Resolution of Conformer-Specific All- trans -1,6-diphenyl-1,3,5-hexatriene UV Absorption Spectra

Resolution of Conformer-Specific All-trans-1,6-diphenyl-1,3,5-hexatriene UV Absorption SpectraAndrzej M. Turek,*,‡ Jack Saltiel,*,† Tallapragada R. S. Krishna,† and Govindarajan Krishnamoorthy†,#

†Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States‡Faculty of Chemistry, Jagiellonian University, 30 060 Cracow, Poland

*S Supporting Information

ABSTRACT: All-trans-1,6-diphenyl-1,3,5-hexatriene (ttt-DPH) exists in solution as a mixture of s-trans,s-trans and s-cis,s-trans conformers. The latter is higher in energy, and itscontribution increases with increasing temperature. ttt-DPHUV absorption spectra broaden with increasing temperatureand undergo blue shifts with decreasing polarizability. Wedescribe here the resolution of two spectrothermal matrices ofttt-DPH UV absorption spectra into two conformer-specificcomponents. The first matrix consists of DPH spectrameasured in n-dodecane in the 283 to 374 K T range andthe second of ttt-DPH absorption spectra measured in the even numbered n-alkanes (n-C8−n-C16) at temperatures selected toachieve isopolarizability (284−372 K). Principal component analysis (PCA) treatments showed that reasonable two-componentsystems are attained by compensation for T-induced broadening and shifting in the pure conformer spectra. The self-modeling(SM) method used to resolve the n-C12 matrix is successfully tested on a simulated matrix closely mimicking ttt-DPHexperimental spectra in n-C12. Compensation for nonlinear effects yields robust two-component matrices from the experimentalspectra. Their resolution into pure component spectra is based on the application of the Lawton and Sylvestre (LS) non-negativity criterion at the spectral onset to define the spectrum of the low energy s-trans-conformer and the optimum linearityvan’t Hoff (vH) plot criterion to find the spectrum of the higher-energy s-cis-conformer. Resolved spectra are somewhat sensitiveto the choice of the spectral region in which the LS criterion is applied. The surprising result is that both resolutions lead to theconclusion that the molar fraction of the s-cis-conformer equals, or even exceeds, the molar fraction of the s-trans-conformer asthe highest T's employed in our study are approached.

■ INTRODUCTIONInterest in the photochemistry and photophysics of α,ω-

diphenylpolyenes, 1, stems from their role as models for the

retinyl polyenes that are related to vitamin A and the visual

pigments.1−4

Following our extensive studies on the photoisomerization andfluorescence of cis- and trans-stilbene4−6 (1, n = 1), we turnedour attention to all-trans-1,6-diphenyl-1,3,5-hexatriene7 (ttt-DPH, 1, n = 3) because it is the first member of the serieswhose lowest singlet excited state is not the initially accessed11Bu state on one photon absorption but the forbidden, doublyexcited 21Ag state.

1−4 Consequently, the major component inthe fluorescence spectrum of ttt-DPH corresponds to theforbidden 21Ag → 11Ag transition, which gains intensity through21Ag/1

1Bu vibronic coupling. Both lowest ttt-DPH excitedsinglet states resulting from this mixing S1, mainly 21Ag and S2mainly 11Bu contribute fluorescence because they aresufficiently close in energy to exist in thermal equilibrium,8,9

which is established within femtoseconds10−13 of the initial

formation of the 11Bu state. Those two fluorescence spectraoriginate from the s-trans,s-trans conformer (s-t-DPH), thelowest-energy conformer of ttt-DPH. Also contributing to ttt-DPH fluorescence is a third fluorescence spectrum that wasassigned to the less abundant s-cis,s-trans conformer (s-c-DPH).14 The presence of s-c-DPH fluorescence is evident inthe λexc dependence of the fluorescence spectra,14 consistentwith Havinga’s nonequilibration of excited rotamers (NEER)principle.15 Raising T increases the equilibrium population of s-c-DPH, thereby increasing its fluorescence contribution, Chart1.14,16 Resolution of ttt-DPH fluorescence into s-c-DPH and s-t-DPH fluorescence spectra was easily accomplished by relyingon the dependence of the spectra on λexc.

14 We also achievedthe resolution of the s-t-DPH fluorescence spectrum into its11Bu and 21Ag components,16 which was considerably morechallenging because, although their relative contribution varieswith T, the pure component spectra broaden and undergodifferential blue shifts as the T is increased and the mediumpolarizability is decreased. The success of the resolution of ttt-

Received: February 6, 2012Revised: May 9, 2012Published: May 14, 2012

Article

pubs.acs.org/JPCA

© 2012 American Chemical Society 5353 dx.doi.org/10.1021/jp301198p | J. Phys. Chem. A 2012, 116, 5353−5367

pubs.acs.org/JPCA

DPH fluorescence into three components relied upon (1)neutralizing the shifts by measuring the spectra underisopolarizability conditions (in even numbered n-C8−n-C16)and (2) applying broadening compensation to the spectra.16

The contribution of the s-c-DPH conformer to ttt-DPH UVabsorption is known to increase at the long wavelength onset ofthe spectrum.14 However, the shapes of the pure conformerspectra and the extent to which each conformer contributes tothe observed ttt-DPH absorption spectrum over the entirespectral range are unknown. This paper closes that knowledgegap. We measured ttt-DPH UV absorption spectra in n-dodecane, n-C12, in the 283 to 374 K T range and in n-alkane(n-C8−n-C16) solvents at selected T's and resolved the resultingtwo spectrothermal matrices into conformer-specific absorptionspectra by applying our previously developed broadening andshifting compensation procedures in conjunction with principalcomponent analysis with self-modeling, PCA-SM, and singular-value decomposition with self-modeling, SVD-SM. The deriveds-c-DPH absorption spectrum exhibits a weak shoulder at long λbut, although broader, is remarkably similar to the s-t-DPHabsorption spectrum. A recent criticism of our isopolarizabilityapproach17 is shown to be without merit.

■ EXPERIMENTAL SECTION

Materials. The sources of the materials and the purificationmethods used in this work were as previously described.16 ttt-DPH (Aldrich, 98% purity) was chromatographed on silica gelwith ethyl acetate/petroleum ether (1:99 v/v) as the eluent andthen twice recrystallized from n-hexane (Aldrich, spectrophoto-metric grade), except that prior to use in fluorescencemeasurements in n-hexadecane, the ttt-DPH was recrystallizedthree time from ethanol. Petroleum ether from Baker, reagentgrade, was distilled prior to use. n-Alkanes (n-octane, n-decane,n-dodecane, n-tetradecane, and n-hexadecane) used inabsorption measurements were from Aldrich (anhydrous, 99+%) and purified prior to use by passing them twice through Ag-activated alumina, followed by distillation under reducedpressure. For the fluorescence measurements, the n-hexadecanewas used as received.

