Electronic spectra of 2- and 3-tolunitrile in the gas phase. I. A study of methyl groupinternal rotation via rovibronically resolved spectroscopyJosé Arturo Ruiz-Santoyo, Josefin Wilke, Martin Wilke, John T. Yi, David W. Pratt, Michael Schmitt, andLeonardo Álvarez-Valtierra Citation: The Journal of Chemical Physics 144, 044303 (2016); doi: 10.1063/1.4939796 View online: http://dx.doi.org/10.1063/1.4939796 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/144/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Determination of ground and excited state dipole moments via electronic Stark spectroscopy: 5-methoxyindole J. Chem. Phys. 144, 044201 (2016); 10.1063/1.4940689 Rotationally resolved electronic spectra of 9,10-dihydrophenanthrene. A “floppy” molecule in the gas phase J. Chem. Phys. 126, 224308 (2007); 10.1063/1.2732753 The structures of fluorene– ( H 2 O ) 1,2 determined by rotational coherence spectroscopy J. Chem. Phys. 119, 1970 (2003); 10.1063/1.1584031 A combined nuclear dynamics and electronic study of the coupling between the internal rotation of the methylgroup and the intramolecular proton transfer in 5-methyltropolone J. Chem. Phys. 117, 7525 (2002); 10.1063/1.1503317 π * –σ * hyperconjugation mechanism on the rotational barrier of the methyl group (I): Substituted toluenes inthe ground, excited, and anionic states J. Chem. Phys. 113, 2168 (2000); 10.1063/1.482029

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THE JOURNAL OF CHEMICAL PHYSICS 144, 044303 (2016)

Electronic spectra of 2- and 3-tolunitrile in the gas phase. I. A studyof methyl group internal rotation via rovibronically resolved spectroscopy

José Arturo Ruiz-Santoyo,1 Josefin Wilke,2 Martin Wilke,2 John T. Yi,3 David W. Pratt,4Michael Schmitt,2 and Leonardo Álvarez-Valtierra1,a)1División de Ciencias e Ingenierías, Universidad de Guanajuato, León, Guanajuato 37150, México2Institut für Physikalische Chemie, Heinrich-Heine-Universität, 40225 Düsseldorf, Deutschland3Department of Chemistry, Winston-Salem State University, Winston-Salem, North Carolina 27110, USA4Department of Chemistry, University of Vermont, Burlington, Vermont 05405, USA

(Received 13 November 2015; accepted 23 December 2015; published online 28 January 2016)

Rotationally resolved fluorescence excitation spectra of the origin bands in the S1 ← S0 transitionof 2-tolunitrile (2TN) and 3-tolunitrile (3TN) have been recorded in the collision-free environmentof a molecular beam. Analyses of these data provide the rotational constants of each molecule andthe potential energy curves governing the internal rotation of the attached methyl groups in bothelectronic states. 2TN exhibits much larger barriers along this coordinate than 3TN. Interestingly, theelectronic transition dipole moment in both molecules is markedly influenced by the position of theattached methyl group rather than the position of the cyano group; possible reasons for this intriguingbehavior are discussed. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4939796]

I. INTRODUCTION

The properties of aromatic molecules substituted withfunctional groups have been a topic of interest for manyyears, beginning with the pioneering studies of Hammettand co-workers of the effects of different substituents on therates and mechanisms of aromatic substitution reactions.1,2

Later, interest gradually shifted towards the study of particularfunctional groups and increased applications of the concepts ofmolecular orbital (MO) theory to interpret the observed trendsin the properties of isolated molecules and their chemicalbehavior.3 An early example is provided by the divisionof substituents into two kinds, those that have orbitals thatcannot (by symmetry reasons) overlap with the π orbitals ofthe aromatic ring and those that can, giving rise to a propertyknown as “hyperconjugation.”4 While controversial at thattime, the existence of such effects in many molecules has beenconfirmed by numerous magnetic resonance studies of freeradicals and neutral compounds,5 which clearly show that themotions of hyperconjugating groups, like the methyl group,are often hindered by substantial torsional barriers.

