Resolution of Conformer-Specific All-trans-1, 6-diphenyl-1, 3, 5

Article pubs.acs.org/JPCA

Resolution of Conformer-Specific All-trans-1,6-diphenyl-1,3,5hexatriene UV Absorption Spectra Andrzej 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 (tttDPH) exists in solution as a mixture of s-trans,s-trans and scis,s-trans conformers. The latter is higher in energy, and its contribution increases with increasing temperature. ttt-DPH UV absorption spectra broaden with increasing temperature and undergo blue shifts with decreasing polarizability. We describe here the resolution of two spectrothermal matrices of ttt-DPH UV absorption spectra into two conformer-specific components. The first matrix consists of DPH spectra measured in n-dodecane in the 283 to 374 K T range and the second of ttt-DPH absorption spectra measured in the even numbered n-alkanes (n-C8−n-C16) at temperatures selected to achieve isopolarizability (284−372 K). Principal component analysis (PCA) treatments showed that reasonable two-component systems 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-DPH experimental spectra in n-C12. Compensation for nonlinear effects yields robust two-component matrices from the experimental spectra. Their resolution into pure component spectra is based on the application of the Lawton and Sylvestre (LS) nonnegativity criterion at the spectral onset to define the spectrum of the low energy s-trans-conformer and the optimum linearity van’t Hoff (vH) plot criterion to find the spectrum of the higher-energy s-cis-conformer. Resolved spectra are somewhat sensitive to the choice of the spectral region in which the LS criterion is applied. The surprising result is that both resolutions lead to the conclusion that the molar fraction of the s-cis-conformer equals, or even exceeds, the molar fraction of the s-trans-conformer as the highest T's employed in our study are approached.

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formation of the 11Bu state. Those two fluorescence spectra originate from the s-trans,s-trans conformer (s-t-DPH), the lowest-energy conformer of ttt-DPH. Also contributing to tttDPH fluorescence is a third fluorescence spectrum that was assigned to the less abundant s-cis,s-trans conformer (s-cDPH).14 The presence of s-c-DPH fluorescence is evident in the λexc dependence of the fluorescence spectra,14 consistent with Havinga’s nonequilibration of excited rotamers (NEER) principle.15 Raising T increases the equilibrium population of sc-DPH, thereby increasing its fluorescence contribution, Chart 1.14,16 Resolution of ttt-DPH fluorescence into s-c-DPH and s-tDPH fluorescence spectra was easily accomplished by relying on the dependence of the spectra on λexc.14 We also achieved the resolution of the s-t-DPH fluorescence spectrum into its 11Bu and 21Ag components,16 which was considerably more challenging because, although their relative contribution varies with T, the pure component spectra broaden and undergo differential blue shifts as the T is increased and the medium polarizability is decreased. The success of the resolution of ttt-

INTRODUCTION Interest in the photochemistry and photophysics of α,ωdiphenylpolyenes, 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 and fluorescence of cis- and trans-stilbene4−6 (1, n = 1), we turned our attention to all-trans-1,6-diphenyl-1,3,5-hexatriene7 (tttDPH, 1, n = 3) because it is the first member of the series whose lowest singlet excited state is not the initially accessed 11Bu state on one photon absorption but the forbidden, doubly excited 21Ag state.1−4 Consequently, the major component in the fluorescence spectrum of ttt-DPH corresponds to the forbidden 21Ag → 11Ag transition, which gains intensity through 21Ag/11Bu vibronic coupling. Both lowest ttt-DPH excited singlet states resulting from this mixing S1, mainly 21Ag and S2 mainly 11 B u contribute fluorescence because they are sufficiently close in energy to exist in thermal equilibrium,8,9 which is established within femtoseconds10−13 of the initial © 2012 American Chemical Society

Received: February 6, 2012 Revised: May 9, 2012 Published: May 14, 2012 5353

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

The Journal of Physical Chemistry A

Article

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 T dependence of the index of refraction, n, of n-C12, and (c) thermochromism of ttt-DPH in n-C12.

DPH fluorescence into three components relied upon (1) neutralizing the shifts by measuring the spectra under isopolarizability 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 UV absorption is known to increase at the long wavelength onset of the spectrum.14 However, the shapes of the pure conformer spectra and the extent to which each conformer contributes to the observed ttt-DPH absorption spectrum over the entire spectral range are unknown. This paper closes that knowledge gap. We measured ttt-DPH UV absorption spectra in ndodecane, 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 resulting two spectrothermal matrices into conformer-specific absorption spectra by applying our previously developed broadening and shifting compensation procedures in conjunction with principal component analysis with self-modeling, PCA-SM, and singularvalue decomposition with self-modeling, SVD-SM. The derived s-c-DPH absorption spectrum exhibits a weak shoulder at long λ but, although broader, is remarkably similar to the s-t-DPH absorption spectrum. A recent criticism of our isopolarizability approach17 is shown to be without merit.

Measurements. UV absorption spectra were measured with a Cary 300B UV−vis spectrophotometer. Fluorescence measurements were made with a Hitachi F-4500 spectrophotometer equipped with a 150 W Xe arc source and a Hamamatsu R3788 photomultiplier tube (the Hitachi F-4500 employs horizontal excitation and emission slits instead of vertical). Index of refraction measurements were carried out with a Valentine refractometer, serial no. 450173 (Vista California). Temperatures were maintained to within ±0.1 °C using a Haake-FS constant-T circulator or a Neslab-RTE 4DD circulation bath. Ethylene glycol was circulated for the higher T's. Solution temperatures were measured with an Omega Engineering Model 199 RTD digital thermometer. Sample preparation and handling were performed under nearly complete darkness (red light). For absorption measurements, the experiment in n-C12 is typical. A 4.15 × 10−5 M ttt-DPH solution was used, and spectra were measured at 10 T's at ∼10 °C intervals in the 282.8−374.0 K range. Spectra were recorded at 0.25 nm increments in the 250−650 nm range. Each ttt-DPH absorption spectrum was corrected for solvent absorption under the same conditions. The spectra were baseline-corrected and represented as a function of wavenumber, interpolated to small equal intervals (1 cm−1). The isopolarizability T's used for absorption measurements in the n-alkane series cover the same range 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, nC16). Data Analysis. Data pretreatment and PCA-SM calculations were performed on a Dell microcomputer working with appropriate routines in the environment of MATLAB version 6.1.

