J . Phys. Chem. 1993,97, 9351-9355
9351
Computational Studies of the Molecular Structure and Electronic Spectroscopy of Carotenoids Robert E. Connors’ and Douglas S. Burns Department of Chemistry, Worcester Polytechnic Institute. Worcester, Massachusetts 01 609
Roya Farhoosh and Harry A. Frank’ Department of Chemistry, University of Connecticut, 21 5 Glenbrook Road, Storrs. Connecticut 06269 Received: April 5, 1993”
Semiempirical INDO/S spectral calculations have been carried out for the all-trans carotenoids, 3,4,7,8tetrahydrospheroidene, 3,4,5,6-tetrahydrospheroidene,and 3,4-dihydrospheroidene, as well as the all-trans and 15, 15’-cis isomers of spheroidene. These biologically important molecules contain seven, eight, nine, and ten conjugated double bonds, respectively. In order to make calculations on these large systems tractable, their structures have been approximated with the ?r-electron conjugated moieties. Geometries used for the INDO calculations were obtained by computing fully optimized structures for the carotenoids with the AM1 Hamiltonian. Steric interaction involving methyl substituents results in some twisting along the carotenoid chain. Singledouble bond alternation is clearly evident for each molecule. Agreement between INDO calculated excitation energies and relative oscillator strengths for the allowed excited states are in good agreement with the experimental data. Calculations have also been performed for several distorted forms of 1 5 15’-cis-spheroidene to model absorption spectral data that have been obtained for spheroidene bound to reaction centers of Rhodobacter sphaeroides wild type strain 2.4.1.
Introduction Carotenoids play at least two very important roles in photosynthesis.’ First, they supplement the light capturing ability of chlorophyll by absorbing light in regions of the visible spectrum where chlorophyll is not a very efficient absorber. The energy is then transferred to chlorophyll which is capable of carrying out the primary electron-transfer process in the reaction center. Second, carotenoids protect the photosynthetic apparatus by quenching chlorophyll triplet states before they can sensitize the formation of singlet state (‘Ag) oxygen-a powerful oxidizing agent of chlorophyll. Both of these processes, light harvesting and photoprotection,requireenergy transfer. The light-harvesting function utilizes singlet-singlet energy transfer from carotenoids to chlorophylls and is usually discussed in terms of formalisms advanced by Fiirster and Dexter.293 The photoprotectionprocess involves triplet-triplet energy transfer from chlorophylls to carotenoids. This dual energy-transfer function is possible because carotenoids,in general, have relatively high energy singlet states and low energy triplet states (compared to chlorophylls),so that both processes are energetically favorable. The excited-state properties of these carotenoids are not well characterized. Optical spectroscopic studies have revealed that the excited-state complexion of carotenoids consists of one state (the so-called llB, state in C2h symmetry) into which absorption is strongly allowed and another lower-lying state (the so-called 21A, state) into which absorption is symmetry forbidden, but a detailed understanding of what molecular features control the light absorption properties of these molecules is lacking.4 For example, the question of the stereochemistry of the photosynthetic bacterial reaction center-bound carotenoid has been debated in the literature for several years. The first assignment of the configuration of the carotenoid was made by Boucher et a L 5 on the basis of electronic absorption and circular dichroism (CD) data. They proposed that carotenoids incorporated into the reaction center of Rhodospirillum rubrum (Rs. rubrum) strain G9 adopt a twisted, protohelical-shaped, 15,15’-cisconfiguration. Agalidis et a1.6 and Lutz et a1.7 confirmed this assignment but *Abstract published in Advcmce ACS Abstracts, August 15, 1993.