Interest in the torsional motion of methyl groups was laterenhanced by the prediction by Pople and co-workers6 thatboth the preferred orientation and the magnitude of torsionalbarriers might change upon electronic excitation and by thenearly simultaneous discovery of such an effect in the nπ∗

absorption spectrum of CF3NO by Gordon et al.7 Experimentalstudies of such effects have greatly increased in recent yearsowing to the use of supersonic expansions and tunable lasers.A pioneering report was the study of the different isomers offluorotoluene (FT) by Ito and co-workers;8 they found thatfor o-fluorotoluene (2FT), V3(S0) = 228.1 cm−1 and V3(S1)= 21.8 cm−1; for m-fluorotoluene (3FT), V3(S0) = 16.9 cm−1

a)Author to whom correspondence should be addressed. Electronic mail:leoav@fisica.ugto.mx

and V3(S1) = 123.7 cm−1; and finally, for p-fluorotoluene(4FT), V6(S0) = −4.8 cm−1 and V6(S1) = −33.7 cm−1. Theyalso found that the preferred orientation of the methyl groupchanges by 60◦ on electronic excitation of 2FT, but did notchange in either 3FT or 4FT. These remarkable effects maybe interpreted to be a consequence of light-induced changesin the π-electron distributions of adjacent double bonds.9,10

Most of the work on the excited electronic statesof substituted benzenes published to date has involvedelectron-donating substituents; very little has been focusedon electron-withdrawing ones, such as ketones, esters,carboxylic acids, –CX3, –CN, –NO2 groups, and substituentshaving multiple bonds. Here, we focus on ortho- and meta-cyano derivatives of toluene, using high resolution electronicspectroscopy techniques. We seek to determine whether thebarriers to the torsional motion of the attached methyl groupalso depend upon the position of substitution and whether thepatterns of change (if observed) are similar to or different fromthose previously reported for electron-donating substituents.

II. EXPERIMENTAL

2-tolunitrile (2TN) and 3-tolunitrile (3TN) were pur-chased from Aldrich and used without further purification.Dry argon was used in all experiments as inert carrier gas.

In the vibrationally resolved experiments, samples wereseeded into 20 psi of argon gas and expanded into a vacuumchamber (10−5 Torr) through a 1 mm diameter orifice pulsedvalve (General Valve Series 9) operating at 10 Hz. Twocentimeters downstream of the valve, the free jet was excitedwith the second harmonic of a Quanta Ray Nd3+:YAG(Model DCR-1A) pumped dye laser (Model PDL-1). Thedye (Rhodamine 575) laser output was frequency doubledwith an external β-barium borate (BBO) crystal providinga spectral resolution of ∼0.6 cm−1 in the UV. From the

0021-9606/2016/144(4)/044303/9/$30.00 144, 044303-1 © 2016 AIP Publishing LLC

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FIG. 1. Vibrationally resolved fluores-cence excitation spectra of 2TN (a) and3TN (b) in the gas phase. The frequencyof the electronic origin is indicated foreach molecule.

point of intersection between the jet and the laser beam, themolecules were excited and the fluorescence was collectedwith a photomultiplier tube (PMT). Finally, the collected datawere processed by a boxcar integrator (Stanford ResearchSystems) and recorded with Quick Data Acquisition software(version 1.0.5).

Rotationally resolved electronic experiments were per-formed using a molecular beam laser spectrometer, describedin detail elsewhere.11 Briefly, the molecular beam was formedby expansion of the vaporized sample seeded in argon carriergas (∼ −18 psi) through a heated (∼313 K) 240 µm quartznozzle into a differentially pumped vacuum system. Theexpansion was skimmed 2 cm downstream with a 1 mmdiameter skimmer and crossed 13 cm further downstream bya continuous wave (CW) Ar+ pumped ring dye laser. The CWlaser was operated with Rhodamine 110 dye and intracavityfrequency doubled in a BBO crystal, yielding ∼200 µW ofUV radiation with a linewidth of ∼1 MHz.

The fluorescence excitation spectra of 2TN and 3TNwere detected, using spatially selective optics, by a PMT anda photon counting system. The PMT signals, together with theiodine absorption spectrum and the relative frequency markers,

were simultaneously collected and processed by the jb95 dataacquisition software.12 Absolute frequency calibrations of thespectra were performed by comparison with the I2 absorptionspectrum.13 The relative frequency markers were obtainedfrom a stabilized etalon with a free spectral range, in thefundamental of the dye, of 299.7520 ± 0.0005 MHz.