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EXPERIMENTAL SECTION Materials. The sources of the materials and the purification methods used in this work were as previously described.16 tttDPH (Aldrich, 98% purity) was chromatographed on silica gel with ethyl acetate/petroleum ether (1:99 v/v) as the eluent and then twice recrystallized from n-hexane (Aldrich, spectrophotometric grade), except that prior to use in fluorescence measurements in n-hexadecane, the ttt-DPH was recrystallized three time from ethanol. Petroleum ether from Baker, reagent grade, was distilled prior to use. n-Alkanes (n-octane, n-decane, n-dodecane, n-tetradecane, and n-hexadecane) used in absorption measurements were from Aldrich (anhydrous, 99+ %) and purified prior to use by passing them twice through Agactivated alumina, followed by distillation under reduced pressure. For the fluorescence measurements, the n-hexadecane was used as received.

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RESULTS UV Absorption Measurements in n-Dodecane. The T dependence of ttt-DPH absorption spectra in n-C12 is shown in Figure 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 spectra broaden and undergo a pronounced blue shift.9 Also evident is 5354



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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).

an apparent change in relative vibronic band absorbance and a diminution in absorbance that exceeds the change expected because of the decrease in density. In a pioneering study, Hausser et al. associated the blue shift with the change in the solvent’s index of refraction, n, which decreases upon increasing T.18 Subsequently, it was shown that the 11Ag−11Bu energy gap increases linearly as the medium polarizability α = (n2 − 1)/(n2 + 2) is decreased.9,19−23 To calculate α for our n-C12, we measured the T dependence of n. Our values agree well with literature values.24 Plots of n versus T and of the frequency of the first vibronic band of the ttt-DPH absorption spectrum versus 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 the presence of the two conformers of ttt-DPH, namely, the s-c- and s-t-DPH rotamers. The other two factors are due to thermochromism, which causes shifting and broadening of the spectra with increasing temperature. Resolution of the pure conformer spectra must be preceded by neutralizing the thermochromic factors. We developed shifting and broadening compensation methods on a simulated matrix, as described in the next section. Simulated Spectra. A simulated set of ttt-DPH spectra, mimicking those measured in n-C12, was created in order to arrive at the procedure for compensation of thermal broadening and shifts. The assumed pure component spectra of the s-t- and s-c-DPH conformers were scaled by assuming that the ratio of the molar absorptivities at ν̃max is 3/2 in favor of the s-transconformer. Fractional equilibrium contributions of the two conformers at the 10 T's used in the n-C12 experiment were calculated with the use of the van’t Hoff equation, assuming ΔH0 = 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 maximum absorbance was then added to each spectrum in order to simulate noise present in our experimental measurements. The two sets of spectra were interpolated to yield spectra with absorbance at 1 cm−1 increments and differentially broadened, as previously described.25 Briefly, each mixture spectrum, except the one at the lowest T, is convolved with a corresponding cumulative thermal spread function. Cumulative thermal spread functions are generated as convolution products of partial thermal spread functions describing the amount of thermal broadening between successive T's. The partial thermal

spread functions have the form of the normalized Gaussian distribution ⎡ ⎞2 ⎤ 1 1 ⎛⎜ ν ̅ − νmean ̅ ⎢ ⎟⎥ exp − ⎜ gji(ν ̅ ) = ⎢ 2 ⎝ σg(ΔTji) ⎟⎠ ⎥ (2π )1/2 σg(ΔTji) ⎦ ⎣

(1)

where σg(ΔTji) is the standard deviation of the normalized Gaussian distribution, which depends on the difference of the two successive temperatures, Δ(Tji) = Tj − Ti. For two successive temperatures such that Tj > Ti, this dependence assumes the form σji = k Tj − Ti

(2)

where k is a parameter characteristic for the system that must be specified in order to create the broadened spectral matrix. We used k = 150 cm−1 for the simulation. Convolution of two normalized Gaussian profiles gives a normalized Gaussian profile whose variance equals the sum of variances of both convolved profiles.26 It follows that for three successive T's such that Tk > Tj > Ti, one can write σg2(ΔTki) = σg2(ΔTji) + σg2(ΔTkj)

(3)

where each term in eq 3 is defined by eq 2 and σ2g(ΔTki) is the variance of the cumulative thermal Gaussian distribution encompassing the increase of temperature, first between Ti and Tj and then between Tj and Tk. The convolution is distributive with respect to addition.26 Therefore, in modeling the set of broadened absorption spectra of a two-component mixture, one can broaden the combined two-component spectra, or the one-component matrices can be broadened separately and then added, as was done in this work. Each resulting spectrum was then shifted to match the position of the first vibronic band in the corresponding experimental spectrum in Figure 1a. The applied shift is therefore identical to the empirical shift in Figure 1c. As intended, the resulting simulated spectra, 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 converts the differentially shifted and broadened spectra to uniformly shifted and broadened spectra. Shifting and broadening compensations are done sequentially. The spectra can be compensated for the shift first and then broadened to match the broadening at the highest T (S ⇒ B), or the procedure can 5355



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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.

first to the second eigenvalue as a function of the number of shift points applied to the second, the moving spectral profile.27 The number of shift points that correspond to the maximum ev1/ev2 ratio define the best alignment of the two spectra, thus identifying the optimally shifted target spectrum. The same result can be achieved by adapting the opposite concept to that introduced by Massart et al. in their Orthogonal Projection Approach (OPA)28 or by using correlation optimized warping as proposed by Vest Nielsen et al.29 Before proceeding to the spectral resolution, we draw attention to intrinsic minor drawbacks in the broadening and shifting procedures. With respect to broadening, it is easy to demonstrate that, even in the case of convolution of a set of one-component spectra (with different amplitudes), with a set of thermal spread functions, instead of creating a twocomponent matrix, the first eigenvector of which corresponds to the average one-component spectrum and the second has the form of the second derivative of the first,25 a threecomponent data matrix is obtained. Although the contribution of the third eigenvector to the matrix is negligible, it possesses a well-defined structure that resembles the fourth derivative of the first eigenvector. Regarding the shifting algorithms, improper, identical behavior of the three referenced approaches can be illustrated for a two-component mixture with variable concentration of the two species. Even for an ideal twocomponent system of unbroadened and unshifted spectra, the shifting procedures attempt to shift the spectra toward the reference spectrum corresponding to the mixture containing the highest concentration of the major component. This outcome stems from the fact that all of these shifting techniques strive to maximize the covariance between the two spectral vectors; the higher the covariance, the greater the similarity between the spectra. They are ideally suited for lining up 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 is reflected in a change in the shape of the mixture spectrum. In a multicomponent spectrothermal matrix, the most dissimilar spectra are those measured at the two extreme temperatures.

