Beta Carotene

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JOURNAL OF RAMAN SPECTROSCOPY J. Raman Spectrosc. 2003; 34: 413–419 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/jrs.1013 Density functional and vibrational spectroscopic analysis of b-carotene S. Schlucker, A. Szeghalmi, M. Schmitt, J. Popp† and W. Kiefer∗ ¨ ¨ Institut fur Physikalische Chemie der Universitat Wurzburg, Am Hubland, D-97074 Wurzburg, Germany ¨ ¨ ¨ Received 2 December 2002; Accepted 28 March 2003 We report a computational study on the structu
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   JOURNAL OF RAMAN SPECTROSCOPY  J. Raman Spectrosc. 2003; 34 : 413–419Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/jrs.1013 Density functional and vibrational spectroscopicanalysis of  b -carotene S. Schl ¨ ucker, A. Szeghalmi, M. Schmitt, J. Popp † and W. Kiefer ∗ Institut f¨ ur Physikalische Chemie der Universit ¨ at W¨ urzburg, Am Hubland, D-97074 W¨ urzburg, Germany Received 2 December 2002; Accepted 28 March 2003 We report a computational study on the structural, energetic and vibrational spectroscopic characteristicsof b -carotene employing density functional theory (DFT). The optimized geometry and the completevibrational spectrum calculated at the BPW91/6–31G* level,including infrared (IR) intensitiesand Ramanactivities, are presented. The centrosymmetric structure of b -carotene is verified both theoretically andexperimentally, by identifying a stable calculated structure with C i symmetry and the mutually exclusiveoccurrence of bands in the experimental Fourier transform IR and Raman spectrum, respectively. Thecalculatedvibrationalspectrareflectthemajorcharacteristicfeaturesobservedexperimentally.Differencesin the calculated IR intensities and Raman activities for a few dominant modes of two b -caroteneconfigurationisomers,theall- trans andthenaturalabundant(C 6 –C 7 )s- cis form,areexplainedqualitativelyby the corresponding eigenvectors. At the level of theory employed, s- cis - b -carotene was found to be8.8 kJ mol − 1 morestablethantheall- trans form.Calculationson b -carotenemodelsystemswereperformedto separate electronic from steric contributions. The higher stability of s- cis - b -carotene is explained byan energetically favored b -ionone ring conformation, compensating for its shorter conjugation length incomparison with the all- trans form. Copyright  2003 John Wiley & Sons, Ltd.KEYWORDS: density functional theory; ˇ -carotene; configurational isomers INTRODUCTION Terpenoids, also termed terpenes or isoprenoids, belongto a diverse and widespread class of natural products,which are the formal polymerization products of isoprene.According to the number of isoprene units, terpenoids areclassified as mono- (C 10 ), sesqui- (C 15 ), di- (C 20 ), sester- (C 25 )triterpenoids (C 30 ), carotenoids (C 40 ) and polyisoprenoids. 1 Among the carotenoids are carotenes and xanthophylls,which are hydrocarbons and oxygen-containing derivatives,respectively. Carotenoids show yellow to red colors becauseof their large number of conjugated double bonds. Inparticular, ˇ -carotene consists of a polyene chain withnine conjugated double bonds and two ˇ -ionone rings.It is the biosynthetic precursor of vitamin A 1 or retinol,which is formed by the cleavage of ˇ -carotene at the Ł Correspondence to: W. Kiefer, Institut f¨ur Physikalische Chemieder Universit¨at W¨urzburg, Am Hubland, D-97074 W¨urzburg, Germany. E-mail: wolfgang.kiefer@mail.uni-wuerzburg.de † Present address: Institut f¨ur Physikalische Chemie,Friedrich-Schiller-Universit¨at Jena, Helmholtzweg 4, D-07743 Jena,Germany.Contract/grant sponsor: Deutsche Forschungsgemeinschaft;Contract/grant number: GRK 690/1.Contract/grant sponsor: Fonds der Chemischen Industrie. central double bond. By oxidation of this primary alcoholto an aldehyde, rhodopsin is formed. Rhodopsin undergoesa series of photochemical reactions after irradiation withvisible light, yielding activated rhodopsin or all- trans -retinalopsin. Finally, an electrical signal in the rod cellsof vertebrates is generated. 