III. RESULTS AND INTERPRETATION

Figure 1 shows the vibrationally resolved fluorescenceexcitation spectra of 2TN and 3TN in a supersonic jet. Theelectronic origin bands are observed at 35 768.95 (2TN) and35 815.53 cm−1 (3TN), values that differ by ∼4 cm−1 fromthose that were earlier reported by Ito et al.14 and Fujii et al.15

The 2TN spectrum lacks visible low-frequency activity, butthe 3TN spectrum exhibits three bands at +21.8, +58.2, and+81.6 cm−1 above the electronic origin.

Figure 2 shows the rotationally resolved S1 ← S0fluorescence excitation spectrum of the origin band of 2TN.This band spans approximately 3.7 cm−1 and contains twosub-bands separated by about 0.098 cm−1. We interpret these

FIG. 2. Rotationally resolved fluores-cence excitation spectrum of the originband of 2TN (top). Shown below thisspectrum are the two contributing sub-bands, spaced by about 0.098 cm−1, thathave been assigned in the fit.

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044303-3 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

two bands as being the A-A and E-E sub-bands associatedwith the hindered internal rotation of the attached methylgroup. The relevant Hamiltonians are10

H = AAP2a + BAP2

b + CP2c, (1)

for the A-A sub-bands and

H = AE P2a + BE P2

b + CP2c + DaPa + DbPb, (2)

for the E-E sub-bands. Here,

AA = A + FW (2)Aρ2a, BA = B + FW (2)

Aρ2b, (3)

AE = A + FW (2)E ρ2

a, BE = B + FW (2)E ρ2

b, (4)

Da =W (1)λaA

r, Db =

W (1)λbBr

, (5)

W (1)vσ = −2 ⟨vσ |p|vσ⟩ , (6)

W (2)vσ = 1 + 4F

v′,v

⟨vσ |p|v ′σ⟩Evσ − Ev′σ

, (7)

where F is the internal rotor constant, W (1) and W (2)are first- and second-order perturbation terms, derived byHerschbach,16 and ρa and ρb are the contributions of therotational motion of the –CH3 group about its C3 axis to themoments of inertia about the molecular a and b axes, givenby

ρg =

�λg Iφ

�

Ig=

�λgBg

�

rF. (8)

Here, the λg and Bg [g = a,b] are direction cosines and therotational constants, respectively (the rotor axis is assumed tolie in the ab plane) and

r = 1 −

g

λ2g IφIg

. (9)

Hence, the A-A sub-band is expected to be “rigid-rotor” like,but the E-E sub-band should be perturbed.

Analysis of the data shown in Fig. 2 showed that the red-shifted sub-band is more perturbed than the blue-shifted sub-band. Hence, we first fit the latter sub-band using rigid-rotorHamiltonians for the two states. The spectrum exhibits mainlyb-type character, evidencing a near-perpendicular orientationof the S1 ← S0 transition moment with respect to the a-inertialaxis of the molecule. To fit this sub-band, we first generatedabout 3730 b-type rovibronic transitions based on ab initioestimates17 of rotational constants. Then, we made quantumnumber assignments of single transitions in the simulatedspectrum to corresponding transitions in the experimentalspectrum, using the program jb95.12 Finally, we used a leastsquares fitting procedure to optimize the rotational constants,based on comparison of observed and calculated line positions.The final fit utilized 308 rovibronic transitions and resulted ina standard deviation of 2.01 MHz.

Fitting the E-sub-band required a different strategy. First,from a theoretical structure calculation made in Gaussian andvisualized using its graphical interface, the angle that the C3axis of the methyl group makes with the a-inertial axis of themolecule was estimated to be about 54◦(±1◦ ) in 2TN. Usingthe experimental rotational constants from the A-sub-band, the

theoretically calculated values of F, and the computed valuesof V3 from ab initio calculations, the reduced barrier height s(V3 = 9Fs/4) values were either interpolated or extrapolated,in order to estimate the experimental values of W (1)

E in eachelectronic state. Thereafter, we computed the correspondingvalues for Dg(= FW (1)

E ρgPg , g = a,b) from the calculated W (1)E

values. Finally, the resulting Dg values, together with theexperimental A-sub-band rotational constants, were used asa starting point to fit the experimental E-sub-band spectra.We first generated about 4275 b-type rovibronic transitionsusing rigid rotor Hamiltonians, complemented by first-orderperturbation terms, for both electronic states. The final fitutilized 322 rovibronic transitions and resulted in a standarddeviation of 2.02 MHz. Individual lines in the complete fitexhibit Voigt profiles, with a Gaussian contribution of 18.6MHz and a Lorentzian contribution of 20.6 MHz. The rotationaltemperature for both sub-bands is 4.8(±1) K. The fit spectraare shown in the bottom two traces in Fig. 2; the inertialparameters derived from the fits are summarized in Table I.