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 broadening compensation procedure that converts experimental spectra to spectra that are uniformly broadened to the highest experimental T.16,25 The steps in that procedure are complementary to those used above to apply differential broadening to the simulated spectra. Taking the spectrum at the highest T as a reference, the parameter k in eq 2 must be identified that yields the set of T-specific spread functions required to achieve in each spectrum the broadening present at the highest temperature. In spectral matrices for which nonlinear thermochromic effects are confined to broadening, the choice of the optimum value of k was based on minimizing the relative magnitude of the eigenvalue associated with the main broadening eigenvector (easily recognized from its resemblance to the second derivative of the first eigenvector).16,25 Following convolution with the derived optimum set of cumulative thermal spread functions, the spectra are shifted to the common spectral range determined by the highest T reference spectrum (see below). Shifting Compensation Followed by Compensation for Broadening (S ⇒ B). The thermochromic shift in the spectra reflects the polarizability effects on the pure conformer spectra and the change in spectral shape due to the change in their relative contribution to each equilibrium mixture. The spectra of mixtures of molecules having no or negligibly small dipole moments are expected to undergo synchronous thermal shifts. Thermally induced shifts (assumed uniform in the simulation) must be removed before proceeding to the resolution of such spectral systems. This requires an unsupervised (unbiased) approach that efficiently shifts the multicomponent spectra to the desired common spectral range. We know of no algorithm that provides for shifting of all of the spectra simultaneously. However, spectral alignments can be performed sequentially for pairs of spectra. For instance, Cattell’s approach starts with a two-column matrix consisting of a pair of spectra, one of which is kept stationary, and traces the evolution of the ratio of the 5356



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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 line corresponds to k = 150 cm−1, the value used in the simulation.

system. Two of the eigenvectors reflect the presence of the two spectrally distinct components, and the other two reflect the nonlinear changes, shifting and broadening, that convert the pure component spectra into moving targets. The shapes of the eigenvectors associated with shifting and broadening closely resemble the shapes of the first30 and second25 derivatives of the first eigenvector, respectively. Relevant eigenvectors from the PCA treatment of the simulated spectral matrix in Figure 2a before and after shifting compensation are compared with the first and second derivatives of the first eigenvector (i.e., the average spectrum) in Figure 3. The derivatives were obtained using the Savitzky−Golay approach31 and, in the case of the second derivative, smoothed using the Whittaker smoother.32 Those derivative vectors have unit length, as do the eigenvectors. The near identity of panels (a) and (b) shows that shifting compensation does not significantly alter the derivatives nor, by inference, the major eigenvector of the spectral matrix. Comparison of panels (a) and (c) in Figure 3 reveals the strong resemblance between the first derivative and the second eigenvector and between the second derivative and the third eigenvector. We therefore conclude that, for the original matrix, shifting and broadening are reflected in the second and third eigenvectors, respectively. Panel (d) shows that after shifting compensation, the first derivative is no longer evident, and the significance of the broadening vector that resembles the second derivative is elevated from third to second. It should be noted that the shifted spectral matrix behaves as a three-component system with a very weak contribution from the third component. The features of the

The cited shifting routines line up such spectra by applying inappropriate additional shifts to account for the changes in spectral shape that are associated with the change in component composition. In the case of our simulated twocomponent spectral system in Figure 2a, these additional small shifts 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 and moving sequentially to the next to the highest T. Those shift errors are small (83 cm−1 total) relative to the applied shifts that correspond to ∼390 cm−1 for the total T range, Figure 1c. However, in Figure 2a, the assumed s-c-DPH spectrum was arbitrarily chosen with its first band maximum 123 cm−1 redshifted relative to the corresponding band maximum in the assumed s-t-DPH spectrum. Larger thermochromic shifts are predicted by changing the relative position of the band maxima of 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 st-DPH (see the Supporting Information, SI). Application of the known solvatochromic shift dependence on solvent polarizability α (Δν = 104α cm−1)9,19 to both model conformer spectra with the 369 cm−1 shift and assuming ΔH = 4.5 kcal/ mol in favor of the s-t-DPH conformer gives a simulated spectral set that closely mimics the observed thermochromic shift 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 are differentially shifted and broadened. It is not surprising therefore that SVD or PCA treatment of the spectra in Figure 2a shows that they are well-represented as a four-component 5357



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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 the standard deviation from the van’t Hoff plot. (b) The optimum van’t Hoff plot. (c) The recovered pure component spectra at the highest and lowest T's; the vertical line designates the extent of the spectral region to which the LS non-negativity constraint was applied.

stepwise application of broadening compensation, we should focus on minimizing ev3 in the upper panels and on minimizing ev2 in the lower panels of Figure 4. The problem is that one cannot apply the eigenvalue ratio criterion without considering the shapes of the evolving eigenvectors. To illustrate the point, we consider panels (c) and (d) in Figure 3. In the original simulated spectra, the magnitude of ev2 reflects the magnitude of the applied differential shifts, but as one incrementally corrects the spectra for those shifts, one approaches the situation in panel (d) where ev2 represents the broadening. At some intermediate point during the shift correction process, the magnitude 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 ⇒ B or B ⇒ S, provided that the correct k = 150 cm−1 value is applied in the broadening compensation step. However, the correct k value is more readily identified from the evolution of eigenvalue ratios when using the S ⇒ B sequence. As described above, the pairwise shift routine that we applied leads to small systematic shift overcompensation errors. Correction for those errors leads to minor improvement. The fully shift corrected spectra are shown in Figure 5, along with evolutions of eigenvalue ratios as those shifted spectra are corrected for broadening, panels (b) and (c). Application of the minor corrections to the pairwise generated shifts does not change the overall trends in Figure 4c and d. However, the minima for the ev4/ev1 and ev4/ev2 ratios are deeper and coincide more closely 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 the shift-corrected spectral matrix in the broadening compensation procedure.