Measurements. UV absorption spectra were measuredwith a Cary 300B UV−vis spectrophotometer. Fluorescencemeasurements were made with a Hitachi F-4500 spectropho-tometer equipped with a 150 W Xe arc source and aHamamatsu R3788 photomultiplier tube (the Hitachi F-4500employs horizontal excitation and emission slits instead ofvertical). Index of refraction measurements were carried outwith a Valentine refractometer, serial no. 450173 (VistaCalifornia). Temperatures were maintained to within ±0.1 °Cusing a Haake-FS constant-T circulator or a Neslab-RTE 4DDcirculation bath. Ethylene glycol was circulated for the higherT's. Solution temperatures were measured with an OmegaEngineering Model 199 RTD digital thermometer. Samplepreparation and handling were performed under nearlycomplete darkness (red light). For absorption measurements,the experiment in n-C12 is typical. A 4.15 × 10−5 M ttt-DPHsolution was used, and spectra were measured at 10 T's at ∼10°C intervals in the 282.8−374.0 K range. Spectra were recordedat 0.25 nm increments in the 250−650 nm range. Each ttt-DPHabsorption spectrum was corrected for solvent absorptionunder the same conditions. The spectra were baseline-correctedand represented as a function of wavenumber, interpolated tosmall equal intervals (1 cm−1). The isopolarizability T's used forabsorption measurements in the n-alkane series cover the samerange that was used for the spectra in n-C12 (284.25, n-C8;315.85, n-C10; 340.65, n-C12; 359.85, n-C14; and 371.95 K, n-C16).

Data Analysis. Data pretreatment and PCA-SM calcu-lations were performed on a Dell microcomputer working withappropriate routines in the environment of MATLAB version6.1.

■ RESULTS

UV Absorption Measurements in n-Dodecane. The Tdependence of ttt-DPH absorption spectra in n-C12 is shown inFigure 1a. The spectra were recorded at the following T's:282.75, 292.34, 303.39, 315.57, 323.85, 334.75, 342.38, 353.20,365.12, and 373.95 K. As the T is increased, the spectrabroaden and undergo a pronounced blue shift.9 Also evident is

Chart 1

Figure 1. (a) The T dependence of ttt-DPH UV absorption spectra in n-C12 (∼10 °C intervals in the 10−100 °C range; see text), (b) the Tdependence of the index of refraction, n, of n-C12, and (c) thermochromism of ttt-DPH in n-C12.

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp301198p | J. Phys. Chem. A 2012, 116, 5353−53675354

an apparent change in relative vibronic band absorbance and adiminution in absorbance that exceeds the change expectedbecause of the decrease in density. In a pioneering study,Hausser et al. associated the blue shift with the change in thesolvent’s index of refraction, n, which decreases upon increasingT.18 Subsequently, it was shown that the 11Ag−11Bu energy gapincreases linearly as the medium polarizability α = (n2 − 1)/(n2

+ 2) is decreased.9,19−23 To calculate α for our n-C12, wemeasured the T dependence of n. Our values agree well withliterature values.24 Plots of n versus T and of the frequency ofthe first vibronic band of the ttt-DPH absorption spectrumversus α are shown in Figure 1b and c, respectively.PCA of the spectra in Figure 1a reveals a four-component

system. Two of the components are structural, reflecting thepresence of the two conformers of ttt-DPH, namely, the s-c- ands-t-DPH rotamers. The other two factors are due tothermochromism, which causes shifting and broadening ofthe spectra with increasing temperature. Resolution of the pureconformer spectra must be preceded by neutralizing thethermochromic factors. We developed shifting and broadeningcompensation methods on a simulated matrix, as described inthe next section.Simulated Spectra. A simulated set of ttt-DPH spectra,

mimicking those measured in n-C12, was created in order toarrive at the procedure for compensation of thermal broadeningand shifts. The assumed pure component spectra of the s-t- ands-c-DPH conformers were scaled by assuming that the ratio ofthe molar absorptivities at νmax is 3/2 in favor of the s-trans-conformer. Fractional equilibrium contributions of the twoconformers at the 10 T's used in the n-C12 experiment werecalculated with the use of the van’t Hoff equation, assumingΔH0 = 4.000 kcal/mol and ΔS0 = 11.233 eu. For instance,those parameters give xs‑cis/xs‑trans = 0.25/0.75 at T = 298.15.Homoscedastic noise on the order of 1/1000 of the maximumabsorbance was then added to each spectrum in order tosimulate noise present in our experimental measurements.The two sets of spectra were interpolated to yield spectra

with absorbance at 1 cm−1 increments and differentiallybroadened, as previously described.25 Briefly, each mixturespectrum, except the one at the lowest T, is convolved with acorresponding cumulative thermal spread function. Cumulativethermal spread functions are generated as convolution productsof partial thermal spread functions describing the amount ofthermal broadening between successive T's. The partial thermal

spread functions have the form of the normalized Gaussiandistribution

νπ σ

ν νσ =

Δ− −

Δ

⎡

⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟

⎤

⎦⎥⎥g

T T( )

1(2 ) ( )

exp12 ( )ji

ji ji1/2

g

mean

g

2

(1)

where σg(ΔTji) is the standard deviation of the normalizedGaussian distribution, which depends on the difference of thetwo successive temperatures, Δ(Tji) = Tj − Ti. For twosuccessive temperatures such that Tj > Ti, this dependenceassumes the form

σ = −k T Tji j i (2)

where k is a parameter characteristic for the system that mustbe specified in order to create the broadened spectral matrix.We used k = 150 cm−1 for the simulation. Convolution of twonormalized Gaussian profiles gives a normalized Gaussianprofile whose variance equals the sum of variances of bothconvolved profiles.26 It follows that for three successive T's suchthat Tk > Tj > Ti, one can write

σ σ σΔ = Δ + ΔT T T( ) ( ) ( )ki ji kjg2

g2

g2

(3)

where each term in eq 3 is defined by eq 2 and σg2(ΔTki) is the

variance of the cumulative thermal Gaussian distributionencompassing the increase of temperature, first between Tiand Tj and then between Tj and Tk. The convolution isdistributive with respect to addition.26 Therefore, in modelingthe set of broadened absorption spectra of a two-componentmixture, one can broaden the combined two-componentspectra, or the one-component matrices can be broadenedseparately and then added, as was done in this work. Eachresulting spectrum was then shifted to match the position of thefirst vibronic band in the corresponding experimental spectrumin Figure 1a. The applied shift is therefore identical to theempirical shift in Figure 1c. As intended, the resulting simulatedspectra, Figure 2b, closely resemble the experimental spectra.Recovery of the original pure component spectra from the

mixture spectra in Figure 2a requires a method that convertsthe differentially shifted and broadened spectra to uniformlyshifted and broadened spectra. Shifting and broadeningcompensations are done sequentially. The spectra can becompensated for the shift first and then broadened to matchthe broadening at the highest T (S ⇒ B), or the procedure can

