157 157 4e′← 1e′′ 82 80.75e′← 1e′′ . . . 198 5e′← 1e′′ . . . 122.76a′1← 0a′′1 . . . 264 6a′1← 0a′′1 183 183.51e′← 2e′′ . . . −88 1e′← 2e′′ −17 −19.70a′1← 3a′′1 −130 −130 0a′1← 3a′′1 −51 −51.21e′← 4e′′ −152 −152 1e′← 4e′′ −80 −80.91e′← 5e′′ −202 −202 1e′← 5e′′ . . . −122.90a′1← 6a′′1 . . . −254 0a′1← 6a′′1 −188 −186.9

with the angular momentum of the internal rotor defined by

p = −i~d

dα(7)

and the torsional angle α. The kinetic energy term Fp2 is thatof a free rotor model with the torsional constant F, while thesecond term introduces a barrier consisting of different n-foldperiodic potentials. The torsional constant F is defined as

F =h

8π2Iα, (8)

where Iα is the moment of inertia of the methyl top withrespect to the torsional axis.

To compare theory with experiment, the Hamiltonianin Equation (6) was setup in free rotor basis function anddiagonalized, yielding the eigenvalues and eigenfunctions ofthe torsional problem. The values for the torsional constantsand torsional barriers in ground and excited states of bothconformers and the wavenumbers of the torsional transitionsare compiled in Table III, and compared with the experiment.The fit is excellent. Note that the quite large reduction of thevalue of the torsional constant F upon electronic excitationin 2-TN is nicely explained by the resonance structures inFigure 7. The C–H distances in the methyl group increase,leading to an increased moment of inertia (Iα) of the top, ordecreased torsional constant F.

Also for the torsional barriers, the combination of resultsfrom high resolution rotationally resolved electronic spectros-copy and vibronic spectroscopy improves the accuracy of theresults considerably. A one-dimensional fit of the torsionalbarriers for 2-TN and 3-TN to torsional transitions in bothstates from the low resolution experiment yielded approximatevalues for the torsional constants F, and the V3 and V6 barrierterms in each electronic state. These were subsequently refinedby a combined fit of the first and second order perturbationcoefficients and the AE splitting from the high resolution study.In an iterative manner, these results were used for a better

prediction of torsional transitions in absorption and emission,which could be located this way. In the end, a global fit wasperformed using all pieces of experimental evidence: the firstand second order perturbation coefficients, the AE splitting, thetorsional transitions in emission and in absorption to obtain thebarriers and torsional constants with a high accuracy.

ACKNOWLEDGMENTS

Computational support and infrastructure were providedby the “Centre for Information and Media Technology” (ZIM)at the Heinrich-Heine-University Düsseldorf (Germany). Thefinancial support of the Deutsche Forschungsgemeinschaft(SCHM1043/12-1) is gratefully acknowledged. L.A.V. ac-knowledges DAIP-UG for the financial support provided onbehalf of the High Resolution Spectroscopy Lab in León,México.

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