noisy third eigenvector of this matrix were revealed only upon severe smoothing using the Whittaker smoother.32 The evolution of eigenvalue ratios obtained in the process of thermal broadening compensation before and after shifting the simulated spectra was examined to determine whether it provides a basis for selecting the preferred compensation sequence B ⇒ S or S ⇒ B. Various combinations of these ratios as a function of k, the broadening parameter in eq 2, for the two sequences are compared in Figure 4a and b for B ⇒ S and Figure 4c and d for S ⇒ B. The vertical line at 150 cm−1 in each panel marks the value k used to generate the set of thermal spread functions for the convolutions that produced the differentially broadened simulated spectra in Figure 2a. We expected that compensation for thermal broadening would be reflected in at least some of the eigenvalue ratios achieving their minima at k = 150 cm−1 because use of that k value should lead uniquely to uniformly broadened spectra. For the B ⇒ S route, however, the only eigenvalue ratios in Figure 4a,b that show well-defined minima at that value involve ev6, an eigenvalue that corresponds to an eigenvector with negligible contribution. 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. The pronounced difference in the compensation sequence is obvious 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 by considering that, for the original spectral matrix, broadening is associated with the third eigenvector, whereas for the shiftcompensated spectral matrix, broadening is associated with the second eigenvector. It seems reasonable, therefore, that upon 5358



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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-cDPH (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.

smaller than the original model values (reduced by 2.15 and 1.34%, respectively). Thermodynamic parameters obtained without correction for the small shifts due to the change in the concentration of the components equal 3.86 kcal/mol and 10.82 eu, respectively. The retrieved absorption spectra of the strans 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 spectra in Figure 2, extrapolations to lower T's are required, as previously described.25 In applying this approach, a new set of highly elevated T's was created by adding to each T in the simulation the difference between the lowest and the highest T. The resolved spectra in Figure 6c were each broadened to each of the new T's, and the two sets of spectra were subjected separately to PCA treatment. Each set of differentially broadened pure component spectra could be reproduced as a linear combination of three eigenvectors. The dependence of the first two coefficients, α and β, on T was fitted well by a second-order polynomial, whereas the third, γ, required use of a polynomial of the third order. Extrapolation of these Tdependent coefficients to the T's of the original matrix afforded pure component s-t- and s-c-DPH spectra for each T. With the use of the derived thermodynamic parameters and the van’t Hoff equation, the contributions of the pure component spectra were determined at each T and were used to create the predicted two-component mixture spectra, Figure 7a. Because the number of shift points for each reproduced two-component spectrum was known, each spectrum was shifted to predict the original spectral matrix in Figure 2b. Essentially exact recovery of the original spectral matrix was achieved, Figure 7b. The original spectra in Figure 2b, reproduced in black in Figure 7b,

SVD treatment of the broadening- and shifting-compensated spectral matrix reveals a two-component system. The s-t-DPH spectrum was determined by applying the Lawton and Sylvestre (LS) non-negativity criterion33 while moving along the stoichiometric line of the combination coefficients in the direction that diminishes the contribution of the s-cis conformer. Because the s-c-DPH absorption spectrum extends to the red of the s-t-DPH spectrum, establishing a baseline in a designated region of the spectral onset eliminates s-c-DPH absorption and yields the pure s-t-DPH spectrum. In practice, the presence of random noise in the spectra leads to some uncertainty in the choice of the wavenumber value confining the spectral range on which the baseline is imposed by applying the LS non-negativity criterion. The choice was optimized by the use of the determination coefficient that is close to zero if there was little linear relationship between the variables (the baseline absorbance and wavelength).34 The s-t-DPH spectrum shown in Figure 6c was obtained by imposing a horizontal baseline to frequencies ≥ 25 090 cm−1. The combination coefficients of the s-c-DPH absorption spectrum were obtained by optimizing the adherence of the ratio of conformer contributions to the van’t Hoff equation, eq 4, as previously described ln

fc (1 − fc )

=

ΔS ΔH − R RT

(4)

where the f i are molar fractions. 16,25,35 The principal eigenvectors and the α,β-stoichiometric combination coefficient line are shown in Figure 6a, and the optimum van’t Hoff plot is shown in Figure 6b. The values of ΔH° and ΔS° obtained from that plot, 3.9 kcal/mol and 11.08 eu, respectively, are slightly 5359



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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 second derivative of the first eigenvector, Figure 9, the curve associated with thermally induced spectral broadening. We sought next to compensate the shifted DPH spectra for thermal broadening. Evolutions of the ratios of the most significant eigenvalues ev(i)/ev(1) and ev(i)/ev(2) as a function of the compensation parameter k are shown in Figure 10a and b, respectively. Examination of the changes in Figure 10 reveals no clear choice for the broadening compensation parameter, in contrast to the simulation, where several eigenvalue minima pointed to the k = 150 cm−1 value, Figure 5a and b. More encouraging is the striking similarity in the dependencies of ev2, the eigenvalue associated with the broadening eigenvectors, in the simulation and in the experimental spectra, Figure 11a and b, respectively. It can be seen 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

are invisible underneath the red reconstructed spectra that are based on the resolved pure component spectra. Resolution of Experimental Spectra of ttt-DPH in nC12. The procedure used to obtain the pure component spectra from the simulated spectral matrix, Figure 2b, was applied in the resolution of the spectra in Figure 1a. Figure 8 shows those spectra shifted to the range occupied by the spectrum measured at the highest T. Because in the above simulation the pure s-tDPH and s-c-DPH spectra were modeled using spectra obtained from a preliminary resolution of the experimental ttt-DPH spectral set, Figure 8 includes the same small shifts that in the simulation corrected the shift overcompensation due to shape changes caused by variable conformer composition. PCA treatment of the shift-compensated spectra in Figure 8 reveals that, as in the treatment of the shift-compensated simulated spectra, the second eigenvector bears a strong resemblance to 5360



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Figure 11. Evolution of ev2 for the shift-corrected simulated spectral matrix (a) and for the shift-corrected experimental spectral matrix (b) as a function 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 the standard deviation from the van’t Hoff plot. (b) The optimum van’t Hoff plot (the inset gives fractional conformer composition) and (c) the recovered pure component spectra; the vertical line designates the extent of the spectral region on which the LS non-negativity constraint was applied.

