THE RAMAN EXCITATION PROFILE SPECTRUM OFB-CAROTENE Dissertation for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY ROBERT JAMES THRASH 1977 LIBRARY Michigan State University l. i u. This is to certify that the thesis entitled THE RAMAN EXCITATION PROFILE SPECTRUM of B-CAROTENE presented by ROBERT GAMES THRASH has been accepted towards fulfillment of the requirements for PH . D. degree in CHEMISTRY ”7 . If) 717, J, “v-1? #7., Major professor Date July 21, 1977 0-7639 ABSTRACT THE RAMAN EXCITATION PROFILE SPECTRUM OF B-CAROTENE By Robert James Thrash The Raman excitation profile spectrum of B-carotene was obtained in the energy range 16,900 cm"1 to 19,000 cm-l. This covers the region from the low energy tail of the strong visible absorption to where preresonance Raman effects become small. The spectrum, measured at room tem- perature in cyclohexane, consists of five features appear- ing at 18,830 cm'l, 18,710 cm'l, 18,600 cm-l, 18,380 cm‘l, and 18,280 cm-l. The two stronger features were assigned as carbon—carbon double bond stretching (18,830 cm'l) and carbon-carbon single bond stretching (18,380 cm‘l) modes, while the remaining features were assigned as carbon-hydrogen bending modes. It is suggested that these five features all belong to a low-lying 1Ag electronic state in B-carotene (C2h symmetry assumed). The origin of this state could not be found experimentally, but it is expected to be at 17,230 i 100 cm'l. This low—lying 1Ag state may play an important role in photosynthesis. B-carotene is known to serve as an ac- cessory pigment, transferring excitation energy to chlorophyll. If the energy transfer occurs via a Farster-type mechanism, then this low-lying state must be involved. THE RAMAN EXCITATION PROFILE SPECTRUM OF B-CAROTENE By Robert James Thrash A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1977 This work is dedicated to my wife, Pat, without whose support it would not have been possible. 11 ACKNOWLEDGMENTS I am deeply grateful for the support, guidance, and friendship provided by Dr. George E. Leroi. The inde- pendent atmosphere made pursuing this research project quite enjoyable and rewarding. Mr. Howard Fang is also deserving of thanks for many lively discussions as well as for much help in building the experimental apparatus. The remaining group members, happily many in number, are thanked for many great picnics and much encouragement. I gratefully acknowledge financial support from MSU and NSF. Finally, I wish to thank my parents for buying my first chemistry set and their constant encouragement. 111 LIST OF LIST OF CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER TABLE OF CONTENTS TABLES . . . . . . . . . . . . . . . . . FIGURES. . . . . . . . . . . . . . . . . . I. Introduction . . . . . . . . II. Theory . . . . . . . . . III. Experimental . . . . . . . . . . . . cw Dye Laser. . . . . . . . cw Dye Laser Alignment. . . . . . . Monochromator and Associated Parts. Experimental Procedure. . . . . . . IV. Results. . . . . . . . . . . . . V. Discussion . . . . . . . . . . . . . Interpretation . . . . . . . Comparison With Other Polyenes . . Implications of this 1Ag State . Suggestions for Future Work. . . . APPENDIX A . . . . . . . . . . . . . . . . . . . . APPENDIX B O O O O O O O O O O O O O O O O O O O 0 APPENDIX C . . . . . . . . . . . . . . . . . . . REFERENCES 0 I O O O O O O O O O O O O O O O O O 0 iv Page vi 1A 1h 18 22 30 “2 5h 5h 76 78 81 8A 87 88 98 Table II. III. IV. VI. VII, LIST OF TABLES Sample Excitation Profile Parameters and Calculated Points . . . . . . Tuning Ranges for the Dyes Useful in the cw Dye Laser. . . . . . . . . Parameters and Calculated Points of the Six State Excitation Profile Calculation . . . . . . . . . . . . Parameters and Calculated Points of the Seven State Excitation Profile Calculation . . . . . . . . . . . . Parameters and Calculated Points of the Seven State Calculation Using a6 = a7 = 105 . . . . . . . . . . . Energies of the Observed Excitation Profile Features and Their Differences. Comparison With Other Polyenes. . Page l2 17 59 62 66 71 77 Figure 10 11 12 13 1“ LIST OF FIGURES 8-Car0tene o o o o o o o o o o o o o o o o 0 Sample Excitation Profile Calculation Tunable Dye Laser Optical Cavity Configurations. . . . . . . . . . . . . . Power Output versus Wavelength Using Sodium Fluorescein with the 50% Reflectivity Output Mirror. . Correct Image of M2 on Card (2x). . . . . . Sample Housing. . . . . . . . . . . . . . . Block Diagram of the Experimental Apparatus . . . . . . . . . . . . . . . . . Wavelength Voltage Bucking Control Circuit . . . . . . . . . . . . . . . . . . 60 Hz Notch Filter. . . . . . . . . . . . . Current Amplifier and Voltage Integrator. . . . . . . . . Beer's Law Plots at 512 nm and 522 nm. . . . . . . . . . . . . . . . . Typical Point Using Electronic Integration . . . . . . . . Typical Point Using the Digital Computer. . . . . . . . . . . . . Typical Point Using Triangulation . vi Page 13 16 19 21 2h 25 27 28 29 32 35 38 no Figure 15 16 17a 17b 18 19 20 21 22 23 2A Excitation Profile Obtained by Electronic Integration, with a Portion of the Visible Absorption Spectrum. . . . . . . Visible Absorption Spectra of B-carotene at High and Low Concentrations. . . . . . . . . Visible Absorption Spectra of s-carotene Before (-) and After (---) an Excitation Profile Experiment. Visible Absorption Spectra of Fresh (-) and Two-Week Old (---) g-carotene Solutions . . . . . . . . . . . . Excitation Profile Obtained Using the Digital Computer. . . . . . . Excitation Profile Obtained by Triangulation . . . . . . . . . . Six State Calculation Using “6 = 2000. . . . . . . . . . . . Seven State Calculation Using 06 a7 = 2000. o o o o o o o o 0 Seven State Calculation Using a6 8 a7 "' 105 o o o o g g . Excitation Profile of B-carotene in the 0-0 Region . . . . Lycopene and Isorenieratene . vii Page “3 “5 147 U8 50 52 58 61 65 75 82 CHAPTER I INTRODUCTION The class of molecules known as linear polyenes, that is molecules consisting of an unbranched chain of alter- nating carbon-carbon single and double bonds, possesses both allowed and forbidden excited electronic states. Forbidden electronic states are those excited states which are inaccessible from the ground state by the ordinary electric dipole absorption of one photon. The polyene chromophore in the B-carotene molecule may be considered as having a center of symmetry despite the possible ab- sence of this symmetry element in the molecule as a whole (see Figure 1). This symmetry manifests itself in the electronic states by providing even or odd parity to the wavefunctions with respect to coordinate inversion. Group theory gives selection rules for ordinary one— photon