Figure 3 shows the high-resolution fluorescence excita-tion spectrum of the origin band of the S1 ← S0 transitionof 3TN. This band spans approximately 5.8 cm−1 and alsocontains two sub-bands, separated by about 1.457 cm−1.Again, the A-A sub-band is blue-shifted, and both sub-bandsare principally b-type in character. Following proceduressimilar to those described above, about 1165 b-type rovibronictransitions were generated to fit the A-sub-band using rigidrotor Hamiltonians for both electronic states, about 300transitions were assigned and resulted in a standard devia-tion of 2.04 MHz. For the E-sub-band, about 1230 b-typerovibronic transitions were generated using perturbed Hamil-tonians for both electronic states, about 305 lines were assi-gned, which resulted in a standard deviation of 4.74 MHz.The rotational temperature for both sub-band fits is 7.7(±1) K.Each sub-band exhibits Voigt profiles, with a Gaussiancontribution of 16.0 MHz and a Lorentzian contribution of18.0 MHz. The inertial parameters derived from the fits ofboth sub-bands in the 3TN spectrum, also shown in Fig. 3, arereported in Table I.

Figures 4(a) and 4(b) show portions of the observedand calculated spectra of the 2TN and 3TN, respectively, atfull experimental resolution (about 0.11 cm−1), illustratingthe contributions of the two components (red and greenlines) and the convoluted simulated spectrum (envelope) thataccurately reproduce the experimental spectrum (top traces).These middle traces are proof of the degree of accuracy of thefits despite the large degree of overlap of the two sub-bandsin both molecules. The contrast between the middle and thebottom simulations will be discussed later.

From the experimentally determined values of Da andDb for both molecules in both states, and the angle that theC3 internal rotor axis makes with the a-axis of the molecule,we used our program HTF18 for a simultaneous fit ofthe barrier heights V3 and V6 and of the torsional constantsF in both electronic states to the experimentally determinedtorsional splitting of the A and the E band origins, to thedifference of the rotational constants ∆Bg = Bv,σ=0

g − Bv,σ=±1g

of the A (σ = 0) and the E (σ = ±1) bands (containingthe second order perturbation coefficients W (2)

Aand W (2)

E , cf.

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044303-4 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

FIG. 3. Rotationally resolved fluores-cence excitation spectrum of the originband of 3TN (top). Shown below thisspectrum are the two contributing sub-bands, spaced by about 1.457 cm−1, thathave been assigned in the fit.

Equations (3) and (4)), to the torsion–rotation parametersDg (containing the first order perturbation coefficients W (1)

E ,cf. Equation (5)), and to torsional transitions of differentv in absorption Ev′σ ← Ev′′σ or in emission Ev′σ → Ev′′σ,where v and σ designate the torsional wavefunction, using theLevenberg–Marquardt algorithm as a local minimizer. The

standard deviations of the fit parameters were determinedfrom the covariance matrix using the uncertainties of theexperimental values. This analysis yields V3(S0) = 178.09and V3(S1) = 188.0 cm−1 for 2TN and V3(S0) = 13.58 andV3(S1) = 37.57 cm−1 for 3TN (see Table II for furtherdetails).19

TABLE I. Rotational constants (A, B, and C) and torsion-rotation parameters (Da and Db) of the zero-pointvibrational levels of the S0 and S1 electronic states of 2- and 3-tolunitrile, derived from fits of the A- andE-sub-bands in their rotationally resolved S1← S0 fluorescence excitation spectra. Numbers in parenthesesindicate uncertainties in the last significant figure.