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

the simulation, is 60 cm−1 smaller than the value at the ev2 minimum, it seemed reasonable to select k = 160 cm−1 in eq 2 for the experimental case. SVD treatment of the resulting shiftand broadening-compensated spectral matrix, Figure 8b, revealed a two-component system. Proceeding as in the simulation, the s-t-DPH spectrum was located on the α,βstoichiometric line at β = 6.325 by applying the LS nonnegativity criterion to the onset spectral region bounded by 25

300 cm−1. It should be noted, however, that due to the low absorbance of the s-c-DPH spectrum at the onset spectral region, the frequency interval in the s-t-DPH spectrum where the baseline is imposed is not uniquely defined. This lends some uncertainty to the location of the s-t-DPH spectrum on the stoichiometric line and to its shape. The location of the combination coefficients of the s-c-DPH spectrum on the stoichiometric line was based on optimizing the linearity of the 5361



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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 an outlier.

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 in order of diminishing absorbance at the first vibronic bands. (b) Reconstructed experimental spectra based on the resolved conformer spectra in Figure 18a in red superposed on the experimental spectra in panel (a) in blue (see text).

resolved pure component spectra reproduce the experimental spectra exactly is demonstrated by the inability to discern the black experimental spectra beneath the red reconstructed spectra in Figure 13b. The derived shift dependencies of the pure conformer spectra and of the mixture spectra on T are compared with the shifts in the experimental spectra in Figure 14. The polarizability plots in Figure 14 show that the derived pure component spectra allow excellent reproduction of the thermochromism in the experimental spectra. Furthermore, the spectrum of s-c-DPH appears to be more sensitive to T-induced changes than the spectrum of s-t-DPH. It is tempting to conclude with Catalán17 that spectral shifts due to T-induced polarizability changes are significantly larger than shifts due to solvent-induced polarizability changes. However, part, and perhaps all, of the solvatochromism/thermochromism discrepancy in the observed spectral shifts can be traced to T effects that are independent of polarizability. First, just the application of differential broadening, as in Figure 13a, to the pure conformer spectra leads to the illusion of shifts (see the zoomed lowest-energy band region of Figure 13a in the SI), and second, the very mixing of different compositions of the

van’t Hoff plot as in the simulation. The principal eigenvectors and the α,β-stoichiometric combination coefficient line are shown in Figure 12a, the optimum van’f Hoff plot is shown in Figure 12b, and the resolved s-t- and s-c-DPH absorption spectra are shown in Figure 12c. We draw attention to the near identity of Figures 6 and 12 as it is not coincidental. It illustrates our ability to model the experimental system almost exactly and lends support to the validity of the resolved spectra in Figure 12c. The van’t Hoff plot gives ΔH° = 3.80 kcal/mol and ΔS° = 11.00 eu. The large entropy difference accounts for the unexpected result that the s-c-DPH conformer becomes dominant at the high end of our T range, inset of Figure 12b. As in the simulation, the resolved spectra in Figure 12c are for the highest experimental T. The procedure used above in the simulation was used to create pure conformer spectra with broadening appropriate for each experimental T. The contributions of the two conformer spectra at each experimental spectrum were calculated using the derived van’t Hoff parameters and combined to yield the unshifted twocomponent spectra, Figure 13a. Back shifting was achieved by fitting each set of resolved conformer spectra to the corresponding experimental spectrum, Figure 13b. That the 5362



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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.

pure component spectra according to the van’t Hoff parameters gives the appearance of a shift in the first band of the mixture spectra (see below and the SI). Resolution of Experimental Spectra of ttt-DPH in nAlkanes: Isopolarizability Conditions. The isopolarizability T's used in this study were those used in the resolution of tttDPH fluorescence spectra,16 spanning the T range used above to record the ttt-DPH spectra in n-C12. At the selected T's, each of 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 isopolarizability spectral matrix, Figure 15a, reveals a robust two-component system, instead of the expected three-component system. Although the use of isopolarizability T's should eliminate shifts in the pure conformer spectra, they should continue to be subject to T-induced differential broadening. As explained above, one consequence of the variable contribution of the s-cDPH spectrum in the spectra in Figure 15a is an apparent blue shift with increasing T. Indeed, subjecting the spectra to the shift procedure described above for the n-C12 spectral matrix predicts that maximum similarity with respect to the spectrum recorded at the highest T (n-C16) and a possibly better twocomponent 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 the maximum similarity criterion that shifts spectra to a common range. 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 uniform broadening in all of the alkane spectra consistent with that of the 372 K ttt-DPH spectrum in n-C16. Use of 25 300 cm−1, the value that delineated the baseline region for which application of the LS non-negativity criterion defined the combination coefficients of the s-t-DPH spectrum in the resolution of the nC12 spectrothermal matrix, was deemed inappropriate for the isopolarizability matrix. A red shift in the resolved spectra was expected because of the higher polarizability of n-C16 relative to that of n-C12 at any given T. To account for this shift, we initially selected 24 850 cm−1 to delineate the baseline region and locate the s-t-DPH spectrum on the normalization line. The combination coefficients of the s-c-DPH spectrum were then determined with the use of the van’t Hoff optimum linearity constraint. The optimum van’f Hoff plot is shown in Figure 16a, and the resolved s-t- and s-c-DPH absorption spectra are shown in Figure 16b. Figure 16c compares the spectra of the experimental broadening-compensated matrix with spectra constructed with the use of the resolved pure component spectra, as described above. The van’t Hoff plot gives ΔH° = 4.10 ± 0.57 kcal/mol and ΔS° = 11.13 ± 2.00 eu, consistent with the values derived above from the resolution of the n-C12 spectral matrix. The choice of k = 160 cm−1 as the broadening compensation parameter was evaluated by examining the evolution of eigenvalue ratios as a function of k, Figure 17. Both ev3 and ev4 attain minimum values at k close to 310 cm−1, panel (a), whereas ev4/ev2 has its minimum value at k = 260 cm−1. An argument in favor of the larger value can be made because the third eigenvector of the initial matrix resembles the second 5363



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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 the standard deviation from the van’t Hoff plot and (b) the optimum van’t Hoff plot (inset as in Figure 16a).