2 In addition to its importancein the process of vision, a second important biologicalfunction of ˇ -carotene is to serve as an accessory pigment inphotosynthesis. All photosyntheticorganisms such as plantsand diverse bacteria contain chlorophyll a. Molecules suchas chlorophyll b, xanthophylls and carotenoids including ˇ -carotene are present in accessory pigments which absorblight that chlorophyll a does not absorb. 2 Carotenoids and ˇ -carotene in particular have beenextensively studied by various spectroscopic methods.Among them are vibrational spectroscopic techniques suchas resonance Raman (RR) spectroscopy 3–11 and Ramanspectroscopy with near-infrared (NIR) excitation. 11–13 Thefirst normal coordinate analysis (NCA) of a ˇ -carotenemodel system was published 20 years ago by Saito andTasumi. 3 In a more recent work on ˇ -carotene and severalxanthophylls, semi-empirical calculations (AM1 level) werereported and special emphasis was put on understandingthe electronic absorption spectra and on the comparison of Copyright  2003 John Wiley & Sons, Ltd.  414 S. Schl¨ucker et al . Ramanspectraobtainedunderresonantversusnon-resonantconditions. 11 In order to calculate molecular propertiesaccurately, however, inclusion of electron correlation isrequired. In addition to post-Hartree–Fock (HF) methodssuch as Møller–Plesset (MP) perturbation theory, DFT has become very popular because of its good performance atreasonable computational costs. 14 The influence of electroncorrelation on energies and geometries of retinal andits derivatives, for example, was calculated with DFT. 15 In other studies, the photoisomerization pathway of aretinal chromophore model was examined. Because oftheir scaling with the number of electrons and basisfunctionsenteringtheconfigurationalstatefunctions(CSF), 16 these high-level ab initio methods are computationallyvery expensive. Examples include the complete activespace self-consistent field (CASSCF) method 17 , 18 and multi-configuration second-order perturbation theory (MCPT2). 19 In computational studies employing DFT in particular,the trans–cis isomerization in long linear polyene chainsserving as ˇ -carotene model systems 20 and the reactionof singlet oxygen with a carotenoid model system were,for example, investigated. 21 Although quantum chemicalcalculationsonlargemolecularsystemshavebecomefeasiblenowadays, to the best of our knowledge, no ab initio orDFT calculations examining the structural, energetic andvibrational spectroscopic characteristics of ˇ -carotene have been published so far.The knowledge of structural and vibrational spectro-scopic properties of ˇ -carotene is highly desirable fordifferent purposes. First, interactions such as hydrogen bonding between carotenoid and porphyrin moieties inlight-harvesting complexes, for example, can be examined by computational chemistry. 22 Second, vibrational spec-troscopic properties are required for both wavenumber-and time-resolved vibrational spectroscopic experiments.In wavenumber-resolved IR and Raman spectroscopy, anunambiguous assignment of vibrational bands to the cor-responding normal modes is required. In time-resolvedvibrational spectroscopy, probing photophysical processessuch as the S 1 ! S 0 internal conversion in ˇ -carotene, avisualisation of nuclear motions during normal modes isillustrative for understanding the phenomenon of vibroniccoupling in polyatomic molecules. 