A-Sub-band E-Sub-band

2TN S0 S1 S0 S1

A (MHz) 2892.6 (1) 2853.4 (1) 2891.3 (1) 2852.8 (1)B (MHz) 1500.4 (1) 1460.2 (1) 1499.6 (1) 1459.8 (1)C (MHz) 993.5 (1) 971.7 (1) 993.5 (1) 971.8 (1)Da (MHz) 81.5 (1) 42.2 (1)Db (MHz) −55.0 (13) −30.2 (25)∆I(amu Å2) −2.87 (1) −3.14 (1) −3.14 (1) −3.29 (1)Origin (cm−1) 35 768.95 35 768.85Rotational temperature (K) 4.8 (1)a/b character % 10.3/89.7

3TN

A (MHz) 3331.8 (1) 3256.0 (1) 3321.3 (1) 3226.0 (1)B (MHz) 1203.0 (1) 1177.8 (1) 1201.5 (1) 1174.5 (1)C (MHz) 883.9 (1) 866.1 (1) 883.9 (1) 866.3 (1)Da (MHz) −4366.1 (1) −2550.2 (1)Db (MHz) −1449.1 (1) −877.3 (1)∆I(amu Å2) −0.02 (1) −0.81 (1) −1.03 (1) −3.55 (1)Origin (cm−1) 35 815.53 35 814.08Rotational temperature (K) 7.7 (1)a/b character % 10.8/89.2

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044303-5 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

FIG. 4. Portions of the rovibronically resolved experimental spectra of 2TN (a) and 3TN (b). The upper trace is a portion of the observed experimental spectrum;the second trace is a simulated spectrum using the indicated TDM orientation and the third trace is simulated spectrum with the other TDM orientation. In thecase of 3TN, it is quite evident that the second simulation resembles the experimental trace (TDM almost perpendicular to the –CH3 top axis); the same is alsoassumed to occur for the 2TN case. On both, 2TN and 3TN spectra, the A and E sub-bands almost completely overlap. Since the QIE’s act only on the E lines,but not on the A lines, the variation of the intensities is not as large as in cases with completely separated A and E sub-bands.

IV. DISCUSSION

A. Nature of the S0 and S1 states

Comparison of the measured ground state rotationalconstants of 2TN and 3TN (shown in Table I) with the

previously measured microwave values20–23 shows excellentagreement. As expected for an aromatic molecule withtwo substituent groups, A, B, and C are all different;and A is approximately twice as large as the average ofB and C. However, upon electronic excitation, a small

TABLE II. Fits of the torsional barriers and internal rotor constants to the wavenumbers of the torsional transitionsin absorption and emission,14 to the experimental AE splitting, to the torsion–rotation parameters Da and Db, andto the difference of the rotational constants ∆Bg = B

v,σ=0g −Bv,σ=±1

g of the A(σ = 0) and the E (σ =±1) tors-ional sub-bands. For details, see text. Numbers in parentheses indicate uncertainties in the last significant figures.

2TN expt. Calculated 3TN expt. Calculated

∆AE (1e′← 1e′′) −0.09814a −0.098 ∆AE (1e′← 1e′′) −1.457a −1.4572e′← 1e′′ . . . 88.1 2e′← 1e′′ 22b 20.33a1′← 0a1

′′ 139c 138.8 3a1′← 0a1

′′ 58b 57.24e′← 1e′′ 157c 157.4 4e′← 1e′′ 82b 80.22e′′← 1e′ . . . −80.0 2e′′← 1e′ −17b −18.10a1′′← 3a1

′ −130c −130.3 0a1′′← 3a1

′ −51b −50.94e′′← 1e′ −152c −151.4 4e′′← 1e′ −80 −80.2Da′′ 81.50a 81.49 Da

′′ 4366.10a 4366.10Db′′ −55.00a −54.99 Db

′′ 1449.10a 1449.10∆Ba

′′ 1.30d 1.59 ∆Ba′′ 10.50d 14.03

∆Bb′′ 0.80d 0.72 ∆Bb

′′ 1.50d 1.54Da′ 42.20a 42.20 Da

′ 2550.20a 2550.20Db′ −30.20a −30.20 Db

′ 877.30a 877.30∆Ba

′ 0.60d 0.83 ∆Ba′ 30.00d 33.41

∆Bb′ 0.40d 0.42 ∆Bb

′ 3.30d 3.95

F′′ 5.49(5)e F′′ 5.18(5)e

V3′′ 178.09(31)e V3

′′ 13.58(23)e

V6′′ 31.3(78)e V6

′′ −13.68(560)e

F′ 5.16(7)e F′ 5.02(6)e

V3′ 188.0(47)e V3

′ 37.57(49)e

V6′ 51.8(27)e V6

′ −25.91(439)e

aThis work. Values in MHz.bFrom Ref. 14 in cm−1.cSee Ref. 19.dThis work ∆Bg = B

v,σ=0g −Bv,σ=±1

g in MHz.eThis work. Values in cm−1.