absorption which require g + u or u + g transitions while forbidding g + g or u + u transitions.1 Since the ground state of the polyene molecules is a g state,2 then those excited electronic states which are also g states are the forbidden states referred to above. Elec- tronic states which are not accessible from the ground state due to spin multiplicity changes will not be dealt with in detail. In Chapter V it will be shown that spin forbidden transitions cannot play a significant role in Virtual Center of Symmetry Figure l. B-carotene. the experiments described in this thesis. Since most polyene ground states are singlet states, the forbidden states to be discussed are excited singlet g states of s-carotene. Since the 1930's there has been considerable doubt whether the lowest excited singlet state of polyene mole- cules has g or u symmetry.3 Early molecular orbital theory calculations, which agreed well with observed absorption spectra, predicted the lowest excited singlet state to be a u (therefore allowed) state. The emission properties of these molecules did not support this claim. Large fluores- cence Stokes shifts and long fluorescent lifetimes seemed to indicate the presence of some unobserved singlet state lower in energy than the strongly allowed u state. Recent experimental work on diphenyloctatetraene and similar molecules has demonstrated the existence of such a state of sufficiently low transition amplitude to be forbidden, hence a g state.“7 B-carotene is a linear polyene of considerable biological importance. Complete knowledge of its excited electronic state properties would be helpful in evaluating its role in photosynthesis. Because of the encouraging results obtained on the other polyene molecules and for its biological implications, B—carotene was chosen as a molecule in which to look for a low energy g state. Group theory predicts selection rules for two-photon absorption spectroscopy which allow g - g and u - u transi- 8 As tions while forbidding g - u and u - g transitions. a result, the observation of two-photon absorption processes would be an ideal way to locate this type of forbidden electronic state. For molecules in dilute solution the best method for detecting a two-photon absorption process is to monitor two-photon induced fluorescence.9 This tech- nique is useful primarily because of its high sensitivity even when the sample is in low concentration. However, there is recent evidence to indicate that B-carotene does 10 and that the not fluoresce when excited in the visible, fluorescence which was previously reported is likely to be from impurities. The direct observation of two-photon absorption could also be a possible technique for observ- ing the desired forbidden electronic states. However, these experiments generally require very high sample con- centrations and suffer the low sensitivities inherent in an absorption experiment. In view of the possible im- purity interference and inability to observe two-photon induced fluorescence or direct absorption (due to necessarily low sample concentrations of less than 10'2 M), it became necessary to use a different technique to study B-carotene. An alternative technique for seeking low energy for- bidden electronic states of the type expected for B-caro- tene is to examine the Raman excitation profile spectrum of the system.11 An excitation profile is obtained when one plots the Raman scattering intensity as a function of the excitation energy. This results in a graph which has the appearance of an absorption spectrum, but need not reproduce the ordinary absorption spectrum and contains additional information. In particular, the excitation profile may contain features indicating the presence of forbidden electronic transitions. A more complete descrip- tion of an excitation profile spectrum is given in the next chapter. The resonance Raman spectrum of B-carotene is well known,12 as is its excitation profile in the region of the strongly allowed visible transition.13 It is the purpose of this work to examine the excitation profile of e-carotene at energies somewhat lower than the strongly allowed state, in order to seek a forbidden electronic state in this energy region. This is the first work on the excitation profile spectrum of B-carotene in the preresonance region. Chapter II of this thesis briefly describes the theory necessary to understand the appearance of forbidden transitions in the excitation profile. Chapter III dis- cusses the experimental methods used in obtaining the excitation profiles and Chapters IV and V present and dis- cuss the results of this study. CHAPTER II THEORY Approximate formulas have been derived to demonstrate the appearance of forbidden electronic states in the 11’1“ These formulas also excitation profile spectrum. provide a method for estimating what the molecular pa- rameters must be in order to observe the forbidden state with an acceptable signal-to-noise ratio. An outline of the derivation and a discussion of the assumptions in- volved will be given here (from Friedman and Hochstrasser, Reference 1“). The amplitude for Stokes Raman scattering from a molecule originating in its ground electronic and vibra- tional state is proportional to Ro+v where: a RO+V = g 11 . 1 + A63 2"”; The subscripts o and v indicate the vibrational quantum numbers of the initial and final states, respectively. The energy differences AsJ are: where eJ is the energy of the 3th electronic state and ED is the energy of the exciting photon. The PJ are the damping factors and the aJ are given by: aJ = . 3 The quantity 03 is the geometric mean of the dipole strengths for the transitions connecting the initial and 14 For clarity final states with the intermediate state, 3. and mathematical simplicity it is initially desirable to assume that only two states are important in the summation over all the excited electronic states. This is equivalent to assuming that the forbidden state, which is being sought, and a nearby allowed electronic state are the only ones sufficiently close in energy to the exciting photon energy to be important contributors to the scattering intensity. This reduces equation 1 to: a a R = 1 + 2 . 1: o+v l 1 A61 + Eirl A6 + —1P 2 2 2 Here the subscript 1 refers to the term involving the forbidden electronic state and the 2 refers to the term involving the nearby allowed state. The Raman scattering intensity is related to the (complex) amplitude squared, which is: a a a + 2 ). a a 0: IR —_‘1 1 0*V Expansion of Equation 5 produces four terms: 02 a2 2 1 2 IRO+ I ‘ + 6a v 2 l 2 2 l 2 A81 + Erl A22 + Era s + “182 l 1 1 AelA52 + Frlrz + Aez§ifl - Ael§ir2 6b a a + a1 2 1 1 . 