0022-365419312097-9351$04.00/0
noticed only a very small oscillator strength in the 350-450-nm absorption region for spheroidene either bound in Rhodobacter sphaeroids (Rb. sphaeroides) 2.4.1 or incorporated into Rb. sphaeroides R-26 reaction centers. The authors argued convincingly on the basis of differential absorption spectra from reaction centers containing different carotenoids that a feature appearing at 370 nm was attributed to a band shift of the bacteriochlorophyllSoret band upon carotenoid binding and not to the “cis-peak“ that is expected to be observed for a carotenoid in a cis geometric configuration. A detailed theoretical understanding of why the “cis-peak” is absent from these spectra has never been presented. Resonance Raman spectroscopy has provided an assignment of the stereochemistry of the reaction center-bound carotenoid. Koyama et a/.* carried out resonance Raman studies on several different isomers of 8-carotene and concluded that the spectral properties of the 15,15’-cis configuration were closest to those of the reaction center carotenoid, and so it should also assume a (planar) 15,lS-cis configuration. Lutz et aL9have also concluded on the basis of resonance Raman and proton NMR data that the overall carotenoid stereochemistryis indeed largely a planar 15,15’4s isomer with some twisting near the ends of the molecule. They further suggested without theoretical justification that the twisting in the carotenoid chain may lead to a dimunition of the cis-peak intensity. Previous EPR and optical spectroscopicdata by Frank and co-workersloJ1 have also suggested that the stereochemistryof the reaction center-boundcarotenoid involves twists at the ends of the molecule. The crystallizationand X-ray analysisof different carotenoidcontaining photosynthetic bacterial reaction centers have suggested that the carotenoid stereochemistry is likely to be very similar in all cases.Ql3 Thecarotenoidscontained in these reaction centers were spheroidene in Rb. sphaeroides and 1,2-dihydroneurosporenein Rhodopseudomonas viridis (Rps.viridis). The structure of 1,2-dihydroneurosporenewas fit best to the electron density by assuming that the molecule adopted a 13’-s-cis conformation with an additional out-of-plane twist at the C14’C15’ bond. The spheroidene structure that emerged as the best fit was a cis isomer twisted near the C14’-C13’ region of the molecule. It is important to note that the electron density on the @ 1993 American Chemical Society
9352 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
Connors et al.
AM1. INDO
AM1, INDO
9
H INW
10 AMl, INW
Figure 1. All-trans carotenoid structures from top to bottom: 3,4,7,8-
tetrahydrospheroidene, 3,4,5,6-tetrahydrospheroidene,3,4-dihydrospheroidene, and spheroidene. The shorter moieties which were used for AM1 and INDO/S calculations are indicated. ends of the polyene chains was incomplete in these cases. Also, the best fit structureswere not necessarilythe only ones consistent with the electron density. Subsequent X-ray and NMR analyses have supported the assignment to a more planar 15,15’-cis configuration. This is also consistent with the resonance Raman assignment.14-16 In this work we present semiempirical INDO/S spectral calculations carried out for the all-trans carotenoids, 3,4,7,8tetrahydrospheroidene, 3,4,5,6-tetrahydrospheroidene,and 3,4dihydrospheroidene,as well as the all-trans and 15,15’-cis isomers of spheroidene. These molecules contain seven, eight, nine, and ten conjugated double bonds, respectively, and provide a systematic series for the elucidationof how the positions of carotenoid energy states may affect the funotion of these molecules in the biological system. In addition, exploratory calculations have been performed for several twisted formsof 15,15’-cis-spheroidene to examinewhether the absence of a cis-peak in the reaction center carotenoid absorption spectrum,6.7 could be traced to a distortion of the polyene chain away from planarity. ComputationalMethods. All calculations were performed on an Encore Multimax 520 computer. In order to make the calculations on these large systems tractable, we have approximated their structures with shorter moieties that retain all of the n-electron conjugation. Fully optimized geometries for the carotenoids were computed using the AM1 Hamiltonian and standard minimization techniques of the MOPAC program.” Input for single-point INDO/SI* calculations included the AM1 optimizedgeometriesfurther truncated to contain the conjugated section of the carotenoid chain under the assumption that this portion of the moleculeis the chromophore responsiblefor optical transitions appearing in the visible and near ultraviolet regions of the spectrum. In the case of spheroidene, a terminal methyl group was replaced with a hydrogen to accommodate size limitations of the INDO/S program. The AM1 optimized structure of the 15,15’-cis-spheroidene conjugated model was modified to produce forms twisted by Oo, 30°, 45O, 60°,and 90’ about theC4-Cs bond by using PCMODEL (ROT-Bcommand),19 without varying other geometric parameters. The twisted structures were used as input for INDO/S calculations. Figure 1 presents the full structures of the carotenoids that are the focus of this study with indications of the portions of the molecules that were modeled by AM1 and INDO/S. Excitedstate energies were computed relative to the uncorrelated ground state with configuration interaction (CI) using 30 single and 172 double excitations. Mataga’s formula was used for repulsion integra1s.m
Figure 2. Conjugatedportions of the AM1 optimized geometries. From toptobottom, thestructuresaremodelsforthefollowing:all-trans3,4,7,8tetrahydrospheroidene,3,4,5,6-tetrahydrospheroidene,3,4-dihydrospheroidene, all-trans spheroidene, and 15,15’-ci~-spheroidene.