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044303-6 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

SCHEME 1.

but significant decrease in all rotational constants occursin both molecules; for 2TN: ∆A(= A′ − A′′) = −39.2, ∆B(= B′ − B′′) = −40.2, and ∆C (= C ′ − C ′′) = −21.8 MHz; for3TN: ∆A = −75.8, ∆B = −25.2, and ∆C = −17.8 MHz.These changes reflect an increase in the overall size ofthe molecules that is characteristic of ππ∗ transitions, seeScheme 1.

Inertial defect values [∆I (= Ic − Ia − Ib)] also areinfluenced by electronic excitation. The inertial defect in theS0 state of 2TN is ∆I ′′ = −2.87 amu Å2, a value that is close tothe value expected for a non-rotating methyl group possessingtwo out-of-plane hydrogen atoms (−3.3 amu Å2), compared to∆I ′ = −3.14 amu Å2 in the S1 state. Apparently, the attachedmethyl group in 2TN is slightly more hindered in its torsionalmotion in the S1 state, as the increase in magnitude of the V3value would suggest. 3TN provides a striking example of thisbehavior; it has ∆I values of −0.02 amu Å2 in the S0 state and−0.81 amu Å2 in the S1 state. Clearly, the internal rotation ofthe methyl group in 3TN is “essentially free” in both states,especially in the ground state. That such a correlation betweenV3 barrier heights and inertial defects might exist is apparenton the examination of the data for several other aromaticmolecules, see Table III.24–29

B. The electronic transition dipole moment (TDM)vector orientation

Figure 5 illustrates the frontier MOs that are mainlyinvolved in the S1 ← S0 transition determined from ab initiocalculations [DFT/B3LYP/6-311G(d,p)]17 for 2TN and 3TNand their “parent” molecules: toluene and benzonitrile. Itis evident that a linear combination of single transitionsamong the frontier MOs best represents the overall S1 ← S0excitation for each molecule. The electronic excitations in theparent molecules involve only two single electron transitions,LUMO ← HOMO and LUMO + 1 ← HOMO − 1 in tolueneand LUMO + 1 ← HOMO and LUMO ← HOMO − 1 inbenzonitrile. In the tolunitriles, the overall electronicexcitation is composed of several single transitions, dominatedby the LUMO ← HOMO transition in 2TN (∼58%) and in3TN (∼47%). Additionally, the virtual MOs in both moleculesresemble those of benzonitrile; but a comparison of theoccupied ones with those of toluene will reveal that theyare more markedly influenced by the presence of the methylgroup.

The S1-S0 transitions in all four molecules are ππ∗

transitions; hence, their TDM vectors are expected to liein the aromatic plane. From the relative intensities of thea-type and b-type transitions in the experimental spectra (seeTable I), the angle that this vector makes with the a-inertialaxis of the molecule, θTM, may be determined from the relation

tan2 (θTM) = IbIa, (10)

where the Ig (g = a, b) are the relative intensities ofg-type lines in the spectrum. The computed angles are|θTM| = 71.3◦ (±1) for 2TN and |θTM| = 70.9◦ (±1) for 3TN.The corresponding results for the parent molecules, toluene30

and benzonitrile,31 are |θTM| = 90◦; both molecules exhibitb-polarized spectra, evidencing an in-plane perpendicularorientation of their TDM vectors with respect to thea-inertial axis of each molecule. Clearly, 2TN and 3TNare similar; |θTM | lies almost parallel to the b-inertial axesin both molecules. However, the presence (and location) ofthe two substituent groups makes the matter of the exactsign determination (and the interpretation of the results) moreinteresting.