6c Ael TFF1P2 + A5121?2 - A€2§ir1 The two terms in part 6a are in their final form, but terms 6b and 6c may be reduced to: a 0*(Ae A6 + 1P P + As liI’ - As 2'-iI' ) 1 2 1 2 'E 1 2 12 2 22 1 6b. D and a'a (A6 A22 1r r2 + As llr - Ae 11r ) 1 2 1 E‘F 22 1 12' 2 60' D where D is given by: %(A€1F2)(A€§+ 1r2) 7 F'1F’2 ° Adding terms 6b' and 60' gives two new terms: * + A A +1r r (“1“ 2 “1“2) ( 81821i 1 2) 8a D and a a.(Ae lif -Ae lif ) + a.a (As l1? ~Ae l1? ) l 2 12 2 22 l 1 2 22 1 l2 2 . 8b D 2 I All of the terms needed for |Ro , which are 6a, 8a, and +v 8b, must be real due to the absolute square. However, if it is now assumed that a and 02 are real, then the term 1 8b vanishes leaving 02 a2 (As Ae +1? P )(Za a ) IR '2 _ l + 2 + l 2 E l 2 1 2 9 o+v Ac1+IT'P1 A82+ITP2 (Aei+%fi)(Ae§+%T§) Taking the exciting photon energy to be resonant with the forbidden electronic state, the situation of impor- tance in the current experiments, gives the three terms the following significance: The first term is a resonance Raman term, but it will contribute very little to the scattering intensity since “1 is very small in comparison to a2 because of the for- bidden nature of al. The second term is a preresonance Raman term arising from the nearby allowed electronic state and is the major contributor to the Raman scattered in- tensity at this exciting photon energy. The third term 1“ This is the is referred to as an interference term. term which will produce a feature in the excitation pro— file indicating the forbidden state. It is of significant magnitude due to the cross product 0102. It is useful to obtain the ratio of the interference 10 (I) term to the preresonance (P) term. This ratio pro- vides a means of estimating the parameters which will produce an observable feature in the excitation profile spectrum. (The resonance term containing ai is neglected since a2 >> a 1.) 1 (AelA82+nT1P2)(2alaz) 2 1 2 2 1 2 (A€1+HT1)(A62+ET2) 2 “2 B l 2 A8 2+n-r2 I/P = 10 This expression reduces to: l 2a1(AelA:2+u-I‘1P2) 11 I/P = 2 l 2’ a2(Ael+uT1) Taking y as the signal-to-noise ratio, I/P should be greater than y'1 for a significant feature to be observed. Let (12/0:1 - 10”, then (neglecting the r's) the effect will be observed if A22 A81 > 1ou/2y. '12 If the exciting radiation is resonant with al (that is, taking A61 2 r1), then interference will be detected when A A82 > 10 Pl/ZY. l3 11 If y - 5, then preresonance must be observed 103 cm-1 away from the allowed state (taking Fl-l cm'l) in order to observe interference with a forbidden state at that energy. The values substituted in these equations are only approximate and used here for demonstration purposes. Later these expressions will be employed to reproduce the observed excitation profile spectrum for B-carotene. Using Equation 9 it is possible to determine the ex- pected appearance of a Raman excitation profile spectrum. To this end a program was written for an HP250 calculator (given in Appendix A) to evaluate Equation 9 for various values of the parameters. The result of the calculation for the parameters listed in Table I is shown in Figure 2. Since the experimentally determined excitation profile is obtained by plotting individual points (each point being a measure of the Raman scattered intensity from B-carotene at a specific exciting photon energy), Figure 2 is a good approximation to the actual excitation profile. 12 Table I. Sample Excitation Profile Parameters and Ca1- culated Points. a1 . 1 r1 = 30 cm'1 e1 . 18,800 cm”1 a2 = 1000 r2 . 100 cm‘1 e2 a 20,700 cm'1 ep(cm-1) IRI2 sp(cm-1) IRI2 ep(cm-1) IRI2 18600 .231 18760 .289 18920 .306 610 .23u 770 .297 930 .311 620 .236 780 .307 9H0 .315 630 .239 790 .310 950 .319 6H0 .2u2 18800 .283 960 .323 650 .2uu 810 .252 970 .327 660 .2u7 820 .251 980 .331 670 .250 830 .258 990 .336 680 .253 8A0 .266 19000 .3u0 690 .256 850 .273 18700 .260 860 .278 710 .263 870 .28A 720 .267 880 .289 730 .272 890 .293 7u0 .277 18900 .298 750 .282 910 .302 Figure 2. 13 Excitation Profile (Arbitrary Units) 1 18,500 19,000 (Frequency (cm-1)) Sample Excitation Profile Calculation. CHAPTER III EXPERIMENTAL An excitation profile spectrum is obtained by measur- ing the Raman scattering of the sample excited by numerous different photon energies in the region of interest. The plot of the scattering magnitude as a function of incident photon energy is the excitation profile. Clearly some arrangement must be made to obtain the Raman spectrum of the sample at many pumping energies. cw Dye Laser The excitation source typically used for Raman spec- troscopy is a high power gas laser, such as an Argon ion laser. The several wavelengths available from these gas lasers can be used to obtain excitation profile data, but they have obvious tuning limitations. The wavelength region of interest for s-carotene is from 510 nm to 580 nm. This covers the range from the low energy tail of the absorption spectrum to the point where preresonance effects become very small. Since there are only a few gas laser lines in this range it was necessary to construct a continuous wave (cw) tunable organic dye laser for this investigation. Though this cw dye laser is similar to 1A 15 units which have since become commercially available, it possesses some unique features so its construction will be detailed here. The basic three-mirror folded optical cavity is shown in Figure 3a. This geometry was chosen rather than simpler two-mirror cavities for two reasons. First, the folding mirror M2 introduces an astigmatism which can be used to correct the astigmatism introduced by the dye volume placed at Brewster's angle.15 Second, this geometry eliminates the need for passing the high intensity pumping radiation through one of the dye laser mirrors, which would require costly special optics and optical coatings. The high intensity pumping radiation necessary to produce lasing in the dye solution is provided by a Spectra-Physics model 16A Argon ion laser. This gas laser is capable of producing four watts of output power if operated in what is referred to as the "all-lines mode". This means adjusting the optical cavity of the gas laser so that it may lase on most of its possible wavelengths simultaneously. To take full advantage of this high power multi-line pumping radiation it was necessary to use a dye flow system which would neither sustain damage due to decomposed dye nor introduce a chromatic aberation on the pumping radiation. An unconfined (that is, no dye cell) flowing jet stream is used to transport the dye solution at a high velocity through the active pumping region. A Spectra-Physics model 376 dye circulator and nozzle 16 .mCOHpmsstmcoo mpa>mu Hmoapqo nomad can manmcse .m madman \/ 9 \xxx ll \ \ mwwa on amazoaucmmsma ma m2 soapsHom mmu mo 30am: poppfiz Ucm namm “VIM; w: mace a m .059 x \ wcfiuwso smppwaam coapomsMMHo Emmm LIII'II'I'I'I.