Figure 2. (a) Assumed pure component spectra at 282.75 K used in the simulation. (b) Simulated spectral matrix based on the spectra in (a).



be reversed by applying broadening compensation first (B ⇒S). The two approaches are evaluated below.Thermal Broadening Compensation Followed by Shifting

Compensation (B ⇒ S). We previously described a broadeningcompensation procedure that converts experimental spectra tospectra that are uniformly broadened to the highestexperimental T.16,25 The steps in that procedure arecomplementary to those used above to apply differentialbroadening to the simulated spectra. Taking the spectrum atthe highest T as a reference, the parameter k in eq 2 must beidentified that yields the set of T-specific spread functionsrequired to achieve in each spectrum the broadening present atthe highest temperature. In spectral matrices for whichnonlinear thermochromic effects are confined to broadening,the choice of the optimum value of k was based on minimizingthe relative magnitude of the eigenvalue associated with themain broadening eigenvector (easily recognized from itsresemblance to the second derivative of the first eigenvec-tor).16,25 Following convolution with the derived optimum setof cumulative thermal spread functions, the spectra are shiftedto the common spectral range determined by the highest Treference spectrum (see below).Shifting Compensation Followed by Compensation for

Broadening (S ⇒ B). The thermochromic shift in the spectrareflects the polarizability effects on the pure conformer spectraand the change in spectral shape due to the change in theirrelative contribution to each equilibrium mixture. The spectraof mixtures of molecules having no or negligibly small dipolemoments are expected to undergo synchronous thermal shifts.Thermally induced shifts (assumed uniform in the simulation)must be removed before proceeding to the resolution of suchspectral systems. This requires an unsupervised (unbiased)approach that efficiently shifts the multicomponent spectra tothe desired common spectral range. We know of no algorithmthat provides for shifting of all of the spectra simultaneously.However, spectral alignments can be performed sequentially forpairs of spectra. For instance, Cattell’s approach starts with atwo-column matrix consisting of a pair of spectra, one of whichis kept stationary, and traces the evolution of the ratio of the

first to the second eigenvalue as a function of the number ofshift points applied to the second, the moving spectral profile.27

The number of shift points that correspond to the maximumev1/ev2 ratio define the best alignment of the two spectra, thusidentifying the optimally shifted target spectrum. The sameresult can be achieved by adapting the opposite concept to thatintroduced by Massart et al. in their Orthogonal ProjectionApproach (OPA)28 or by using correlation optimized warpingas proposed by Vest Nielsen et al.29

Before proceeding to the spectral resolution, we drawattention to intrinsic minor drawbacks in the broadening andshifting procedures. With respect to broadening, it is easy todemonstrate that, even in the case of convolution of a set ofone-component spectra (with different amplitudes), with a setof thermal spread functions, instead of creating a two-component matrix, the first eigenvector of which correspondsto the average one-component spectrum and the second hasthe form of the second derivative of the first,25 a three-component data matrix is obtained. Although the contributionof the third eigenvector to the matrix is negligible, it possesses awell-defined structure that resembles the fourth derivative ofthe first eigenvector. Regarding the shifting algorithms,improper, identical behavior of the three referenced approachescan be illustrated for a two-component mixture with variableconcentration of the two species. Even for an ideal two-component system of unbroadened and unshifted spectra, theshifting procedures attempt to shift the spectra toward thereference spectrum corresponding to the mixture containingthe highest concentration of the major component. Thisoutcome stems from the fact that all of these shiftingtechniques strive to maximize the covariance between the twospectral vectors; the higher the covariance, the greater thesimilarity between the spectra. They are ideally suited for liningup differentially shifted spectra of one-component systems.When two or more spectrally distinct components are involved,the change in the relative concentration of the components isreflected in a change in the shape of the mixture spectrum. In amulticomponent spectrothermal matrix, the most dissimilarspectra are those measured at the two extreme temperatures.

Figure 3. Euclidean normalized first (black) and second (red) derivatives of the original (a) and shifted (b) matrix and the second (blue) and third(green) eigenvectors of the original (c) and shifted (d) matrix.



The cited shifting routines line up such spectra by applyinginappropriate additional shifts to account for the changes inspectral shape that are associated with the change incomponent composition. In the case of our simulated two-component spectral system in Figure 2a, these additional smallshifts with respect to the reference spectrum are equal to 16, 15,13, 11, 9, 7, 6, 4, and 2 cm−1 starting from the lowest andmoving sequentially to the next to the highest T. Those shifterrors are small (83 cm−1 total) relative to the applied shiftsthat correspond to ∼390 cm−1 for the total T range, Figure 1c.However, in Figure 2a, the assumed s-c-DPH spectrum wasarbitrarily chosen with its first band maximum 123 cm−1 red-shifted relative to the corresponding band maximum in theassumed s-t-DPH spectrum. Larger thermochromic shifts arepredicted by changing the relative position of the band maximaof the spectra used in the simulation from s-c-DPH 123 cm−1

red-shifted to 123, 246, and 369 cm−1 blue-shifted relative to s-t-DPH (see the Supporting Information, SI). Application of theknown solvatochromic shift dependence on solvent polar-izability α (Δν = 104α cm−1)9,19 to both model conformerspectra with the 369 cm−1 shift and assuming ΔH = 4.5 kcal/mol in favor of the s-t-DPH conformer gives a simulatedspectral set that closely mimics the observed thermochromicshift in the first band in the experimental spectra in Figure 1a.We will return to this issue below.The spectral changes in the simulated matrix involve changes

in the contribution of two components whose spectra aredifferentially shifted and broadened. It is not surprisingtherefore that SVD or PCA treatment of the spectra in Figure2a shows that they are well-represented as a four-component

system. Two of the eigenvectors reflect the presence of the twospectrally distinct components, and the other two reflect thenonlinear changes, shifting and broadening, that convert thepure component spectra into moving targets. The shapes of theeigenvectors associated with shifting and broadening closelyresemble the shapes of the first30 and second25 derivatives ofthe first eigenvector, respectively. Relevant eigenvectors fromthe PCA treatment of the simulated spectral matrix in Figure 2abefore and after shifting compensation are compared with thefirst and second derivatives of the first eigenvector (i.e., theaverage spectrum) in Figure 3. The derivatives were obtainedusing the Savitzky−Golay approach31 and, in the case of thesecond derivative, smoothed using the Whittaker smoother.32

Those derivative vectors have unit length, as do theeigenvectors. The near identity of panels (a) and (b) showsthat shifting compensation does not significantly alter thederivatives nor, by inference, the major eigenvector of thespectral matrix. Comparison of panels (a) and (c) in Figure 3reveals the strong resemblance between the first derivative andthe second eigenvector and between the second derivative andthe third eigenvector. We therefore conclude that, for theoriginal matrix, shifting and broadening are reflected in thesecond and third eigenvectors, respectively. Panel (d) showsthat after shifting compensation, the first derivative is no longerevident, and the significance of the broadening vector thatresembles the second derivative is elevated from third tosecond. It should be noted that the shifted spectral matrixbehaves as a three-component system with a very weakcontribution from the third component. The features of the