1
Figure 3. Conjugated portion of the AM1 optimized structure of 3.4-
dihydrospheroidene showing important geometric features.
Results and Discussion AM1 Optimized Geometries. The conjugated portions of the AM 1 optimizedgeometriesof the carotenoids are shown in Figure 2. The presenceof methylgroups along thepolyenechain imparts features that cause deviations of angles and distances from the straight zigzag pattern of an ideal polyene with constant C-C and C=C bond lengths and bond angles. Figure 3 shows the molecular structure of the 3,4-dihydrosperoidene conjugated model with indicationsof thesignificant features that arecommon to all of the carotenoids that we have studied and will serve as a basis for further discussion. Some out-of-plane distortion is found for all of the carotenoids and is presumably related to
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9353
Computational Studies of Carotenoids S, (lAg) and S, ('BU) Energies for Carotenoids
S" 0.0
!;m,,,b,l
2.0
1.o 0.2
12500 7
I
I
0
9
-T
0.0
0.0
10 3.0
=
2.0
7
Number of -C-C- Double Bonds
Figure 4. Experimental and calculated energies of SI(lA,) and Sz(lB,) for carotenoids.
0.4
m.3,
0.2
steric interaction involving the methyl groups. In the case of 3,4-dihydrospheroidene, a 2O0 torsionsal twist of the chain is clearly evident from the side view perspective of Figure 3. We have not carried out an extensive search to determine if the structures obtained for the carotenoids correspond to global minima. It is possible that lower energy conformations exist which are twisted in portions of the chain different from those that we have found. However, it is our view that they are unlikely to differ significantly in energy or influence on the optical properties. In solution at room temperature, a dynamic interconversionbetween energetically similar out-of-planeconformers is envisioned. Another deviation from ideal polyene behavior is found for C-C=C bond angles that are opposite to methyl groups. These angles are calculated to be 118°-1190 compared to values of 122O-12Y obtained when hydrogens are oppositeto these angles. These smaller bond angles result in some small in-plane bending of the carotenoid chain away from the methyl groups. Both of these structural features associated with methyl substitution on the chain have been observed experimentally for other synthetic and naturally occurring carotenoidsthrough X-ray diffraction studies, thus supporting the reliability of the calculations.21 Further, the agreement between structural features calculated by AM1 for isolated molecules and X-ray results obtained from crystalline samples reinforces the previous suggestion that they are intrinsic properties for this type of molecule and are not related to crystal packing forces.21 Single-double bond alternation is observed for all of the optimized structures. All double bond lengths are computed to be equal to 1.35 A. Single bonds along the conjugated chain are equal to 1.44 A when one of the carbons is bonded to a hydrogen but increase to 1.45-1.46 A when a methyl group is present. Some studies have suggested that there may be an elongation of double bonds and shorteningof single bonds near the chain center for longer polyenes and carotenoids;4 however, our AM1 calculations show no such behavior for any of the carotenoids studied. INDO/S Calculations. Recent solution-phase spectroscopic investigationshaveclearlydemonstrated that the 2lA, state which is symmetry forbidden for electric-dipole transitions lies below the strongly absorbing, symmetry allowed 1lB, state for each of the carotenoids discussed here.22 As seen from Figure 4, our INDO/S calculations have correctly predicted this state ordering but have been unsuccessful in reproducing the increase in energy separation that occurs between these two states as the number of conjugated bonds increases along the chain length.22 In fact, the calculated results predict a decrease in the state energy gap as the carotenoid chain is extended.23 Tavan and S c h ~ l t e n , ~ ~ using a PPP model Hamiltonian with single and double excited
v)
1.0
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7
0.0
,13.0 2.0
0.2
1.o
0.0
0.0
1.o
n
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Wavelength [nm] Figure 5. Experimental and theoretical electronicabsorption spectra for all-trans (a) 3,4,7,8-tetrahydrospheroidene,(b) 3,4,5,6-tetrahydrospheroidene, (c) 3,4-dihydrospheroidene,and (d) spheroidene and (e) 15,-
15'-cis-spheroidene. Left axis shows absorbance units for experimental data. Right axis shows oscillator strength for INDO/S results. Excitations of ZIA, are not shown. Transitions predicted to have oscillator strengths less than 0.01 have been omitted from the plots. *-electron CI to examine a series of ideal polyenes, have shown a similar disagreement between theory and experiment. By extending the CI to include triple and quadruple excitations, they were able to correctly predict an increase in the 21Ag-1 1B, energy gap with increasing polyene length. At present, INDO/S calculations at this level of extended CI are not feasible for large carotenoids. Considerably greater success has been achieved in calculating the excitation energies and relative oscillator strengths for the more strongly allowed excited states. Figure 5 shows the experimentalabsorption spectra at room temperature in petroleum ether solvent overlaid with bar graphs of the theoretical spectra for transitions predicted to have oscillator strengths greater than 0.01 .25 Three regions of significantabsorption are clearlyobserved for each of the compounds under study. Agreement between calculated and observed energies and relative oscillator strengths is excellent. The first band system occurs in the 350-500-nm region and corresponds to absorption to the strongly allowed 1lB, (S2)state. Although the absolute values of the calculated oscillatorstrengths for this transition arelikely to have beenoverestimated by INDO/ S,18 the increase in oscillator strength accompanying elongation of the chain is consistent with expectation. The calculated excitation energies for all of the molecules are in excellent
9354
Connors et al.