-I.I.III I'l- Lllll "" ""' OD r a: gonna: psspso \ \ \ as i \ 2.1 .. 17 were used for this purpose. In order to maintain a uni- form dye film in the active region it is necessary to use a rather viscous solvent for the dye. For the dyes used in this laser (see Table II) the best solvent is ethylene glycol. See Appendix B for dye solution preparation. Table II. Tuning Ranges for the Dyes Useful in the cw Dye Laser. Dye Tuning Range Sodium Fluorescein 525 nm to 575 nm Rhodamine 6 G 570 nm to 610 nm Rhodamine B 590 nm to 6&0 nm Tuning of the ow dye laser is accomplished by adding a rotatable diffraction grating to the optical cavity just outside the output mirror, as shown in Figure 3b. Mounted in the Littrow configuration, the grating reflects a selected wavelength (dependent on the grating rotation) back into the laser cavity. This decreases the cavity loss at that specific wavelength, causing the dye to lase only at the chosen wavelength. By adjusting the angle of the diffraction grating the output of the dye laser can be tuned over a broad wavelength range. The dyes useful in this laser, together with their tuning 18 ranges, are listed in Table II. When the tuning tech- nique described above is employed the linewidth of the cw dye laser output is approximately 0.1 nm. The combina- tion of the mirror and grating at the output end produces an optical cavity of very low overall loss. Consequently, in order to obtain usable light output, it is necessary to insert a beam splitter into the optical cavity. This element is located between the output mirror and diffrac- tion grating and couples out approximately ten percent of the radiation present in this part of the cavity. One feature of this overall system, which is very useful, is that the cw dye laser output power is inherently nearly constant over much of the tuning range (except near the tuning limits) without requiring complicated power adjust- ing circuits. The output power as a function of wavelength is shown in Figure A. The power available for the excita- tion profile experiments varied between five and forty milliwatts and remained stable for a period of 10 to 30 minutes at a given wavelength. cw Dye Laser Alignment Since this cw dye laser is "home-made" and easily disassembled and moved, it is necessary to understand the procedure for aligning the optical cavity. Referring to Figure 3a, the specific optical elements of this dye laser are as follows: the concave mirrors Figure A. Intensity (Arbitrary Units) 19 l l l 525 535 595 Wavelength (nm) Power Output versus Wavelength Using Sodium Fluorescein with the 50% Reflectivity Output Mirror. 20 M2 and M3 are five cm radius of curvature mirrors with high reflectivity dielectric coatings useful in the range from about 500 nm to 650 nm. The output mirror M1 is a flat mirror with either 96% reflectivity at 632.8 nm or ~50% reflectivity over the range from 500 nm to 600 nm. The focusing lens is achromatic and has a focal length of 2.5“ cm. When these optical elements are properly selected and adjusted the dye laser cavity is suitable for any of the dyes listed in Table II. Adjusting the optical elements is done as follows: Step 1. With the Argon ion laser operating at low intensity (mlOO mwatts) adjust the output so that it strikes the flowing dye approximately 0.5 cm from the nozzle (all other optical elements removed). Step 2. Adjust the angle of the dye nozzle to Brewster's angle by tilting it until the reflected laser intensity is a minimum. Step 3. Insert the focusing lens in the path of the Argon ion laser beam and bring the light to a sharp focus on the dye stream. Step A. Insert the mirrors M1 and M2 in their ap- proximate locations. Turn up the Argon ion laser to full power. The distance of M2 from the dye will be determined experimentally. The M1 distance should be about 30 cm, but it is not critical. Adjust the reflected light from M2 so that it strikes M1 in the center. Then adjust M1 so that the light strikes a 21 card mounted on top of the ion laser. The light on the card will produce an image which depends on the M2 distance. (It also depends on the M1 distance, but Ml should remain fixed.) Adjust the distance of M2 until the image looks like Figure 5. (Be sure to keep the reflected light striking the center of M1.) Figure 5. Correct Image of M2 on Card (2x) Step 5. This is the most difficult step. It is now necessary to insert mirror M3. The light reflected from M3 must pass through the active region of the dye film (where the pumping light is focused), then strike M2 and be reflected to M1 and thence to the card. Once the light reaches the card, all that remains is to adjust its image to be identical to that from M2 and then superimpose the two images. In doing all this, be sure not to move M2 or Ml. Step 6. The last step is to adjust M1 so that the reflected light now strikes M2 in about the lower middle portion of the mirror and the dye laser should lase (if rhodamine 6 G is the dye being used; if 22 one of the others, the grating may also need to be aligned to obtain lasing). The diffraction grating (1200 grooves/mm, blazed at 500.0 nm) is simply aligned by placing it about 20 cm behind the output mirror and adjusting the first order reflection so that it exactly reenters the dye laser. Now slight rotation about the vertical axis of the grating should change the dye laser output radiation (tuning). Once aligned and operating, the dye laser will need only periodic minor adjustments of M3 to keep it perform- ing at full output power. However, when restarting the laser after turning off the dye flow it will be necessary to adjust slightly all three mirrors due to minor changes in the dye flow characteristics. Monochromator and Associated Parts The monochromator used for dispersing the Raman scat- tered radiation was a Spex lAOl double monochromator with slits adjusted so that it could be used as a single monochromator to maximize throughput. The scattered radia- tion was detected using an RCA C3103A photomultiplier tube cooled with solid dry ice. The sample solution being studied was contained in an ordinary 1 cm spectro- photometer cuvette having all four sides optically polished. During the experiment the sample cell was placed 23 in a housing mounted directly on the entrance slit of the monochromator. This housing, shown in Figure 6, con- tained a 2.5" cm focal length collection lens which focused the 90° scattered radiation onto the entrance slit. The housing also had provisions for mounting colored glass filters on the entrance and exit holes in order to control stray