Figure 4. Evolution of eigenvalue ratios as a function of the broadening parameter k for B ⇒ S (a,b) and for S ⇒ B (c,d); the vertical green linecorresponds to k = 150 cm−1, the value used in the simulation.



noisy third eigenvector of this matrix were revealed only uponsevere smoothing using the Whittaker smoother.32

The evolution of eigenvalue ratios obtained in the process ofthermal broadening compensation before and after shifting thesimulated spectra was examined to determine whether itprovides a basis for selecting the preferred compensationsequence B⇒ S or S⇒ B. Various combinations of these ratiosas a function of k, the broadening parameter in eq 2, for the twosequences are compared in Figure 4a and b for B ⇒ S andFigure 4c and d for S⇒ B. The vertical line at 150 cm−1 in eachpanel marks the value k used to generate the set of thermalspread functions for the convolutions that produced thedifferentially broadened simulated spectra in Figure 2a.We expected that compensation for thermal broadening

would be reflected in at least some of the eigenvalue ratiosachieving their minima at k = 150 cm−1 because use of that kvalue should lead uniquely to uniformly broadened spectra. Forthe B ⇒ S route, however, the only eigenvalue ratios in Figure4a,b that show well-defined minima at that value involve ev6, aneigenvalue that corresponds to an eigenvector with negligiblecontribution. More encouraging results are obtained for the S⇒ B route, for which the more significant eigenvalue, ev4,shows ratio minima close to k = 150 cm−1, Figure 4c,d. Thepronounced difference in the compensation sequence isobvious in the evolution of the ev3/ev1 and ev3/ev2 ratios.Those ratios achieve minima earlier in the S ⇒ B than in the B⇒ S case.The differences in eigenvalue ratio evolutions for the original

and shift-compensated spectral matrices can be understood byconsidering that, for the original spectral matrix, broadening isassociated with the third eigenvector, whereas for the shift-compensated spectral matrix, broadening is associated with thesecond eigenvector. It seems reasonable, therefore, that upon

stepwise application of broadening compensation, we shouldfocus on minimizing ev3 in the upper panels and on minimizingev2 in the lower panels of Figure 4. The problem is that onecannot apply the eigenvalue ratio criterion without consideringthe shapes of the evolving eigenvectors. To illustrate the point,we consider panels (c) and (d) in Figure 3. In the originalsimulated spectra, the magnitude of ev2 reflects the magnitudeof the applied differential shifts, but as one incrementallycorrects the spectra for those shifts, one approaches thesituation in panel (d) where ev2 represents the broadening. Atsome intermediate point during the shift correction process, themagnitude of ev2 ceases to be a measure of the shift.It is comforting that almost identical final matrices are

obtained, independent of the compensation sequence, S ⇒ Bor B ⇒ S, provided that the correct k = 150 cm−1 value isapplied in the broadening compensation step. However, thecorrect k value is more readily identified from the evolution ofeigenvalue ratios when using the S ⇒ B sequence. As describedabove, the pairwise shift routine that we applied leads to smallsystematic shift overcompensation errors. Correction for thoseerrors leads to minor improvement. The fully shift correctedspectra are shown in Figure 5, along with evolutions ofeigenvalue ratios as those shifted spectra are corrected forbroadening, panels (b) and (c). Application of the minorcorrections to the pairwise generated shifts does not change theoverall trends in Figure 4c and d. However, the minima for theev4/ev1 and ev4/ev2 ratios are deeper and coincide moreclosely with the k = 150 cm−1 value (compare panels (c) and(d) in Figure 4 with panels (b) and (c) in Figure 5).Accordingly, the k = 150 cm−1 parameter was applied to theshift-corrected spectral matrix in the broadening compensationprocedure.

Figure 5. (a) The spectra in Figure 2a after shift correction; evolution of eigenvalue ratios as a function of the broadening parameter k for S ⇒ B(b,c); the vertical green line corresponds to k = 150 cm−1, the value used in the simulation.

Figure 6. (a) Stoichiometric combination coefficient line defined by the eigenvectors in the inset; the red parabola on the bottom right is thestandard deviation from the van’t Hoff plot. (b) The optimum van’t Hoff plot. (c) The recovered pure component spectra at the highest and lowestT's; the vertical line designates the extent of the spectral region to which the LS non-negativity constraint was applied.



SVD treatment of the broadening- and shifting-compensatedspectral matrix reveals a two-component system. The s-t-DPHspectrum was determined by applying the Lawton and Sylvestre(LS) non-negativity criterion33 while moving along thestoichiometric line of the combination coefficients in thedirection that diminishes the contribution of the s-cisconformer. Because the s-c-DPH absorption spectrum extendsto the red of the s-t-DPH spectrum, establishing a baseline in adesignated region of the spectral onset eliminates s-c-DPHabsorption and yields the pure s-t-DPH spectrum. In practice,the presence of random noise in the spectra leads to someuncertainty in the choice of the wavenumber value confiningthe spectral range on which the baseline is imposed by applyingthe LS non-negativity criterion. The choice was optimized bythe use of the determination coefficient that is close to zero ifthere was little linear relationship between the variables (thebaseline absorbance and wavelength).34 The s-t-DPH spectrumshown in Figure 6c was obtained by imposing a horizontalbaseline to frequencies ≥ 25 090 cm−1. The combinationcoefficients of the s-c-DPH absorption spectrum were obtainedby optimizing the adherence of the ratio of conformercontributions to the van’t Hoff equation, eq 4, as previouslydescribed

−= Δ − Δf

fS

RH

RTln

(1 )c

c (4)

where the f i are molar fractions.16,25,35 The principaleigenvectors and the α,β-stoichiometric combination coefficientline are shown in Figure 6a, and the optimum van’t Hoff plot isshown in Figure 6b. The values of ΔH° and ΔS° obtained fromthat plot, 3.9 kcal/mol and 11.08 eu, respectively, are slightly

smaller than the original model values (reduced by 2.15 and1.34%, respectively). Thermodynamic parameters obtainedwithout correction for the small shifts due to the change inthe concentration of the components equal 3.86 kcal/mol and10.82 eu, respectively. The retrieved absorption spectra of the s-trans and s-cis conformers are shown in Figure 6c.The resolved spectra in Figure 6c correspond to the highest