23 EXPERIMENTAL AND COMPUTATIONALDETAILS Measurementson ˇ -carotenewerecarriedoutwithaFouriertransform (FT) spectrometer (Bruker, Model IFS120 HR)equipped with a Raman module (Model FRA106). ForIR spectroscopy on ˇ -carotene prepared as a KBr pellet,a globar lamp and a mercury cadmium telluride (MCT)detector were employed. Raman excitation was providedwith a Nd:YAG laser (1064 nm) and an InGaAs detectorwas used. Raman spectra of polycrystalline ˇ -carotene wererecorded in a backscattering geometry (180 ° ) with a laseroutput powerof ¾ 300 mW. When employing NIR excitationat this power level, local heating cannot be excluded; nosample decomposition, however, was observed during theRaman measurements.DFT calculations were carried out using the Gaussian 98suite of programs 24 employing the pure density functionalBPW91 andthe6–31G(d)or6–31G*basisset.For ˇ -caroteneisomersandelectronicmodelsystems(seebelow), C i symme-try constraints were used. Redundant internal coordinatesweregeneratedusingtheprogramMOLDEN. 25 IRintensitiesand Raman activities were calculated analytically. RESULTS AND DISCUSSIONOptimized geometries In Fig. 1, the constitution formulas of the two investigatedisomers of ˇ -carotene together with the labeling of thecarbon skeleton are shown. Both configurational isomers arecentrosymmetric molecules as indicated. The correspondingoptimized geometries of (C 6 –C 7 ) s- cis - and all- trans - ˇ -carotene are displayed in Fig. 2(a) and (b). The calculation ofvibrational spectra yielded only real (positive) wavenumbervalues,indicatingthatstablestructureswereidentified.FromFig. 2(c) and (d), in which the carbon skeleton is presentedin a side view, the local symmetry of the polyene chainsand the conformationof the ˇ -ionone rings are recognizable.The polyene chain is essentially planar, hence for this partof the molecule local C 2h symmetry can be assumed; forthe ˇ -ionone rings a twist conformation is observed. Inthe case of the s- cis isomer, shown in Fig. 2(a) and (c),the calculated dihedral angle C 5 —C 6 —C 7 —C 8 of 42.9 ° indicates that the ˇ -ionone rings are tilted by almost 45 ° relative to the molecular plane and that the terminal double bonds are only in partial conjugation with the polyenechain. In contrast, the calculated dihedral angle of 171.9 ° indicates almost complete conjugation with the polyenechain for the all- trans isomer. A comparison of the absoluteenergies of both isomers reveals that, despite of its reducedconjugation length, the s- cis isomer is 8.8 kJ mol  1 morestable than the all- trans form. Because the computational i (a)(b) 1a1b123455a76911 131589a101213a1415' Figure 1. Constitution formulas of (C 6 –C 7  ) s- cis - (a) andall- trans - ˇ -carotene (b), together with the labeling of thecarbon skeleton (center of inversion i). Copyright  2003 John Wiley & Sons, Ltd. J. Raman Spectrosc. 2003; 34 : 413–419  Studies on ˇ -carotene 415 (a)(b)(c)(d) Figure 2. Geometries of s- cis - (a) and all- trans - ˇ -carotene (b)optimized at the BPW91/6–31G* level. The carbon skeleton isshown in a different perspective in (c) and (d). results refer to the gas phase, crystal packing effects can be excluded. A detailed analysis of this energetic aspect isgiven below. In the following, the characteristic structuralparameters of ˇ -carotene are discussed and a comparison ofexperimental and theoretical data is presented. In Table 1selected experimentally observed 26 and calculated bonddistances and angles of ˇ -carotene are listed. Experimentalvalues are taken from the x-ray structure of ˇ -carotene with(C 6 –C 7 ) s- cis configuration determined by Senge et al . 