radiation. The laser light was focused into the sample by means of a 10 cm focal length lens mounted a short distance from the sample housing. A complete block diagram of the experimental apparatus is shown in Figure 7. The data involve two electrical signals. One signal comes from the monochromator and provides a voltage which is proportional to the wavelength passing through the exit slit. The second is the current signal from the photomultiplier tube, which is proportional to the scat- tered light intensity. Two electronic circuits were de- signed to handle these signals and make them compatible with oscilloscope or X-Y recorder displays. They are described in detail here. The purpose of the wavelength voltage bucking control circuit is as follows. The wavelength drive of the Spex 1901 monochromator controls the slide of a variable potentiometer. When the proper voltage is applied across the potentiometer, the voltage measured from the slide gives the wavelength, where one millivolt corresponds to 0.1 nm. In the wavelength range of interest, this 2n Collecting Lens Cuvette Sample Mounting Block Figure 6. Front View Entrance Slit Foam Rubber Lens Laser Light +3.0 cm+3.5 c1114 Side View Sample Housing. Entrance and Exit Sample Mounting Block 25 Wavelength Monochromator %0 cm f°1 Control ens r -: ":3 :7.‘:::. Dye PMT :”3 """"" ‘ Laser x 7 Sample X-Y Recorder Y Integrator Argon Laser Figure 7. Block Diagram of the Experimental Apparatus. 26 corresponds to approximately six volts. However, during data collection only small changes in wavelength are made (approximately 10 nm) which produce only small changes in a large DC voltage. Thus the main purpose of the buck- ing control circuit is to remove that large DC voltage, leaving the voltage changes to be recorded. This is ac- complished by adding a bucking voltage to that produced by the wavelength potentiometer sufficient to set the total voltage nearly equal to zero; thus only the voltage difference is detected on changing the wavelength. Since a wavelength change of 10 nm produces a voltage change of only 100 mV, the bucking control circuit also contains an amplifier with a gain of 10. The circuit has a pro- vision for precisely adjusting the voltage supplied to the wavelength potentiometer as well as a control to set the bucking zero point. The schematic diagram for this circuit is shown in Figure 8. The circuit connects directly to the wavelength potentiometer of the mono- chromator and its output leads to the X input of an X-Y recorder through a 60 Hz notch filter. This filter was inserted in the circuit to eliminate the 60 Hz noise which is picked up along the great lengths of wire connecting the various components. The schematic diagram for this filter is shown in Figure 9. The most important electronic circuit in this experi- ment is the current amplifier-voltage integrator. Shown schematically in Figure 10, it consists of two major 27 Neon Lamp 1/8 Amp 1\ 56.2 k9 l DPDT "8 u v L " + ‘ Boston Tech Dual Power Supp 15 V 100 ma. 8.2 km -15V com. +15V - I" 1 AM— ;?200 k9 100 kn 5 kn 100 kn A J— 't' n:- A A A To Monochromator Output Wavelength Pot Figure 8. Wavelength Voltage Bucking Control Circuit. 28 30 k9 Input 30 k9 1/2 I“? 15 kn 1/2 7A7 7.5 kn l l_ 10 k9 *- 1r luF Figure 9. 60 Hz Notch Filter. Output 29 Output BNC AMP. INT. N.O. Reset ——-l F—T _L.. l—Jwv—l I I I j I 66 M9 111'? Input BNC LHO0A2 + CD 10 RC 1.5 M9 1.5 M9 -15 V +15 V Figure 10. Current Amplifier and Voltage Integrator. 30 parts. The current coming from the phototube is treated by the first part of the circuit to produce a voltage signal which is proportional to the scattered light in- tensity. This voltage signal can be sent directly to the Y input of the recorder for the purpose of recording the normal Raman spectrum of the sample. However, at the option of the experimenter a switch can be thrown, sending the voltage signal to the second part of the circuit which electronically integrates the voltage signal. This inte- grated signal, when recorded, is directly proportional to the area under the Raman peak being investigated. The circuit is particularly important because it is this peak area which is the experimental quantity being mea- sured. The next section describes the use of all of these elements in obtaining the experimental data. Experimental Procedure The B-carotene used in these experiments was the synthetic, all-trans form obtained from Sigma Chemicals Company. It was stored in a dark bottle under nitrogen, in a freezer, and used without further purification. Thin-layer chromatography revealed one fluorescent im- purity in the sample. The solvent for all the solutions was spectro-grade cyclohexane, also used without further purification. Solutions of B-carotene in cyclohexane of sufficient concentration for the Raman excitation 31 profile experiments were prepared in the following way. An excess of B-carotene was added to a small quantity of cyclohexane (approximately 25 m1.). After dissolution for about 15 minutes in darkness the colored solution was transferred by pipet to the sample cuvette, with special care being taken not to transfer any undissolved B-carotene. At this point the visible absorption spectrum was obtain— ed as a means of determining the sample concentration. Figure 11 shows two Beer's law plots at different wave- lengths (512 nm and 522 nm). The slopes (determined by least squares) were used to calculate the sample concen- “M trations. The concentrations ranged between 7 x 10- to l x 10-5 M in B-carotene. A fresh sample was always prepared just prior to performing an experiment. The cuvettes used in these experiments were equipped with tight fitting Teflon stoppers for two reasons. First, the cyclohexane would otherwise evaporate rapidly, thereby changing the sample concentration during the course of an experiment. Second, nitrogen gas was bubbled through each sample for five minutes just prior to each experi- ment in an effort to reduce the effect of dissolved oxy— gen, which is to enhance singlet-triplet transitions. After sample preparation in this manner the cuvette was placed in the sample housing to minimize the effects of room light. As mentioned earlier, the Raman excitation profile spectrum consists of a plot of the Raman scattering 32 8 ,/ t5. / .0 l d. ‘ $4 I o I a) l n x/ d: I I I ” ,’ 522 nm,- a: I ’a"’ I ,a" I ’a’ ,’ ”,n" Slope = 1052.26 If, a”“’" flgv“' L l l .l l 1 x 10'" 5 x 10‘“ Concentration (M) Figure 11. Beer's Law Plots at 512 nm and 522 nm. 33 intensity as a function of excitation photon energy. More specifically, what is plotted is the intensity of a selected B-carotene Raman transition as a function of excitation photon energy. In