T used in the simulation. For exact comparison with the spectrain Figure 2, extrapolations to lower T's are required, aspreviously described.25 In applying this approach, a new set ofhighly elevated T's was created by adding to each T in thesimulation the difference between the lowest and the highest T.The resolved spectra in Figure 6c were each broadened to eachof the new T's, and the two sets of spectra were subjectedseparately to PCA treatment. Each set of differentiallybroadened pure component spectra could be reproduced as alinear combination of three eigenvectors. The dependence ofthe first two coefficients, α and β, on T was fitted well by asecond-order polynomial, whereas the third, γ, required use of apolynomial of the third order. Extrapolation of these T-dependent coefficients to the T's of the original matrix affordedpure component s-t- and s-c-DPH spectra for each T. With theuse of the derived thermodynamic parameters and the van’tHoff equation, the contributions of the pure component spectrawere determined at each T and were used to create thepredicted two-component mixture spectra, Figure 7a. Becausethe number of shift points for each reproduced two-componentspectrum was known, each spectrum was shifted to predict theoriginal spectral matrix in Figure 2b. Essentially exact recoveryof the original spectral matrix was achieved, Figure 7b. Theoriginal spectra in Figure 2b, reproduced in black in Figure 7b,

Figure 7. (a) Unshifted predicted spectra: s-t-DPH (blue), s-c-DPH (green), and mixtures (red); (b) shifted predicted spectra: s-t-DPH (blue), s-c-DPH (green), and mixtures (red) superposed over the Figure 2a spectra (black).

Figure 8. (a) Shift-compensated experimental spectra from Figure 1a. (b) Broadening-compensated spectra of panel (a) with k = 160 cm−1, and (c)the spectra displayed in (b) normalized to unit area.



are invisible underneath the red reconstructed spectra that arebased on the resolved pure component spectra.Resolution of Experimental Spectra of ttt-DPH in n-

C12. The procedure used to obtain the pure component spectrafrom the simulated spectral matrix, Figure 2b, was applied inthe resolution of the spectra in Figure 1a. Figure 8 shows thosespectra shifted to the range occupied by the spectrum measuredat the highest T. Because in the above simulation the pure s-t-DPH and s-c-DPH spectra were modeled using spectraobtained from a preliminary resolution of the experimentalttt-DPH spectral set, Figure 8 includes the same small shifts thatin the simulation corrected the shift overcompensation due toshape changes caused by variable conformer composition. PCAtreatment of the shift-compensated spectra in Figure 8 revealsthat, as in the treatment of the shift-compensated simulatedspectra, the second eigenvector bears a strong resemblance to

the second derivative of the first eigenvector, Figure 9, thecurve associated with thermally induced spectral broadening.We sought next to compensate the shifted DPH spectra for

thermal broadening. Evolutions of the ratios of the mostsignificant eigenvalues ev(i)/ev(1) and ev(i)/ev(2) as afunction of the compensation parameter k are shown in Figure10a and b, respectively. Examination of the changes in Figure10 reveals no clear choice for the broadening compensationparameter, in contrast to the simulation, where severaleigenvalue minima pointed to the k = 150 cm−1 value, Figure5a and b. More encouraging is the striking similarity in thedependencies of ev2, the eigenvalue associated with thebroadening eigenvectors, in the simulation and in theexperimental spectra, Figure 11a and b, respectively. It can beseen that ev2 attains its minimum values at 210 and 220 cm−1

for the simulated and the experimental spectral matrix,respectively. Because 150 cm−1, the known correct value for

Figure 9. (a) Euclidean normalized first (black) and second (red) derivatives of the original and (b) the shifted DPH matrix. (c) The second (blue)and third (green) eigenvectors of the original and (d) the shifted DPH matrix.

Figure 10. Evolution of eigenvalue ratios for the shift-corrected experimental spectra as a function of the broadening parameter k.



the simulation, is 60 cm−1 smaller than the value at the ev2minimum, it seemed reasonable to select k = 160 cm−1 in eq 2for the experimental case. SVD treatment of the resulting shift-and broadening-compensated spectral matrix, Figure 8b,revealed a two-component system. Proceeding as in thesimulation, the s-t-DPH spectrum was located on the α,β-stoichiometric line at β = 6.325 by applying the LS non-negativity criterion to the onset spectral region bounded by 25

300 cm−1. It should be noted, however, that due to the lowabsorbance of the s-c-DPH spectrum at the onset spectralregion, the frequency interval in the s-t-DPH spectrum wherethe baseline is imposed is not uniquely defined. This lendssome uncertainty to the location of the s-t-DPH spectrum onthe stoichiometric line and to its shape. The location of thecombination coefficients of the s-c-DPH spectrum on thestoichiometric line was based on optimizing the linearity of the

Figure 11. Evolution of ev2 for the shift-corrected simulated spectral matrix (a) and for the shift-corrected experimental spectral matrix (b) as afunction of the broadening parameter k.

Figure 12. (a) Stoichiometric combination coefficient line defined by the eigenvectors in the inset; the red parabola on the bottom right is thestandard deviation from the van’t Hoff plot. (b) The optimum van’t Hoff plot (the inset gives fractional conformer composition) and (c) therecovered pure component spectra; the vertical line designates the extent of the spectral region on which the LS non-negativity constraint wasapplied.

Figure 13. (a) Unshifted predicted experimental spectra: s-t-DPH (blue), s-c-DPH (green), and mixtures (red) superposed over unshiftedexperimental spectra (black). (b) Shifted predicted experimental spectra: s-t-DPH (blue), s-c-DPB (green), and mixtures (red) superposed over theFigure 1a experimental spectra (black).



van’t Hoff plot as in the simulation. The principal eigenvectorsand the α,β-stoichiometric combination coefficient line areshown in Figure 12a, the optimum van’f Hoff plot is shown inFigure 12b, and the resolved s-t- and s-c-DPH absorptionspectra are shown in Figure 12c. We draw attention to the nearidentity of Figures 6 and 12 as it is not coincidental. Itillustrates our ability to model the experimental system almostexactly and lends support to the validity of the resolved spectrain Figure 12c. The van’t Hoff plot gives ΔH° = 3.80 kcal/moland ΔS° = 11.00 eu. The large entropy difference accounts forthe unexpected result that the s-c-DPH conformer becomesdominant at the high end of our T range, inset of Figure 12b.As in the simulation, the resolved spectra in Figure 12c are forthe highest experimental T. The procedure used above in thesimulation was used to create pure conformer spectra withbroadening appropriate for each experimental T. Thecontributions of the two conformer spectra at eachexperimental spectrum were calculated using the derived van’tHoff parameters and combined to yield the unshifted two-component spectra, Figure 13a. Back shifting was achieved byfitting each set of resolved conformer spectra to thecorresponding experimental spectrum, Figure 13b. That the

resolved pure component spectra reproduce the experimentalspectra exactly is demonstrated by the inability to discern theblack experimental spectra beneath the red reconstructedspectra in Figure 13b. The derived shift dependencies of thepure conformer spectra and of the mixture spectra on T arecompared with the shifts in the experimental spectra in Figure14.The polarizability plots in Figure 14 show that the derived

pure component spectra allow excellent reproduction of thethermochromism in the experimental spectra. Furthermore, thespectrum of s-c-DPH appears to be more sensitive to T-inducedchanges than the spectrum of s-t-DPH. It is tempting toconclude with Catalan17 that spectral shifts due to T-inducedpolarizability changes are significantly larger than shifts due tosolvent-induced polarizability changes. However, part, andperhaps all, of the solvatochromism/thermochromism discrep-ancy in the observed spectral shifts can be traced to T effectsthat are independent of polarizability. First, just the applicationof differential broadening, as in Figure 13a, to the pureconformer spectra leads to the illusion of shifts (see thezoomed lowest-energy band region of Figure 13a in the SI),and second, the very mixing of different compositions of the

Figure 14. (a) Dependence of the first band position of the absorption spectra of ttt-DPH in n-C12 on polarizability: experimental (black),reproduced (red), s-t-DPH (blue), and s-c-DPH (green). (b) As in (a) except that the lowest T point in the case of s-t-DPH was rejected as anoutlier.