26 In general, alternating carbon–carbon bond lengths forthe polyene chain are noted. The constitution formulasshown in Fig. 1 suggest alternating single and double bonds because of the used valence bond (VB) notation. For bothexperiment and theory, the expected delocalization of the  -electron system, as predicted by molecular orbital (MO)theory, is verified; the C—C bond distances of the polyenechain assume values between those found for single anddouble bonds. In comparison with the X-ray structure, thecalculations overestimate the C—C single bond distances,e.g. C 1 —C 1A / B , C 1 —C 2 and C 6 —C 7 , by up to 0.022˚A or2.2 pm at the level of theory employed. Similar deviationsare observed for the C 15 —C 15 0 and the adjacent C 14 —C 15  bond. In general, the deviations of the theoretical valuesfrom the experimental data are considered to be small, withameandeviationof1.1%forthebonddistancesand0.4%forthe bond angles. Vibrational spectra Symmetry and computational considerations The mutual exclusion principle in vibrational spectroscopyprovides a simple but powerful criterion to test for the Table 1. Selected bond distances and bond angles of ˇ -carotene: experimental data (C 6 —C 7 s- cis configuration) 26 are compared with theoretical values, calculated at theBPW91/6–31G* level, for the s- cis and all- trans forms Exp. (s- cis ) Theo. (s- cis ) Theo. (s- trans )Bond distance (˚A)—C 1 —C 1A 1.529 1.551 1.553C 1 —C 1B 1.528 1.552 1.554C 1 —C 2 1.529 1.551 1.555C 1 —C 6 1.531 1.553 1.551C 2 —C 3 1.526 1.529 1.528C 3 —C 4 1.526 1.531 1.529C 4 —C 5 1.523 1.517 1.514C 5 —C 5  A 1.502 1.513 1.520C 5 —C 6 1.351 1.371 1.381C 6 —C 7 1.449 1.471 1.461C 7 —C 8 1.352 1.370 1.375C 8 —C 9 1.445 1.449 1.447C 9 —C 9 a 1.500 1.512 1.512C 9 —C 10 1.352 1.386 1.388C 10 —C 11 1.442 1.429 1.427C 11 —C 12 1.352 1.382 1.383C 12 —C 13 1.444 1.437 1.435C 13 —C 13 a 1.500 1.514 1.514C 13 —C 14 1.353 1.392 1.393C 14 —C 15 1.441 1.422 1.421C 15 —C 15 0 1.346 1.386 1.387Bond angle ( ° )—C 1 —C 2 —C 3 112.9 112.9 113.3C 2 —C 3 —C 4 104.0 109.0 108.7C 3 —C 4 —C 5 114.4 113.8 113.9C 4 —C 5 —C 6 121.5 122.7 123.5C 5  A —C 5 —C 6 125.9 124.4 123.7C 1 —C 6 —C 5 122.1 122.1 121.2C 5 —C 6 —C 7 122.2 122.8 117.6C 6 —C 7 —C 8 126.7 126.4 131.1C 7 —C 8 —C 9 127.2 126.3 125.4C 8 —C 9 —C 10 119.1 118.2 118.0C 9 a —C 9 —C 10 122.2 123.1 122.7C 9 —C 10 —C 11 127.3 128.4 128.6C 10 —C 11 —C 12 123.0 123.1 123.0C 11 —C 12 —C 13 126.1 126.7 126.9C 12 —C 13 —C 14 117.7 118.3 118.2C 13 a —C 13 —C 14 122.9 122.8 122.8C 13 —C 14 —C 15 127.7 128.3 128.6C 14 —C 15 —C 15 0 123.0 123.8 123.6 presence of a molecular center of inversion. The mutu-ally exclusive occurrence of IR- and Raman-active modesin the experimental FT-IR and NIR-FT-Raman spectrum of ˇ -carotene is indicated exemplarily for dominant bands bydottedlinesinFig. 3.Tothebestofourknowledge,thisisthe Copyright  2003 John Wiley & Sons, Ltd. J. Raman Spectrosc. 2003; 34 : 413–419  416 S. Schl¨ucker et al . 100015002000250030003500NIR FT RamanFT IR Wavenumber/cm -1    T  r  a  n  s  m   i  s  s   i  o  n   R  a  m  a  n   I  n   t  e  n  s   i   t  y Figure 3. Experimental FT-IR and NIR-FT-Raman spectra of ˇ -carotene. first direct comparison of vibrational spectra of ˇ -carotenegiving evidence for its centrosymmetry. According to theemployed symmetry constraints, all 282 normal modes of ˇ -carotenewereclassifiedaseitherRamanactive( a g symme-try)orIRactive( a u symmetry).Theaimofthispaperisnottoreproduce the experimental spectra to a high wavenumberprecision, but to reflect the observed major general featuresand trends. In general, calculated harmonic