Previously, it has been shown that the absolute orientationof the TDM vector of an isolated molecule can be determinedfrom quantum interference effects (QIE’s)27,32 exhibited bymolecules possessing methyl rotors whose motion is hinderedby small barriers. QIE’s have their origin in the simultaneousexistence of hybrid band character in the spectrum, a couplingof the overall rotation with the hindered internal rotation andlow barriers along the torsional coordinate in both electronicstates. 2TN and 3TN are thus clearly potential candidatesfor the observation of these effects. In both cases, the angleeta (η) that describes the orientation of the internal rotoraxis with respect to the inertial a-axis may have the samesign as the angle theta (θ) of the TDM with the a-axis(+,+ or −,−) or they have different signs (+,− or −,+).Figure 4(b) shows a magnified portion of the 3TN highresolution spectrum (top trace) together with two simulatedspectra, one having different signs for η and θ (middle trace)and a second having the same signs for η and θ (bottomtrace). The relative intensities in the two simulated spectraare clearly different. Of the two possibilities, the simulationwith opposite signs more accurately reproduces the relativeintensities in the spectrum. The corresponding analysis for2TN (see Fig. 4(a)) is less conclusive; since the barriers in thetwo electronic states are very similar, the A and E sub-bandsalmost completely overlap, making the analysis of the QIE’s(which act only on E-type lines) more challenging. Theory(CC2/cc-pVTZ) suggests that, as in the case of 3TN, thetwo angles have opposite signs (bottom trace in Fig. 4(a)).So the absolute TDM angles are −71.3◦ in 2TN and +70.9◦

in 3TN, as shown in Fig. 6.This is an unexpected result. Though 2TN and 3TN are

clearly different molecules, we expected both of their S0–S1transitions to be dominated by the properties of the stronglyconjugating –CN group, rather than the weakly (hyper-)conjugating CH3 group. But the TDMs of both moleculesare more nearly perpendicular to the bond attaching the

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044303-7 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

FIG. 5. [DFT/B3LYP/6-311G(d,p)]Frontier molecular orbitals of 2TNand 3TN. The energy level diagramsindicate the principal single electronictransitions and their correspondingcontributions to the overall S1← S0electronic excitation in each molecule.

methyl group to the ring, rather than to the bond attaching thecyano group to the ring. The methyl group is the “dominant”substituent.

Examination of the MO diagrams in Fig. 5 shows whythis might be so. The HOMOs of both parent moleculesshow nodal patterns that either align with the a-axis of themolecule (the substituent axis) or are perpendicular to it.So, their lowest ππ∗ transitions will have TDMs that areparallel to either a or b. But the two HOMOs of 2TN and3TN are both skewed with respect to these axes, since theyare mainly toluene-like, whereas the two LUMOs of 2TNand 3TN are not skewed with respect to these axes, sincethey are mainly benzonitrile-like. Consequently, electronicexcitation of both molecules transfers electrons from toluene-like orbitals to benzonitrile-like orbitals and results in TDM

orientations that are rotated away from the canonical “parallel”and “perpendicular” directions. As a result, the S1 state of bothmolecules exhibit mixed La–Lb character. A similar behavioris found in many “off-axis” substituted benzenes.33

C. The electron withdrawing (–CN) groupand its effect on the methyl torsional barriers

Figures 7 and 8 illustrate the experimentally derivedmethyl-group torsional potential energy surfaces (PESs) of2TN and 3TN in their ground and first excited singletstates. We have succeeded on the accurate torsional barrierdetermination for 2TN, in both S0 and S1 states, in creditsto the ultra-high resolution performed on this work; whereit is observed a slight increase on the V3 value, from 178

TABLE III. Relationship between inertial defect values and methyl torsional barrier heights of several differentaromatic molecules.

∆I (amu Å2) V3 (cm−1)

Molecule S0 S1 S0 S1 References

o-tolunitrile −2.87 −3.14 192.0 218.0 This worko-toluidine −3.51 −1.21 703.0 44.9 24o-fluorotoluene −3.11 . . . 228.1 −21.8 8 and 25o-methylanisole trans −6.51 −4.64 345.0 −36.9 26o-cresol-OD cis∗ −3.25 −0.24 669.1 88.8 27o-cresol-OD trans∗ −3.17 −0.30 371 −83 27m-tolunitrile −0.02 −0.81 13.8 34.5 This workm-toluidine −0.41 −3.40 9.4 322.0 24m-fluorotoluene −0.11 . . . 16.9 123.7 8 and 28m-methylanisole trans −4.06 −6.62 30.4 −225.7 26m-methylanisole cis −4.76 −6.64 57.1 209.5 26m-cresol-OD cisa −3.27 −0.06 21.3 221.8 27m-cresol-OD transa −3.25 −0.14 3.1 204.2 271-methylnaphthalene −3.35 −3.36 809.0 565.0 292-methylnaphthalene −3.18 −2.76 234.0 128.0 29

aInertial parameters corresponding to the rotational isomers of hydroxy deuterated o- and m-cresols.