Figure 15. (a) ttt-DPH absorption spectra in n-C8 at 284.25 K, n-C10 at 315.85 K, n-C12 at 340.65 K, n-C14 at 359.85 K, and n-C16 at 371.95 K inorder of diminishing absorbance at the first vibronic bands. (b) Reconstructed experimental spectra based on the resolved conformer spectra inFigure 18a in red superposed on the experimental spectra in panel (a) in blue (see text).



pure component spectra according to the van’t Hoff parametersgives the appearance of a shift in the first band of the mixturespectra (see below and the SI).Resolution of Experimental Spectra of ttt-DPH in n-

Alkanes: Isopolarizability Conditions. The isopolarizabilityT's used in this study were those used in the resolution of ttt-DPH fluorescence spectra,16 spanning the T range used aboveto record the ttt-DPH spectra in n-C12. At the selected T's, eachof the five n-alkanes has the same index of refraction of 1.4020,corresponding to a common polarizability α = (n2 − 1)/(n2 +2) = 0.242. Surprisingly, PCA treatment of the isopolarizabilityspectral matrix, Figure 15a, reveals a robust two-componentsystem, instead of the expected three-component system.Although the use of isopolarizability T's should eliminate shiftsin the pure conformer spectra, they should continue to besubject to T-induced differential broadening. As explainedabove, one consequence of the variable contribution of the s-c-DPH spectrum in the spectra in Figure 15a is an apparent blueshift with increasing T. Indeed, subjecting the spectra to theshift procedure described above for the n-C12 spectral matrixpredicts that maximum similarity with respect to the spectrumrecorded at the highest T (n-C16) and a possibly better two-component system can be achieved with shifts of 109, 68, 50,and 37 cm−1 for the spectrum in n-C8, n-C10, n-C12, and n-C14,respectively. Those shifts are not real and were not applied.They illustrate an important limitation of the use of themaximum similarity criterion that shifts spectra to a commonrange.To compensate for differential broadening, we initially set k

= 160 cm−1, the value used in the resolution of the n-C12

spectrothermal matrix. The purpose was to achieve uniformbroadening in all of the alkane spectra consistent with that ofthe 372 K ttt-DPH spectrum in n-C16. Use of 25 300 cm−1, thevalue that delineated the baseline region for which applicationof the LS non-negativity criterion defined the combinationcoefficients of the s-t-DPH spectrum in the resolution of the n-C12 spectrothermal matrix, was deemed inappropriate for theisopolarizability matrix. A red shift in the resolved spectra wasexpected because of the higher polarizability of n-C16 relative tothat of n-C12 at any given T. To account for this shift, weinitially selected 24 850 cm−1 to delineate the baseline regionand locate the s-t-DPH spectrum on the normalization line. Thecombination coefficients of the s-c-DPH spectrum were thendetermined with the use of the van’t Hoff optimum linearityconstraint. The optimum van’f Hoff plot is shown in Figure16a, and the resolved s-t- and s-c-DPH absorption spectra areshown in Figure 16b. Figure 16c compares the spectra of theexperimental broadening-compensated matrix with spectraconstructed with the use of the resolved pure componentspectra, as described above. The van’t Hoff plot gives ΔH° =4.10 ± 0.57 kcal/mol and ΔS° = 11.13 ± 2.00 eu, consistentwith the values derived above from the resolution of the n-C12spectral matrix.The choice of k = 160 cm−1 as the broadening compensation

parameter was evaluated by examining the evolution ofeigenvalue ratios as a function of k, Figure 17. Both ev3 andev4 attain minimum values at k close to 310 cm−1, panel (a),whereas ev4/ev2 has its minimum value at k = 260 cm−1. Anargument in favor of the larger value can be made because thethird eigenvector of the initial matrix resembles the second

Figure 16. (a) The optimum van’t Hoff plot (the inset gives the fractional conformer composition). (b) The normalized pure component spectra;the vertical line designates the extent of the spectral region on which the LS non-negativity constraint was applied. (c) The experimental spectra(black) and the recovered spectra (red).

Figure 17. Evolution of eigenvalue ratios relative to ev1 (a) and ev2 (b) for the spectra in Figure 15 as a function of the broadening parameter k.



derivative of the first eigenvector and is associated withbroadening. Nonetheless, we used the 260 cm−1 value becauseit is intermediate between 160 and 310 cm−1 and it seemedlikely that the change in spectral shape upon simply combiningthe broad s-c-DPH spectrum with the better resolved s-t-DPHspectrum would appear as broadening in the PCA treatmentand result in overestimation of the predicted k value.Comparison of the resolved conformer spectra in Figures 12

and 16 reveals that, aside from the difference in relative shifts ofthe two spectra, the vibronic structure of the s-t-DPH spectrumis better resolved in n-C16 than in n-C12 at about the same T(∼100 °C). The difference in the appearance of the s-t-DPHspectrum was traced to the choice of the spectral region onwhich the LS non-negativity criterion is applied. Changing thatregion changes selection of the βs‑trans value on the combinationcoefficient normalization line and, in turn, influences the βs‑cisvalue obtained upon van’t Hoff plot optimization. For instance,setting the baseline delineation limit at 24 600, 24 625, 24 650,and 24 680 cm−1 brings the resolution of the s-trans conformerspectrum into better agreement with the spectrum obtainedfrom the n-C12 spectral matrix but gives van’t Hoff plotoptimum slopes that correspond to ΔH° values of 4603 ± 754,4429 ± 719, 4087 ± 658, and 3844 ± 617 cal/mol, respectively.The resolved spectra associated with the second and fourthcases are shown in Figure 18. Also shown in panel (b) of Figure18 are the predicted experimental spectra based on the pure

component spectra in that panel. The procedure used inconstructing the mixture spectra was the same as that usedabove for the simulated and subsequent spectral matrices. Inthe van’t Hoff plot optimization process, the 24 680 cm−1