wavenumbervalues differ to a certain extent from experimental data because of anharmonicity effects. Only in the case of verysmall molecules such as water, for which the anharmonicityconstantstheexperimentallyobservedwavenumbersmaybeextrapolatedtohypotheticalharmonicvalues.Thelattermaythenbecomparedwithcalculatedharmonicvalues.Adiffer-ent approach includes the usage of scaling factors 27 , a some-how empirical method even if transferable scaling factors 28 are used. Therefore, it must be clearly noted that the goodagreement of the calculated harmonic wavenumbers withthe experimentally observed values obtained in this study isattributed to the well-known error cancelation in DFT. Comparison of experimental and calculated Ramanspectra In Fig. 4, the normalized experimental FT-Raman spectrumof ˇ -carotene (a) and the normalized calculated Ramanspectra of (C 6 —C 7 ) s- cis - (b) and all- trans - ˇ -carotene (c)areshown.Thecalculatedspectra,(b)and(c),werecorrectedfor the ω 0 ω 3 S intensity dependency of the Stokes photons( ω S ); ω 0 is the angular frequency corresponding to the1064 nm line of the Nd:YAG laser employed. In general,considering the large number of 141 Raman-active modes,the experimental NIR-FT-Raman spectrum is dominated by few intense bands. The Raman intensities of the C–Hstretching vibrations are extremely low, which is explainedin terms of insufficient instrument/detector response in thisspectral region. Because of the NIR excitation employed, ***0500100015002000250030003500 Wavenumber/cm -1    R  a  m  a  n   i  n   t  e  n  s   i   t  y (a) Exp.(b) Theo. (s-cis)(c) Theo. (all-trans) Figure 4. Experimental NIR-FT-Raman spectrum of ˇ -carotene (a) and calculated Raman spectra of s- cis - (b) andall- trans - ˇ -carotene (c). the appearance of so-called overtones at 2 Q  i can presumably be excluded. The strongly differing Raman intensities of ˇ -carotene normal modes can be understood in terms oftheir eigenvectors, which are presented for the first time inthis paper. The calculated eigenvectors of the Raman bandsindicated by an asterisk in Fig. 4 are shown in Fig. 5; forclarity of presentation, only eigenvectors at selected carbonatoms are shown. In Fig. 5(a), the eigenvectors of the CH 3 deformation mode, appearing at 1002 cm  1 in the calculatedspectrum Fig. 4(b), are shown. The nuclear displacementsalong the polyene chain and the ˇ -ionone rings explainthe considerable Raman intensity observed experimentally.The largest changes in polarizability occur for the C—Cand C C stretching vibrations at 1185 and 1513 cm  1 ,respectively; the corresponding eigenvector patterns areshown in Fig. 5(b) and 5(c). A comparison with Fig. 4(a)and 4(b) reveals that these modes give rise to the mostintensebandsinboththeexperimentalandcalculatedRamanspectra. The eigenvectors of a ˇ -ionone C–H stretchingvibration at 2925 cm  1 are displayed in Fig. 5(d).A significant deviation regarding the calculated andexperimentally observed Raman intensity is noted for the band at 1463 cm  1 in Fig. 4(b). A possible explanation forthis discrepancy is to regard it as the magnitude of possibleerrors in the calculated Raman activities of all normalmodes.Theapproximatepeakintensityratioofthedominantmodes at 1002, 1185 and 1513 cm  1 (0.13:0.73:1) observedin the calculated spectrum of the s- cis isomer in Fig. 4(b),however, reflects the observed experimental intensity ratio(0.15:0.79:1) in Fig. 4(a) fairly well. In contrast,the intensityratio calculated for the all- trans isomer (0.28:0.58:1) differssignificantly [Fig. 4(c)]. Copyright  2003 John Wiley & Sons, Ltd. J. Raman Spectrosc. 2003; 34 : 413–419
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