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044303-8 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

FIG. 6. Transition dipole moment vectors of benzonitrile, toluene, 2TN, and 3TN from experimental results.

to 188 cm−1, rather than the “no change” reported by Itoet al.14 and Fujii et al.;15 on the other hand, for 3TN, weobserve a considerable increase on the V3 value (by a factorof ∼3) from 13.6 to 37.6 cm−1, upon electronic excitation.Correspondingly, this last result agrees with the V3 valuesreported by Ito et al.,14 where V3 increases from 14 to39 cm−1. Most striking upon comparison of these figures isthe substantially high barrier for 2TN compared to 3TN, inthe ground electronic state. A similar behavior is observedin the fluorotoluenes and toluidines, see Table III. However,the three-fold barrier decreases on electronic excitation of2-fluorotoluene and 2-toluidine and increases on electronicexcitation of 3-fluorotoluene and 3-toluidine, behaviors thatare quite different from those observed in 2TN and 3TN.Our findings for these two molecules are also quite consistentwith those predicted by theoretical calculations of Nakai andKawai.34

The explanation for this unexpected behavior lies, again,in the nature of the molecular orbitals that are involved inthe S1–S0 transitions of 2TN and 3TN. In general, barrierheights in molecules of this type depend most strongly on thedifference in π-electron densities on either side of the positionof attachment of the methyl group.10 In the ground states of thetwo molecules, the relevant MOs are HOMO and HOMO−1.

As can be seen from Fig. 5, this difference is relatively large in2TN but relatively small in 3TN. This explains the differencein magnitudes of the torsional barriers in their S0 states.Excitation of the two molecules to their S1 states transferssome of the π-electron density to LUMO and LUMO+1orbitals, whose symmetry properties are dictated by theattached –CN groups. These are largely “mode-conserving”in the vicinity of the attached –CH3 groups; hence, only smallchanges in barrier are observed.

Importantly, the situation is different in the fluorotoluenesand toluidines because their substituents are electron-donating, rather than withdrawing. So, the presence ofa multiple-bonded, electron-withdrawing substituent has amajor qualitative effect on the barriers to rotation of theattached methyl groups. The determined torsional barriersfor 3TN are consistent with the linear trend found byplotting the Hammett constant vs. the change in the methyltorsional barrier height of aromatic molecules having electron-withdrawing substituents in the meta-position, i.e., withdouble or triple bonds on their chemical structure, such asmethylstyrene35 and ethynyltoluene.36 Thus, the motion of amethyl group in a toluene molecule that is substituted with anelectron-withdrawing group may be very different from onethat is substituted with an electron-donating group.

FIG. 7. Methyl torsional energy sur-faces of 2TN. The torsional parametersfrom the fit are included in the insettables for both electronic states.

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044303-9 Ruiz-Santoyo et al. J. Chem. Phys. 144, 044303 (2016)

FIG. 8. Methyl torsional energy sur-faces of 3TN. The torsional parametersfrom the fit are included in tables forboth electronic states.

ACKNOWLEDGMENTS

We thank W. Leo Meerts and David Plusquellic for theirhelp with the spectral analysis of the quantum interferenceeffects. L.A.V. acknowledges CONACYT (Grant No. 105032)for funding and also to the Mexican Academy of Sciences(AMC) and the Mexican Science Foundation (FUMEC) forthe assistanceship to spend a summer in Pittsburgh, wherethe experimental spectra were taken. J.A.R.S. acknowledgesCONACYT for the doctoral scholarship and for the additionalassistantship to spend a year in Düsseldorf, Germany. M.S.thanks the Deutsche Forschungsgemeinschaft for financialsupport (SCHM 1043/12-1).

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