variant for the s-t-DPH LS limit gives ΔH° = 3.8 ± 0.6 kcal/mol, very close to the value obtained from processing the DPHspectra in n-C12, but as can be seen in the right panel of theabove figure, the resulting s-c-DPH spectrum is more resolvedat the onset. Preference for the 24 625 cm−1 LS limit was basedon shape similarity of the pure component spectra in Figure18a with those derived from the n-C12 spectral matrix, Figure12c. The ΔS° value associated with the resulting higher ΔH° =4.4 ± 0.7 kcal/mol value is 12.23 ± 2.18 eu. The eigenvectors,normalization line, van’t Hoff plot, and T dependence of theconformer contributions are shown in Figure 19. The very goodagreement between the experimental spectra and thosepredicted upon projection of the pure conformer spectra inFigure 18a to the isopolarizability T's is shown in Figure 15b.Comparison of the fits obtained in Figures 15b and 16c showsvery good reproduction of the experimental spectra, but thatuse of k = 160 cm−1 in the broadening compensation proceduregives the best fits for spectra measured at the lower T's, whereasuse of k = 260 cm−1 gives the best fits for spectra at higher T's.The resolved spectra in Figures 16b and 18a are very similar.We consider the differences between them to be well within theuncertainty limits of our resolution.

Figure 18. (a) Normalized spectra for s-t-DPH (blue) and s-c-DPH (green) using 24 625 cm−1 for the LS criterion. (b) Pure spectra for s-t-DPH(blue) and s-c-DPH (green) using 24 680 cm−1 for the LS criterion; also shown are the predicted reconstructed experimental spectra.

Figure 19. (a) Normalization combination coefficient line defined by the eigenvectors in the inset; the red parabola on the bottom left is thestandard deviation from the van’t Hoff plot and (b) the optimum van’t Hoff plot (inset as in Figure 16a).



■ DISCUSSION

Comparison of the Two Sets of Resolved ttt-DPHConformer Absorption Spectra. The s-t-DPH and s-c-DPHUV absorption spectra obtained independently from the n-C12and the isopolarizability spectral matrices in Figures 1a and 15a,respectively, are compared in Figure 20a. The shift in the s-t-DPH spectra is consistent with the difference in polarizabilitybetween n-C12 and n-C16 at 372 K. The small difference inshape is probably associated with the choice of spectral regionsused in the application of the LS non-negativity criterion.However, in view of the somewhat greater viscosity of n-C16relative to n-C12 at the same T, the slightly better resolution ofthe s-t-DPH spectrum in n-C16 could be real. The shapes of thes-c-DPH spectra are also very similar, but, in this case, they areshifted in the opposite direction with respect to each other.This anomalous behavior may be caused by the shiftingprocedure used in lining up the spectra of the n-C12 matrix,which, as pointed out above, leads to shift overcompensation.The resolved conformer spectra from the isopolarizabilitymatrix are more reliable because, under those conditions, no T-induced shifts are expected and shift compensation was notrequired for the resolution.The search for the pure conformer spectra was performed on

the α,β-stoichiometric combination coefficient line (SVD

treatment) for the n-C12 matrix and on the α,β-normalizationcombination coefficient line (PCA treatment) for theisopolarizability matrix. Fractional contributions based on thenormalized spectra were converted to stoichiometric molarcontributions by projecting the resolved spectra from theisopolarizability matrix, appropriately shifted in oppositedirections, onto the stoichiometric line from the n-C12 matrix,Figure 20b. This was achieved with scaling factors of 9.72 × 103

and 7.57 × 103 for the s-t-DPH and s-c-DPH spectra,respectively, corresponding to an effective ttt-DPH concen-tration of 4.14 × 10−5 M and allowing projection of eachbroadening-compensated spectrum from Figure 15a onto theα,β-stoichiometric line. The 1.28 ratio of the scaling factors is ameasure of the difference in oscillator strengths for the lowestone-photon allowed transitions in the s-t-DPH and s-c-DPHconformers. Identification of the α,β-coefficients of theexperimental spectra provides stoichiometric fractional con-tributions of the two conformers, leading to an almost identicalvan’t Hoff plot as that shown in Figure 19b and ΔH° = 4.43 ±0.72 kcal/mol and ΔS° = 12.33 ± 2.18 eu.Reconstruction of the pure conformer spectra from the n-C12

spectral matrix using the eigenvectors from the isopolarizabilitymatrix leads to minor reshaping of those spectra, so that theyvery closely resemble the resolved spectra from the

Figure 20. (a) Normalized s-t-DPH (blue) and s-c-DPH (green) UV absorption spectra from the resolution of the n-C12 (dashed curves) and theisopolarizability (solid curves) spectral matrices. (b) The combination coefficients of the shifted resolved spectra in n-C12 located on theisopolarizability α,β-stoichiometric line: s-t-DPH (black point), s-c-DPH (pink point).

Figure 21. (a) Normalized to unit area s-t-DPH absorption spectra: from the isopolarizability spectral set (black), from the n-C12 spectral set (blue),the latter spectrum shifted (green), and after reconstruction using the isopolarizability eigenvectors (red). (b) As in (a) for the s-c-DPH spectrum.



isopolarizability matrix, Figure 21. Thus, in Figure 21, thereconstructed red spectra are so exactly superposed over theblack experimental spectra from the isopolarizability spectral setthat the latter are not visible.Energetics of s-t- and s-c-DPH Conformer Equilibra-

tion. The presence of the s-c-DPH conformer in thermalequilibrium with the s-t-DPH conformer, Chart 1, was firstinferred from the λexc dependence of ttt-DPH fluorescence inmethylcyclohexane, MCH.14 In that study, the fluorescencespectra of the two conformers were resolved at 14 T's spanningthe −3.2−91.0 °C range. At each T, the fluorescence spectrumof the s-c-DPH conformer was assigned to the differencebetween ttt-DPH spectra obtained for λexc 355 and 385 nm byassuming that only the 11Bu state of the s-t-DPH conformercontributed to the long wavelength onset of the pairs offluorescence spectra. The enthalpy difference between the twoconformers, ΔH = 3.2 ± 0.1 and 3.5 ± 0.2 kcal/mol, wasobtained from the slopes of van’t Hoff plots of fractionalfluorescence contribution ratios at 355 and 385 nm,respectively. Entropy differences, ΔS, were estimated fromthe intercepts of the van’t Hoff plots, i, using