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
TABLE I: CI Coefficients for Important Configurationa 3,4,7,8-THS
----
HOMO-1 LUMO HOMO LUMO + 1 HOMO LUMO HOMO-1, HOMO LUMO, LUMO + 1 HOMO, HOMO LUMO, LUMO HOMO
-
3,4,5,6-THS
3,4-DHS
t-SPH
C-SPH
0.33 0.39
0.33 0.39
0.33
-0.33
-0.38
0.37 0.31
0.33
0.33
-0.31
0.57
0.33 0.55
0.32
0.57
-0.54
0.52
0.93
0.91
0.89
-0.71 0.63
0.71 0.56
0.70 0.55
0.34 0.39
SI (2A,)
350-500 nm,Sz(lB,) 0.79 0.92 300-350 nm,Cis-Peak 0.69 -0.70
LUMO
-
HOMO-1 LUMO HOMO LUMO + 1 +
-0.61
0.63
250-300 nm HOMO-1 -+LUMO + 1 0.57 0.68 0.87 0.86 -0.87 -0.41 HOMO LUMO + 4 Abbreviations: 3,4,7,8-THS = 3,4,7,8-tetrahydrospheroidene,3,4,5,6-THS= 3,4,7,8-tetrahydrospheroidene,3,4-DHS = 3,4-dihydrospheroidenc, r-SPH = all-trans-spheroidene, c-SPH = lS,lS’-cis-spheroidene.
-
-
agreement with the observed Frank-Condon maxima for this transition.26 A g u transition to S3 is also predicted to occur in this region; however, with the exception of 3,4,7,8-tetrahydrospheroidene, this excitation is predicted to be weak and would be obscured by the intense 1*B,absorption. Although SO S3 is predicted to be of moderate intensity for 3,4,7,8-tetrahydrospheroidene, there is no experimental evidence for a transition overlapping SO Sz. It appears that the combination of AM1 and INDO/S has led to an overestimation of the SO- S3oscillator strength for this molecule. The second region of absorption is observed in the 300-350nm region. Both experimentally and theoretically, this transition is far more intense for the 15,15’-cis form of spheroidene than for any of the all-trans molecules (see Figure 5 ) . This excitation corresponds to the cis-peak, which has been discussed by Zechmeister,z7and is characteristicof polyenes and carotenoids with a cis configuration about a central double bond. Examination of the theoretical results show that this transition correlates with a forbidden g g excitation for an ideal all-trans polyene. The fact that the observed spectra and theoretical predictions show weak absorption in this region for the all-trans carotenoids is due to the deviations from ideal C2h molecular symmetry which have been mentioned previously. The third region of significant absorption occurs in the 250300-nm region and is assigned as a g u transition. For the all-trans carotenoids this band carries more intensity than the absorption found in the 300-500-nm region; however, for 15,15’-ci~-spheroidenethe cis-peak is more intense. Table I lists the coefficients for the important configurations (IC,> [ 0.3) in the CI expansion for SI(21Ae) and for the excited states that dominate the three regions of absorption found between 500 and 250 nm. As has been found previously for polyenes, the 21A, state is described theoretically by a mixture of single and double excited configurations.4 The INDO/S calculations indicate that the leading configurations for the carotenoid excited states responsible for significant absorption in the visible and ultraviolet regions of the spectrum are of the single excited type. 15,15‘-cisSpheroidene Models. As discussed above, all of the direct (X-ray) and indirect (spectroscopic) structural determinations have indicated that the reaction center-bound carotenoid adopts some form of a cis-isomeric configuration. Further, there is very little intensity attributable to the reaction center-bound carotenoid cis-peak. If the carotenoid bound in the reaction center is indeed adopting a cis configuration, why then does it lack a cis-peak? In an attempt to provide some insight regarding this question, incremental twisting of the C4-C5 bond has been carried out and its effect on the cis-peak region between 300 and 350 nm monitored. Twisting the moleculeabout this bond does not imply that this is the region of the molecule that is distorted in vivo;
-
-
-
-