derivative of the first eigenvector and is associated with broadening. Nonetheless, we used the 260 cm−1 value because it is intermediate between 160 and 310 cm−1 and it seemed likely that the change in spectral shape upon simply combining the broad s-c-DPH spectrum with the better resolved s-t-DPH spectrum would appear as broadening in the PCA treatment and 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 of the two spectra, the vibronic structure of the s-t-DPH spectrum is 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-DPH spectrum was traced to the choice of the spectral region on which the LS non-negativity criterion is applied. Changing that region changes selection of the βs‑trans value on the combination coefficient normalization line and, in turn, influences the βs‑cis value 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 conformer spectrum into better agreement with the spectrum obtained from the n-C12 spectral matrix but gives van’t Hoff plot optimum 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 fourth cases are shown in Figure 18. Also shown in panel (b) of Figure 18 are the predicted experimental spectra based on the pure

component spectra in that panel. The procedure used in constructing the mixture spectra was the same as that used above for the simulated and subsequent spectral matrices. In the 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 DPH spectra in n-C12, but as can be seen in the right panel of the above figure, the resulting s-c-DPH spectrum is more resolved at the onset. Preference for the 24 625 cm−1 LS limit was based on shape similarity of the pure component spectra in Figure 18a with those derived from the n-C12 spectral matrix, Figure 12c. 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 the conformer contributions are shown in Figure 19. The very good agreement between the experimental spectra and those predicted upon projection of the pure conformer spectra in Figure 18a to the isopolarizability T's is shown in Figure 15b. Comparison of the fits obtained in Figures 15b and 16c shows very good reproduction of the experimental spectra, but that use of k = 160 cm−1 in the broadening compensation procedure gives the best fits for spectra measured at the lower T's, whereas use 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 the uncertainty limits of our resolution. 5364



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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 the isopolarizability (solid curves) spectral matrices. (b) The combination coefficients of the shifted resolved spectra in n-C12 located on the isopolarizability 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.

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treatment) for the n-C12 matrix and on the α,β-normalization combination coefficient line (PCA treatment) for the isopolarizability matrix. Fractional contributions based on the normalized spectra were converted to stoichiometric molar contributions by projecting the resolved spectra from the isopolarizability matrix, appropriately shifted in opposite directions, 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 concentration of 4.14 × 10−5 M and allowing projection of each broadening-compensated spectrum from Figure 15a onto the α,β-stoichiometric line. The 1.28 ratio of the scaling factors is a measure of the difference in oscillator strengths for the lowest one-photon allowed transitions in the s-t-DPH and s-c-DPH conformers. Identification of the α,β-coefficients of the experimental spectra provides stoichiometric fractional contributions of the two conformers, leading to an almost identical van’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 isopolarizability matrix leads to minor reshaping of those spectra, so that they very closely resemble the resolved spectra from the

DISCUSSION Comparison of the Two Sets of Resolved ttt-DPH Conformer Absorption Spectra. The s-t-DPH and s-c-DPH UV absorption spectra obtained independently from the n-C12 and the isopolarizability spectral matrices in Figures 1a and 15a, respectively, are compared in Figure 20a. The shift in the s-tDPH spectra is consistent with the difference in polarizability between n-C12 and n-C16 at 372 K. The small difference in shape is probably associated with the choice of spectral regions used in the application of the LS non-negativity criterion. However, in view of the somewhat greater viscosity of n-C16 relative to n-C12 at the same T, the slightly better resolution of the s-t-DPH spectrum in n-C16 could be real. The shapes of the s-c-DPH spectra are also very similar, but, in this case, they are shifted in the opposite direction with respect to each other. This anomalous behavior may be caused by the shifting procedure 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 isopolarizability matrix are more reliable because, under those conditions, no Tinduced shifts are expected and shift compensation was not required for the resolution. The search for the pure conformer spectra was performed on the α,β-stoichiometric combination coefficient line (SVD 5365



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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, 14.9i cm−1, of the TS suggests that an energy minimum may also exist at the planar geometry. It is also reasonable to expect that enantiomeric structures with dihedral angles with opposite signs (+14.6°, −6.9° and −14.6°, +6.9°) should also be readily accessible.16 Because the s-cis-butadiene moiety forms with equal probability on either side of the triene unit, those five structures would contribute R ln 10 to the entropy difference, accounting for 4.6 eu of the observed ΔS values. A plethora of structures of s-c-DPH existing in equilibrium is consistent with the relatively low definition of vibronic structure in its absorption spectrum. Several aspects of the puzzling photophysical and photochemical behavior of ttt-DPH were noted previously.16 In view of the very large s-c-DPH conformer contributions at equilibrium, especially at the higher T's, and the conclusion that, at least for excitation at longer λ, s-c-DPH and s-t-DPH retain their identity in their lowest excited singlet states, adhering to Havinga’s NEER principle,15 it is instructive to revisit some relevant observations. It is reasonable to expect that the presence of two nonequilibrating ttt-DPH conformers in the singlet excited state, whose ratio varies with T and whose fluorescence and absorption spectra differ substantially, should be reflected in biexponential fluorescence decay and in Tdependent fluorescence quantum yields and lifetimes. It is surprising, therefore, that fluorescence quantum yields are insensitive to the change in T under isopolarizability conditions16 and that fluorescence decays are monoexponential and insensitive to changes in T in several saturated hydrocarbon solvents.36 A careful reexamination of fluorescence decay, especially for excitation at longer λ's that favor s-c-DPH absorption and fluorescence, seems warranted. Biexponential λexc and inert gas pressure-dependent fluorescence decay has been reported for ttt-DPH at 75−95 °C in the vapor phase.38 Short and long fluorescence lifetimes were attributed to vibrationally hot and cold 21Ag → 11Ag transitions of the s-tDPH conformer. The results reported in this paper suggest s-tand s-c-DPH fluorescence as an alternative interpretation. Use of Isopolarizability Conditions. Isopolarizability conditions were used previously16 and in this study with the intention of eliminating T-induced spectral shifts, thus limiting nonlinear T effects to broadening. This premise was questioned recently by Catalán, who presented evidence showing that the shift observed in ttt-DPH absorption spectra upon changing the T has a much steeper dependence on the polarizability α then the shift obtained upon varying the alkane solvent at constant T.17 He reasoned that this difference between ttt-DPH thermochromism and solvatochromism would invalidate our isopolarizability approach because it involved changing both the solvent and T.17 Catalán correctly inferred that changes in the absorption spectra of polyenes, including ttt-DPH, in response to changes in T are due to a combination of the effects of polarizability and changes in molecular structure. However, the structural changes were described as “a kind of conformational tremor”,17,39 and the known variable contribution of distinct molecular conformers, such as s-c-DPH in the case of ttt-DPH, was ignored. Subsequently, Catalán, without mentioning previous experimental and theoretical work on the s-cis conformers of trans,trans-1,4-diphenyl-1,3-butadiene40,41 and ttt-DPH,14,16 proposed the existence of s-cis diphenylpolyene conformers in a theoretical paper.42 In this work, we have