order to obtain a value of this intensity which is independent of instrumental contributions it is necessary to record the ratio of the measured B-carotene band intensity to that of some internal standard. Several instrumental effects are eliminated by this procedure. The scattered Raman intensity depends on the intensity of the source radiation. The cw dye laser pumping radiation does not have constant power as a func- tion of the tuning wavelength. An internal standard Raman band would experience the same laser intensity dependence as the B-carotene scattering, so a ratio of the two eliminates that dependence. Other factors, such as ex- tent of focusing, which affect the apparent pumping inten- sity, are also eliminated by the ratio. If the difference in wavelength of the two bands being considered is very small, then this procedure will also eliminate factors which directly influence the apparent scattered intensity. Among these factors are phototube response variations as a function of wavelength and monochromator throughput variations as a function of wavelength. If proper ac- count is taken of all instrumental contributions to the sample scattering intensity, the excitation profile plot should provide only the molecular response. The internal standard used in all of these experiments is a Raman line 3“ from the solvent, cyclohexane. Specifically, the B- carotene band used is the one at Av = 1525 cm'1 and the cyclohexane band at Av - 1uu7 cm'l. At 600 nm this cor- responds to a difference of 2.8 nm. The intensity ratios actually used in drawing excitation profile plots were obtained in three different, indepen- dent ways. The reason for using several distinct tech- niques was to insure reproducibility in the absence of technique-dependent artifacts. The three techniques will be discussed in detail here. The first and most often used method for obtaining the ratio of B-carotene Raman scattering intensity to cyclohexane reference intensity involved the direct use of the electronic voltage integrating circuit. Figure 12 shows typical experimental data for a single point on the excitation profile. This was obtained by first re- cording the normal Raman spectrum of the neighboring B-carotene and cyclohexane peaks with the amplifier-in- tegrator circuit switched to the amplify mode. Then without changing anything but the monochromator scan speed and recorder vertical response, the amplifier- . integrator was switched to integrate, and the areas under the peaks were recorded several times in quick succession. The monochromator was always scanned from long wavelength to short (that is, going over the B-carotene band first) at a speed of ".0 on the scan control (approximately 5 nm per minute) for the normal spectrum and 30.0 U) k“ f4 Intensity (Arbitrary Units) 11 1525 luu7 Frequency (cm-1) Figure 12. Typical Point Using Electronic Integration. 36 (approximately “0 nm per minute) for the integration (the high scan rates were needed to minimize the effects of the dye laser fluctuations). The analysis of this type of data display is quite straightforward. The vertical change in the integrator signal in passing over the first Raman peak is directly proportional to the area under that peak (marked A in Figure 12). This length, A, is determined by averaging the starting positions (marked 1) and the ending positions (marked 2) of the integrator out- put trace, and then simply measuring the indicated distance, A, in millimeters. The process is repeated for the second peak, giving a value for the distance B. In order to have the complete information ready for plotting on the ex- citation profile graph, all that is necessary is to take the ratio A/B and to indicate the photon energy used to generate this particular pair of Raman signals. It should be pointed out here that a number of data points recorded in this manner displayed considerable fluctuations in the integrator output plots. These fluctuations were the reason for the averaging done in regions 1, 2, and 3 of Figure 12. The cause of the fluctuations remains un- known at this time. At first it was thought that thermal effects caused by the laser light were responsible. How- ever, spinning the sample, which should have eliminated any thermal influence, resulted in no improvement. A second possibility was that the fluctuations were due to noise in the output of the cw dye laser. However, 37 improvement was also not observed when the same type of experiment was performed using the very stable output of the ion laser directly. The fluctuations did not cause any special difficulty and are not considered further. The second and most sophisticated method employed for determining the necessary ratio involved the use of a Digital Equipment Corporation PDP 8/I mini-computer. The computer software and the accessory electronic devices used in the data acquisition were provided by a separate research group and are very well described in Reference 16; thus only the modifications and use will be detailed here. In this method the output from the current ampli- fier was sent to the input of a voltage-to-frequency con- verter. One such device was set up to produce a frequency signal proportional to the intensity of the Raman scattered radiation and a second was used to produce a frequency proportional to the dye laser intensity. These two sig- nals were sent to a computer interface in which they were counted and these digital data were input to the computer. The computer then divided the Raman counts by the dye laser counts, thereby providing a signal as a function of time which was proportional to the Raman scattered inten- sity and independent of the time variations in the dye laser intensity. Since the monochromator was scanned in time, the computer time is proportional to wavelength. A typical output plot of such an experiment is shown in Figure 13. As before, one of these plots was obtained 38 Relative Intensity (Arbitrary Units) Time (Arbitrary Units) Figure 13. Typical Point Using the Digital Computer. 