rather it is intended only to serve as a test for the effect that twisting about an arbitrary bond has on the calculated absorption spectrum. INDO/S theory provides a possible explanation for the unusually low absorption intensity that is observed in the cispeak region for reaction center-bound spheroidene. Figure 6 shows the calculated results for twisting about the c4-C~bond of 15,15’-cis-spheroidene. It is found that apart from a gradual blue shift of the predicted transitions, the long wavelength (350450-nm) portion of the spectrum remains relatively unchanged as the twist angle is increased. However, considerably more perturbation with twisting is calculated for the cis-peak region. For the structure with a twist angle of Oo, three absorption bands are predicted to be found in the cis-peak region a t 348 (0.097), 339 (0.005), and 333 nm (0.45), where the oscillator strengths are indicated in parentheses. The 333-nm transition corresponds to the cis-peak which was discussed in the previous section. As shown in the insets of Figure6, thereis a significant redistribution of intensity amongst these three spectral transitions for large angles of twisting of the carotenoid ?r-electron chain. For example, the distribution in the cis-peak region for a 60° twist about the C4-C5 bond is predicted to be 331 (0.33), 322 (0.15), and 318 nm (0.063). Interestingly, for all of the twist angles presented in Figure 6, the sum of the oscillator strengths for the three bands appearing in the cis-peak region remains nearly constant (=0.55), consistent with the view that there is a redistribution of intensity with twisting. It should be noted that for Oo and 45O, one of the transitions is too weak to be shown in Figure 6. The AM1 fully optimized geometry has a C 4 4 5 twist angle of 13’ and a calculated absorption spectrum nearly identical to that of the Oo structure. Although not providing conclusive evidence, these theoretical results suggest that for a highly twisted cis configuration the characteristicintensity normally found in a single cis-peak for a planar carotenoid is distributed between several different absorption bands somewhat separated in wavelength. For such a situation thecompositeabsorption lineshape in thecis-peak region may be quite broad and difficult to observe in vivo. Additional masking of the absorption by the intense Soret bands of the bacteriochlorophyll and bacteriopheophytin pigment absorptions and further broadening owing to dispersive interactions of the carotenoid within the protein matrix are likely causes for the failure to observe the cis-peak in the absorption spectrum of a reaction center-bound carotenoid. Conclusions
A M 1 optimized geometries have been used as input for singlepoint INDO/S calculations to predict the electronic transitions for large carotenoid molecules. The calculations correctly find
Computational Studies of Carotenoids
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3.0
b
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9355
of the cis-peak intensity into several weaker transitions for large angles of twisting of the r-electron chain may account for the failure to observe the cis-peaksin the absorption spectraof reaction center-bound carotenoids.
Acknowledgment. This work is supported by grants from the National Institutes of Health (GM-30353) and the University of Connecticut Research Foundation. Assistance provided by the College Computing Center at Worcester Polytechnic Institute is greatly appreciated. References and Notes (1) Cogdell, R. J.; Frank, H. A. Biochim. Biophys. Acta 1987,895,63. (2) Forster, Th. Ann. Phys. Leiprig 1968, 2, 55. (3) Dexter, D. L. J. Chem. Phys. 1953, 22, 836. (4) Hudson, B. S.; Kohler, B. E.; Schulten, K. In Excited States; Lim, E. C., Ed.; Academic Press: New York, 1982; Vol. 6, p 1. (5) Boucher, F.; Gingras, G. Photochem. Photobiol. 1984,40, 277. (6) Agalidis, I.; Lutz, M.;Reiss-Husson, F. Biochim.Biophys.Acta 1980, 589, 264. (7) Lutz, M.; Szponarski, W.; Berger, G.; Robert, B.; Neumann, J.-M. Biochim. Biophys. Acta 1907,894,423.