isopolarizability matrix, Figure 21. Thus, in Figure 21, the reconstructed red spectra are so exactly superposed over the black experimental spectra from the isopolarizability spectral set that the latter are not visible. Energetics of s-t- and s-c-DPH Conformer Equilibration. The presence of the s-c-DPH conformer in thermal equilibrium with the s-t-DPH conformer, Chart 1, was first inferred from the λexc dependence of ttt-DPH fluorescence in methylcyclohexane, MCH.14 In that study, the fluorescence spectra of the two conformers were resolved at 14 T's spanning the −3.2−91.0 °C range. At each T, the fluorescence spectrum of the s-c-DPH conformer was assigned to the difference between ttt-DPH spectra obtained for λexc 355 and 385 nm by assuming that only the 11Bu state of the s-t-DPH conformer contributed to the long wavelength onset of the pairs of fluorescence spectra. The enthalpy difference between the two conformers, ΔH = 3.2 ± 0.1 and 3.5 ± 0.2 kcal/mol, was obtained from the slopes of van’t Hoff plots of fractional fluorescence contribution ratios at 355 and 385 nm, respectively. Entropy differences, ΔS, were estimated from the intercepts of the van’t Hoff plots, i, using ln

εcϕ xc ΔS ΔH = ln c + − (1 − xc) εt ϕt R RT

(5)

where subscripts c and t designate s-c- and s-t-DPH, respectively and the other symbols have their usual meanings (eq 5 is analogous to eq 4). Estimated ranges of molar absorptivity coefficient and fluorescence quantum yield ratios gave 5 ≤ ΔS ≤ 10 eu. Use of the derived conformer molar absorptivity coefficients from this work and the fact that the ttt-DPH fluorescence quantum yield and lifetime are insensitive to T and λexc changes in hydrocarbon solvents16,36 gives roughly ΔS = 9 eu, closer to the previous upper limit. A complete resolution of ttt-DPH fluorescence spectra into the s-c-DPH conformer fluorescence spectrum and pure 21Ag and 11Bu fluorescence spectra from the s-t-DPH conformer was subsequently based on PCA treatment with broadening compensation of fluorescence spectra measured in n-alkane solvents under the isopolarizability conditions used in this work for the measurement of absorption spectra.16 That analysis gave a somewhat lower ΔH = 2.83 kcal/mol, a value that is probably less reliable because it is based on only a five T van’t Hoff plot. The ΔH values obtained in this work of 3.8 ± 0.6 and 4.4 ± 0.7 kcal/mol from the n-C12 and isopolarizability spectral matrices, respectively, are in better agreement with the values obtained in the earlier study and agree reasonably well with 3.4 kcal/mol, the value predicted for s-c-DPH relative to the global minimum at s-tDPH by DFT calculations [B3LYP/6-3111+G(d,p)].16 What is remarkable is that ΔS so favors the s-c-DPH conformer and that its contribution to the equilibrium mixture exceeds that of the st-DPH conformer at the upper limit (∼100 °C) of our modest experimental T range (see Figures 12b, 16a, and 19b). The derived values of ΔS in the range of 9−12 eu are coupled to the corresponding ΔH values, reflecting, as expected,37 the experimental uncertainty of the measurements. The larger entropy of the s-c-DPH conformer is consistent with theoretical calculations that predict that, in contrast to the planar s-t-DPH conformer, it exists as a mixture of nonplanar structures.16 The nonplanarity of s-c-DPH was found in the s-cis side of the triene system with a 14.6° phenyl/vinyl dihedral and a 6.9° vinyl/vinyl dihedral angle within the s-cis-butadiene moiety. The calculations revealed an energetically very shallow, planar 5366