39 at every dye laser wavelength needed to produce an excita- tion profile spectrum. In Figure 13 each point has associated with it a number of counts. Since the points are separated by unit time periods, the area under each peak is simply the sum of the count values for the points making up the peak. This data collection technique was not often used because of an overwhelming increase in the time needed for data collection and evaluation, and because of delays caused by lack of availability of com- puter time. However, excitation profiles obtained with this technique were consistent with those obtained using electronic integration. , The third and simplest data collection technique con- sisted merely of carefully recording the Raman spectrum at each dye wavelength (several times, each over the other, to insure adequate reproducibility and proper average) and then measuring the area under each peak by triangulation. Figure 1A shows the result of a typical experimental run. This technique was chosen because it removes all electronic area measuring artifacts, but it was rarely employed because of the subjectiveness in the manual area determinations. Again, the excitation profiles obtained in this way were consistent with those obtained by the other methods. One instrumental factor that could not be eliminated is the fact that the monochromator is linear in wave- length not wave number. At first, this seems like cause Intensity (Arbitrary Units) Figure 1A. HO l l 1525 1NU7 Frequency (cm-l) Typical Point Using Triangulation. Al for concern since the peak areas should be determined as a function of wave number. However, since the peaks were so narrow, the deviation from linearity (of the energy representation) is less than one percent and can be ignored. Thus having the display linear in wavelength poses no problem. In Chapter IV of this thesis an excitation profile spectrum obtained by each of these methods will be shown. The rationale behind the choice of the particular experi- mental parameters (gpgp, slit width) will be discussed in that section. CHAPTER IV RESULTS The Raman excitation profile spectrum of B-carotene reveals five basic features which are different from any feature observed in the ordinary (one-photon) visible absorption spectrum. These new features are peaks in the excitation profile spectrum at 18,830 cm'l, 18,710 1, and 18,280 cm‘l. The cm'l, 18,600 cm'l, 18,380 cm- remainder of this chapter will be devoted to describing in detail how each of the three methods were used to demonstrate the existence of these features, and what other experiments were done to insure that they are indeed due to B-carotene. Figure 15 shows a plot of the excitation profile in the range from 17,600 cm"1 to 19,000 cm'l, obtained using the amplifier-integrator circuit. Included in the figure is a portion of the ordinary visible absorption spectrum for comparison. The features mentioned above at 18,830 1 1 and 18,280 cm'1 are clearly cm'l, 18,710 cm' , 18,380 cm- visible. (The fifth peak is too weak to be seen in this spectrum.) Each point in this plot is the result of a graph similar to Figure 12. That is to say, to produce the plot of Figure 15, 59 such integrations were recorded, each having its own area ratio and corresponding exciting photon energy. (Only 57 points appear in the plot because “2 .Esapowam cofiuaaomn< manfimfi> on» no coappom m npfis .cofipmswmpCH eacospomam an pmcfimuno mHHmoam coapmpaoxm .mH mpswfim AHIEoV mocmsuonm ooo.mH oom.ma ooo.ma _ _ _ \\ \ \\ .00 \ O. \ . \ oeo \ .. \ .. \ . . \ .. \ as... \ o «(J \ no. .0 ha \ o o x .. x .. x \ a \ ..... a . . ‘ . . x a (serum KJPJQTQJV) artsoaa uorseqroxa Ah the points were averaged by taking a quarter of the i-lth point plus half of the 1th point plus a quarter of the i + lth point as the value for the 1th point. Consequently the first and last points were dropped.) The concentration of B-carotene used in this experi- -h M. (At concentrations below about ment was 5 x 10 1 x 10'" M the excitation profile features are lost in the background noise.) In doing experiments at such high concentrations one worries about molecular aggregation giving rise to new absorbing species, which are usually dimers, as observed in other polyene systems.17 In order to determine if such a problem is occurring in these experi- ments, the following test was performed. The visible absorption spectrum of B-carotene at high concentration was recorded using a 1 mm path length cuvette (in order to keep the spectrum on scale). That solution was then diluted by a factor of ten and the spectrum recorded again using a 10 mm path length cuvette. Figure 16 shows the result of this test. The fact that the two spectra appear identical indicates that no new species are formed at the higher concentration. Another problem that may arise in these types of experiments on polyene molecules relates to the photo- chemical stability of the sample. Several hours of ex- posure to the laser radiation (even at low intensity) could produce a new absorbing species by means of cis- trans isomerization. To check this possibility, the Absorbance “5 2.0 dr 5.“ x 10:5 M I n a 10 mm cell 9.9 x 10‘" M in a 1 mm cell 1°.0 di- l I “00 950 500 Wavelength nm Figure 16. Visible Absorption Spectra of B-carotene at High and Low Concentrations. A6 visible absorption spectrum of the sample was recorded before and after each experiment. Figure 17a shows a typical example of such a test. Again the spectra are nearly identical, indicating very little or no change in the sample during an excitation profile experiment. Figure 17b demonstrates that a sample exposed to room light for several days shows considerable change in composition. This was one of the reasons for preparing a new sample before each experiment. Assuming that the design of the experiment eliminates influences of instrumental artifacts, and that the above tests adequately cover their respective problems, then the only remaining possible interference in the excitation profile spectrum is the presence of an impurity. The following discussion describes why impurities are not a significant problem in this type of experiment. The resonance enhanced Raman spectrum of B-carotene has been extensively studied (see Reference 12 and refer- ences contained therein). Thus it is possible to select with confidence those bands in the Raman spectrum which are due to B-carotene. Likewise, bands due only to the solvent, cyclohexane, can be chosen with certainty. If one is very careful to measure the peak area of a band due exclusively to B-carotene and compare it to a band area due exclusively to cyclohexane, then it is extremely unlikely that an impurity could make any contribution to the excitation profile spectrum. The only way an impurity A7 .pcoEasmaxm sawtoaa ccapmpwoxm ca nillv smpm< cam AIV oaomom osopoamolm mo aspomnm soapOhomn< oHnHmH> Ascv nuwccam>m3 oom om: ooa omm . _ Ia -11: to- _ .mpa mpswam mmm IT 04 Ar m4 aousqaosqv A8 .mCOHpsHom osouosmoum Annie eHo essences sea AIS amass so «seesaw sofisasoan< sansafl> .nefl themes Ascv summoam>mz oom om: co: 0mm mmm .III a _ _ q q .1.I I a v I I III III ’ V|IIOI I \\ "lill--'|'ll‘-lu ’ \ ’ \\\ a, \\ 1i m.o o \\ I \\ ’7‘-.. .t. I \\ II\\\ AT o.a eousqaosqv A9 could still contribute would be if it had 3 Raman band precisely overlapping the relevant B-carotene or cyclo- hexane bands. Even so, this