ε ϕε ϕ−

= + Δ − Δxx

SR

HRT

ln(1 )

lnc

c

c c

t t (5)

where subscripts c and t designate s-c- and s-t-DPH, respectivelyand the other symbols have their usual meanings (eq 5 isanalogous to eq 4). Estimated ranges of molar absorptivitycoefficient and fluorescence quantum yield ratios gave 5 ≤ ΔS≤ 10 eu. Use of the derived conformer molar absorptivitycoefficients from this work and the fact that the ttt-DPHfluorescence quantum yield and lifetime are insensitive to T andλexc changes in hydrocarbon solvents16,36 gives roughly ΔS = 9eu, closer to the previous upper limit. A complete resolution ofttt-DPH fluorescence spectra into the s-c-DPH conformerfluorescence spectrum and pure 21Ag and 11Bu fluorescencespectra from the s-t-DPH conformer was subsequently based onPCA treatment with broadening compensation of fluorescencespectra measured in n-alkane solvents under the isopolariz-ability conditions used in this work for the measurement ofabsorption spectra.16 That analysis gave a somewhat lower ΔH= 2.83 kcal/mol, a value that is probably less reliable because itis based on only a five T van’t Hoff plot. The ΔH valuesobtained in this work of 3.8 ± 0.6 and 4.4 ± 0.7 kcal/mol fromthe n-C12 and isopolarizability spectral matrices, respectively,are in better agreement with the values obtained in the earlierstudy and agree reasonably well with 3.4 kcal/mol, the valuepredicted for s-c-DPH relative to the global minimum at s-t-DPH by DFT calculations [B3LYP/6-3111+G(d,p)].16 What isremarkable is that ΔS so favors the s-c-DPH conformer and thatits contribution to the equilibrium mixture exceeds that of the s-t-DPH conformer at the upper limit (∼100 °C) of our modestexperimental T range (see Figures 12b, 16a, and 19b). Thederived values of ΔS in the range of 9−12 eu are coupled to thecorresponding ΔH values, reflecting, as expected,37 theexperimental uncertainty of the measurements. The largerentropy of the s-c-DPH conformer is consistent with theoreticalcalculations that predict that, in contrast to the planar s-t-DPHconformer, it exists as a mixture of nonplanar structures.16 Thenonplanarity of s-c-DPH was found in the s-cis side of the trienesystem with a 14.6° phenyl/vinyl dihedral and a 6.9° vinyl/vinyldihedral angle within the s-cis-butadiene moiety. Thecalculations revealed an energetically very shallow, planar

transition state (TS) connecting two enantiomeric structures,one with +14.6°, +6.9° and the other with −14.6°, −6.9°dihedral angles. The negligibly small imaginary frequency, 14.9icm−1, of the TS suggests that an energy minimum may alsoexist at the planar geometry. It is also reasonable to expect thatenantiomeric structures with dihedral angles with oppositesigns (+14.6°, −6.9° and −14.6°, +6.9°) should also be readilyaccessible.16 Because the s-cis-butadiene moiety forms withequal probability on either side of the triene unit, those fivestructures would contribute R ln 10 to the entropy difference,accounting for 4.6 eu of the observed ΔS values. A plethora ofstructures of s-c-DPH existing in equilibrium is consistent withthe relatively low definition of vibronic structure in itsabsorption spectrum.Several aspects of the puzzling photophysical and photo-

chemical behavior of ttt-DPH were noted previously.16 In viewof the very large s-c-DPH conformer contributions atequilibrium, especially at the higher T's, and the conclusionthat, at least for excitation at longer λ, s-c-DPH and s-t-DPHretain their identity in their lowest excited singlet states,adhering to Havinga’s NEER principle,15 it is instructive torevisit some relevant observations. It is reasonable to expectthat the presence of two nonequilibrating ttt-DPH conformersin the singlet excited state, whose ratio varies with T and whosefluorescence and absorption spectra differ substantially, shouldbe reflected in biexponential fluorescence decay and in T-dependent fluorescence quantum yields and lifetimes. It issurprising, therefore, that fluorescence quantum yields areinsensitive to the change in T under isopolarizabilityconditions16 and that fluorescence decays are monoexponentialand insensitive to changes in T in several saturated hydrocarbonsolvents.36 A careful reexamination of fluorescence decay,especially for excitation at longer λ's that favor s-c-DPHabsorption and fluorescence, seems warranted. Biexponentialλexc and inert gas pressure-dependent fluorescence decay hasbeen reported for ttt-DPH at 75−95 °C in the vapor phase.38

Short and long fluorescence lifetimes were attributed tovibrationally hot and cold 21Ag → 11Ag transitions of the s-t-DPH conformer. The results reported in this paper suggest s-t-and s-c-DPH fluorescence as an alternative interpretation.

Use of Isopolarizability Conditions. Isopolarizabilityconditions were used previously16 and in this study with theintention of eliminating T-induced spectral shifts, thus limitingnonlinear T effects to broadening. This premise was questionedrecently by Catalan, who presented evidence showing that theshift observed in ttt-DPH absorption spectra upon changing theT has a much steeper dependence on the polarizability α thenthe shift obtained upon varying the alkane solvent at constantT.17 He reasoned that this difference between ttt-DPHthermochromism and solvatochromism would invalidate ourisopolarizability approach because it involved changing both thesolvent and T.17 Catalan correctly inferred that changes in theabsorption spectra of polyenes, including ttt-DPH, in responseto changes in T are due to a combination of the effects ofpolarizability and changes in molecular structure. However, thestructural changes were described as “a kind of conformationaltremor”,17,39 and the known variable contribution of distinctmolecular conformers, such as s-c-DPH in the case of ttt-DPH,was ignored. Subsequently, Catalán, without mentioningprevious experimental and theoretical work on the s-cisconformers of trans,trans-1,4-diphenyl-1,3-butadiene40,41 andttt-DPH,14,16 proposed the existence of s-cis diphenylpolyeneconformers in a theoretical paper.42 In this work, we have



established that the increase in the s-cis- to s-trans conformerratio alone with increasing T gives the appearance of a spectralshift (see the SI). Furthermore, Catalan neglected consideringexperimental evidence showing that the thermochromicresponse of the ttt-DPH absorption spectrum is more thantwice as large as the thermochromic response of the 00 band ofthe 11Bu → 11Ag fluorescence spectrum of s-t-DPH.9 In thiswork, the resolution of the ttt-DPH n-C12 spectrothermalmatrix into s-t-DPH and s-c-DPH conformer absorption spectrareveals that (1) the absorption spectrum of s-c-DPH is moresensitive to polarizability changes than the absorption spectrumof s-t-DPH and (2) both conformer absorption spectra aremore sensitive to polarizability changes than the 11Bu → 11Agfluorescence of the s-trans conformer, Figure 14. The fact thatthe 11Bu → 11Ag fluorescence of s-t-DPH exhibits identicalthermochromic and solvatochromic shift dependencies onpolarizability validates our earlier use of isopolarizabilityconditions in facilitating the resolution of conformerfluorescence spectra.16

■ ASSOCIATED CONTENT*S Supporting InformationSimulated ttt-DPH spectral matrices illustrate magnitudes ofapparent shifts due to broadening and changing conformercomposition. This material is available free of charge via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] Address#Department of Chemistry, IIT Guwahati, Guwahati, India781039.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis research was supported by the National ScienceFoundation, most recently by Grant No. CHE-0846636. Wethank Mr. S. Bonnin and Mr. R. Gilbert for the index ofrefraction measurements.

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