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(8) (a) Alford, P. C.; Palmer, T. F. Chem. Phys. Lett. 1982, 86, 248− 253. (b) Alford, P. C.; Palmer, T. F. J. Chem. Soc., Faraday Trans. 2 1983, 79, 433−447. (9) Itoh, T.; Kohler, B. E. J. Phys. Chem. 1987, 91, 1760−1764. (10) Hilinski, E. F.; McGowan, W. M.; Sears, D. F., Jr.; Saltiel, J. J. Phys. Chem. 1996, 100, 3308−3311. (11) Yee, W. A.; O’Neil, R. H.; Lewis, J. W.; Zhang, J. Z.; Kliger, D. S. Chem. Phys. Lett. 1997, 276, 430−434. (12) Hogiu, S.; Werneke, W.; Pfeiffer, M.; Lau, A.; Steinke, T. Chem. Phys. Lett. 1998, 287, 8−16. (13) Hirata, Y.; Mashima, K.; Fukumoto, H.; Tani, K.; Okada, T. Chem. Phys. Lett. 1999, 308, 176−180. (14) Saltiel, J.; Sears, D. F., Jr.; Sun, Y.-P.; Choi, J.-O. J. Am. Chem. Soc. 1992, 114, 3607−3612. (15) Jacobs, H. J. C.; Havinga, E. Adv. Photochem. 1979, 11, 305− 373. (16) Turek, A. M.; Krishnamoorthy, G.; Sears, D. F., Jr.; Garcia, I.; Dmitrenko, O.; Saltiel, J. J. Phys. Chem. A 2005, 109, 293−303. (17) Catalán, J. Chem. Phys. Lett. 2008, 457, 87−90. (18) Hausser, K. W.; Kuhn, R.; Kuhn, E. Z. Phys. Chem., Abt. B 1935, 29, 417−454. (19) Sklar, L. A.; Hudson, B. S.; Petersen, M.; Diamond, J. Biochemistry 1977, 16, 813−818. (20) Andrews, J. R.; Hudson, B. S. J. Chem. Phys. 1978, 68, 4587− 4594. (21) Birks, J. B.; Tripathi, G. N. R.; Lumb, M. D. Chem. Phys. 1978, 33, 185−194. (22) Brey, L. A.; Schuster, G. B.; Drickamer, H. G. J. Chem. Phys. 1979, 71, 2765−2772. (23) Catalán, J.; Hopf, H.; Klein, D.; Martus, M. J. Phys. Chem. A 2008, 112, 5653−5657. (24) Timmermans, J. Physico-Chemical Constants of Pure Organic Compounds; Elsevier: New York, 1950; Vol. 1; 1965; Vol. 2. (25) (a) Saltiel, J.; Sears, D. F., Jr.; Turek, A. M. J. Phys. Chem. A 2001, 105, 7569−7578. (b) Turek, A. M.; Krishnamoorthy, G.; Phipps, K.; Saltiel, J. J. Phys. Chem. A 2002, 106, 6044−6052. (26) Jansson, P. A. In Deconvolution of Images and Spectra; Academic Press: New York, 1997; pp 42−75. (27) Cattell, R, B. In Problems in Measuring Change; Harris, C. W., Ed.; University of Wisconsin Press: Madison, WI, 1963; pp 167−198. (28) Sanchez, F. C.; Toft, J.; Van den Bogaert, B.; Massart, D. L. Anal. Chem. 1996, 68, 79−85. (29) Vest Nielsen, N. P.; Carstensen, J. M.; Smedsgaard, J. J. Chromatogr., A 1998, 805, 17−35. (30) Saltiel, J.; Choi, J.-O.; Sears, D. F., Jr.; Eaker, D. W.; Mallory, F. B.; Mallory, C. W. J. Phys. Chem. 1994, 98, 13162−13170. (31) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627. (32) Eilers, P. H. C. Anal. Chem. 2003, 75, 3631−3636. (33) (a) Lawton, W, H; Sylvestre, E. A. Technometrics 1971, 13, 617. (b) Lawton, W, H; Sylvestre, E. A.; Maggio, M. S. Technometrics 1974, 16, 353. (34) Dowdy, S.; Wearden, S. Statistics for Research, 2nd ed.; Wiley: New York, 1991; pp 259−260. (35) Sun, Y.-P.; Sears, D. F., Jr.; Saltiel, J. J. Am. Chem. Soc. 1988, 110, 6277−6279. (36) Cehelnik, E. D.; Cundall, R. B.; Lockwood, J. R.; Palmer, T. J. Phys. Chem. 1975, 79, 1369−1376. (37) Leffler, J. E. J. Org. Chem. 1955, 20, 1202−1231. (38) Itoh, T. J. Phys. Chem. A 1999, 103, 2247−2250. (39) Catalán, J. Chem. Phys. Lett. 2005, 416, 165−170. (40) Sun, Y.-P.; Bunker, C. E.; Wickremesinghe, P. L.; Rollins, H. W.; Lawson, G. E. J. Phys. Chem. 1995, 99, 3423−3429. (41) Bunker, C. E.; Lytle, C. A.; Rollins, H. W.; Sun, Y.-P. J. Phys. Chem. A 1997, 101, 3214−3221. (42) Catalán, J. Chem. Phys. 2007, 335, 69−78.

established that the increase in the s-cis- to s-trans conformer ratio alone with increasing T gives the appearance of a spectral shift (see the SI). Furthermore, Catalán neglected considering experimental evidence showing that the thermochromic response of the ttt-DPH absorption spectrum is more than twice as large as the thermochromic response of the 00 band of the 11Bu → 11Ag fluorescence spectrum of s-t-DPH.9 In this work, the resolution of the ttt-DPH n-C12 spectrothermal matrix into s-t-DPH and s-c-DPH conformer absorption spectra reveals that (1) the absorption spectrum of s-c-DPH is more sensitive to polarizability changes than the absorption spectrum of s-t-DPH and (2) both conformer absorption spectra are more sensitive to polarizability changes than the 11Bu → 11Ag fluorescence of the s-trans conformer, Figure 14. The fact that the 11Bu → 11Ag fluorescence of s-t-DPH exhibits identical thermochromic and solvatochromic shift dependencies on polarizability validates our earlier use of isopolarizability conditions in facilitating the resolution of conformer fluorescence spectra.16

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ASSOCIATED CONTENT

* Supporting Information S

Simulated ttt-DPH spectral matrices illustrate magnitudes of apparent shifts due to broadening and changing conformer composition. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address #

Department of Chemistry, IIT Guwahati, Guwahati, India 781039. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the National Science Foundation, most recently by Grant No. CHE-0846636. We thank Mr. S. Bonnin and Mr. R. Gilbert for the index of refraction measurements.

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REFERENCES

(1) Hudson, B. S.; Kohler, B. E. Annu. Rev. Phys. Chem. 1974, 25, 437−460. (2) Hudson, B. S.; Kohler, B. E.; Schulten, K. In Excited States; Lim, E. C., Ed.; Academic Press: New York, 1982; Vol. 6 pp 1−95. (3) (a) Allen, M. T.; Whitten, D. G. Chem. Rev. 1989, 89, 1691− 1702. (b) Whitten, D. G. Acc. Chem. Res. 1993, 26, 502−509. (4) Saltiel, J.; Sun, Y.-P. In Photochromism, Molecules and Systems; Dü rr, H. Bouas-Laurent, H., Eds.; Elsevier: Amsterdam, The Netherlands, 1990; pp 64−164. (5) (a) Saltiel, J.; A. S. Waller, A. S.; Sears, D. F., Jr. J. Photochem. Photobiol. A 1992, 65, 29−40. (b) Saltiel, J.; Waller, A. S.; Sears, D. F. J. Am. Chem. Soc. 1993, 115, 2453−2465. (6) Saltiel, J.; Waller, A. S.; Sears, D. F., Jr.; Garrett, C. Z. J. Phys. Chem. 1993, 97, 2516−2522. (7) (a) Saltiel, J.; Ko, D.-H.; Fleming, S. A. J. Am. Chem. Soc. 1994, 116, 4099−4100. (b) Saltiel, J.; Wang, S. J. Am. Chem. Soc. 1995, 117, 10761−10762. (c) Saltiel, J.; Wang, S.; Watkins, L. P.; Ko, D.-H. J. Phys. Chem. A 2000, 104, 11443−11450. (d) Saltiel, J.; Krishnamoorthy, G.; Huang, Z; Ko, D.-H.; Wang, S. J. Phys. Chem. A 2003, 107, 3178−3186. (e) Saltiel, J.; Wang, S. Photochem. Photobiol. Sci. 2006, 5, 883−895. 5367


Resolution of Conformer-Specific All-trans-1, 6-diphenyl-1, 3, 5

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