I
I
(8),Koyama, Y.; Takii, T.; Saiki, K.; Tasukida, K. Photobiochem. Photobioohvs. 1983. 5. 139. (9) iuiz, M.; Agalidis, I.; Hervo, G.; Cogdell, R. J.; Reiss-Husson, F. Biophys. Acta 1978, 503, 287. (10) Chadwick, B. W.; Frank, H. A. Biochim. Biophys. Acta 1986,852,
: : : C,- C, 90' RoL
1.o
0.0 250
300
350
400
450
Wavelength [nm] Figure 6. INDO/S results for twisting about the c4-C~bond of 15,15'-cis-spheroidene. The angle of twist is (a) Oo, (b) 30°, (c) 45O, (d) 60°,and (e) 90°. Excitations t02~A~arenotshown. Transitionspredicted to have oscillator strengths less than 0.01 have been omitted from the plots.
that 21Ag lies below 11B, but at this level of CI are not able to reproduce the increase in energy gap between these states that occurs as the number of conjugated bonds increases along the chain length. The calculated excitation energies and relative oscillator strengths for the electric dipole allowed excited states have been found to be in good agreement with the experimental data, clearly demonstrating that the methodology of combining AM1 and INDO/S provides a reliable approach to predicting the allowed electronic transitions for carotenoids. A redistribution
257. (11) Frank, H. A.; Chadwick, B. W.; Taremi, S.;Kolaczkowski, S.; Bowman, M. FEBS Lett. 1986,203, 157. (12) Deisenhofer, J.; Michel, H. Science 1989, 245, 1463. (13) Feher, G.; Allen, J. P.; Okamura, M. Y.; Rees, D. C. Nature 1989, 339, 111. (14) Yeates, T. 0.;Komiya, H.; Chirino, A.; Rea, D. C.; Allen, J. P.; Feher, G. Proc. Natl. Acad. Sci. USA 1988,85,7993. (15) Arnoux, B.; Ducruix, A,; Reiss-Husson, F.; Lutz, M.; Noms, J.; Schiffer, M.; Chang, C.-H. FEBS Lett. 1989, 258, 47. (16) de Groot, H. J. M.; Gebhard, R.; van der Hoef, I.; Hoff, A. J.; Lugtenburg, J.; Violette, C. A,; Frank, H. A. Biochemistry 1992,31, 12446. (17) Stewart, J. J. P. QCPE Program 455, V5. (18) Ridley, J.; Zener, M. Theor. Chim. Acta 1973, 32, 111. (19) PCMODEL, V1.0,Serena Software: Bloomington, IN. (20) Mataga, N.; Nishimoto, K. 2.Phys. Chem. (Munich) 1957,23,140. (21) Bart, J. C. J.; MacGillavry, C. H. Acta Crystallogr. 1968,824,1569; 1587. (22) DeCoster, B.; Christensen, R. L.; Gebhard, R.; Lugtenburg, J.; Farhoosh, R.; Frank, H. A. Biochim. Biophys. Acta 1992, 1102, 107. (23) The experimental data presented in Figure 4 are for adiabatic transitions derived from the 0-0 bands of fluorescence excitation spectra (SI)
and absorption spectra (Sz). The calculated values correspond to vertical transitions for the ground-state geometry. (24) Tavan, P.; Schulten, K. J. Chem. Phys. 1979, 70, 5407. (25) A complete list of the excited states calculated to lie within the region shown in Figure 5 is available from the authors. (26) The energy of the transition to the IB,, state is known to have a significant dependence on solvent polarizability as described by the formula: Y, = Y~ - K(n2- l/n2 2) where u, and Y' are the frequencies in cm-1 of the transition in a solvent and in the gas-phase, respectively, n is the refractive index of the solvent, and K is a collection of constants and solute properties. The agreement between observed Frank-Condon maxima and the calculated excitation energies suggests that petroleum ether is a good choice of solvent for carotenoidswhen comparing experimental resultswith INDO/S predictions. (27) Zechmeister, L. Cis-Trans Isomeric Carotenoids, Vitamins A, and Arylpolyenes; Springer: Vienna, 1962.
+