should manifest itself by altering the band shapes during the course of the experi- ment. Since the band shapes did not significantly change, the problem of impurities was not pursued further. When the digital computer was used to acquire excita- tion profile data the spectrum shown in Figure 18 was obtained. (Only the two strongest peaks appear in this spectrum because so few points were taken.) The main motivations for using the computer to acquire data were to take advantage of its ability to integrate out temporal fluctuations in the signal, and to use the data to deter- mine the effects of slit width on the excitation profile. The slit width effects could not be determined using the analog methods because of the extremely low light levels at narrow slit widths. In addition to collecting the data plotted in Figure 18, the computer was used to de- termine the B-carotene/cyclohexane peak area ratio at a constant pumping wavelength with three different slit widths: 1000 pm, 500 um, and 200 um.(the monochromator dispersion is 1 nm per mm). The measured area ratios at each slit width were .3799, .3927, and .A067, respectively. It is assumed that the ratio obtained with the 200,m.s11t is the best value since it suffers least from peak overlap. However, 2001nnslits pass too little light to get an adequate signal-to-noise ratio when analog methods are Figure 18. Excitation Profile (Arbitrary Units) 50 l J 1 18,000 18,500 19,000 Frequency (cm'l) Excitation Profile Obtained Using the Digital Computer. 51 employed. With lOOOinnslits, the Raman signals were ample, but the peak area ratio showed considerable deviation from the 2001m1va1ue. Therefore, 5001nnslits were used for all the experiments reported in this work. There was sufficient light for a reasonable signal-to-noise ratio and the devia- tion of the area ratio from that obtained with 2001mislits was small. A third motivation for using the computer was to obtain a Raman excitation profile spectrum which was independent of any mechanical peak area measurement devices (including X-Y recorders). Presumably, the areas measured with the mini-computer are the most precise, but because of the time problem mentioned earlier the method was not often used. Since the features evident in Figure 18 are equiva- lent to those obtained by the other techniques, those methods were considered adequate. Figure 19 shows the excitation profile spectrum ob- tained when triangulation was used to measure the peak areas. (All five features appear. These data were aver- aged in the same way as those of Figure 15.) For this ex- periment a polarization scrambler was placed just before the entrance slit of the monochromator in order to be certain that no polarization anomalies were interfering with the excitation profile. The spectrum is just like the others indicating that polarization anomalies are not interfering. The fifth and weakest feature may only appear in this spectrum because the polarization scrambler Excitation Profile (Arbitrary Units) Figure 19. J 1 18,600 Frequency (cm- 19,000 Excitation Profile Obtained by Triangulation. 53 increases the apparent sensitivity. The main reason for using the triangulation method was to obtain peak areas which were independent of any kind of electronic integrating device. The fact that the excita- tion profile spectrum shown in Figure 19 displays the same features evident in Figures 15 and 18 supports the quality of the data obtained by the other methods. In the following chapter the discussion will center around the data shown in Figure 19, because they are the most complete. It should be remembered, however, that those data are confirmed by the results obtained by com- pletely independent methods. CHAPTER V DISCUSSION This chapter is devoted to the elaboration of the experimental results and their interpretation in terms of the excited states of B-carotene based on the formalism of Chapter II. The chapter will be divided into four parts. The first will deal with the extensions of the material of Chapter II necessary to be useful in inter- preting the B-carotene excitation profile spectrum. The second part will compare the results obtained for B-caro- tene with the results obtained for similar polyenes. The third section will discuss the implications of this work relating to the role of Becarotene, and carotenoids in general, in nature. Finally, the chapter will conclude with suggestions on experimental improvements and future projects. These discussions will center around the experi- mental conclusion that B-carotene possesses a singlet "g" state (presumably 1A3) at 17,300 a 100 cm'l. Interpretation The equations of Chapter II, and in particular Equation 9, which were used to calculate an expected excitation profile shape (Figure 2) can also be easily extended to reproduce the observed B-carotene spectrum in a 5A 55 qualitative way. The calculation of the expected excitation profile, which involved two states (one allowed and one forbidden), produced a curve containing a single feature in the region of the forbidden state. By direct compari- son, then, the minimum number of states necessary to re- produce the B-carotene excitation profile spectrum would be six, because the observed excitation profile displays five features in a region where there is no allowed transi- tion. Anticipating the need to take additional allowed states into account, the form of equation 9 will be ex- tended to a calculation involving seven states. It will be convenient to rewrite Equation 9 in a very slightly different form: 2 2 1 IR' 2 _ “1 + “2 + (A51A52TFP1F2)(“1“2) o+v 2 l 2 2 l 2 2 l 2 2 l 2 Ael+ufl A€2+ET2 (Ael+Fr1)(A62+uf2) 1 (As As + P r )(a a ) + 1 2 F'1 2 2 1 1A 2 l 2 2 1 2 (Ael+nr1)(Aez+Fr2) Recalling the complex nature of the expressions involved and representing the complex form x + 1y by a single letter (e.g. a) then Equation 1A can be reduced to: IR 2 - |a|2 + |b|2 + ab“ + ba* 15 o+v| 56 which originated from IR l2 = (a+b)(a*+h*). 16 o+v Note that Equation 16 is of the same form as Equation 5. If Equation 16 represents a two state situation, then 2 I [R = (a+b+c+d+e+f+s)(a'+b*+c*+d*+e*+f*+g*) 17 O+V represents the desired seven state situation. Carrying out the indicated multiplication in Equation 17 leads to: IR 2 -- Ia:2 + Ital2 + Icl2 + Ian?- + Iel2 + In? + Isl2 o+v| +ab*+ac*+ad*+ae*+af*+ag*+ba'+bc*+bd* +be'+bf*+bg*+ca*+cb'+cd'+ce*+cf*+cg* +da*+db’+dc*+de*+df*+dg*+ea*+eb*+ec*+ed* +ef*+eg'+fa*+fb*+fc*+fd'+fe*+fg*+ga*+gb* +gc*+gd*+ge*+gf' 18 which is just like Equation 15 and thus can be used to generate all the terms necessary to write a seven-state equation just like the two-state Equation 9. It is clear that a calculation using the twenty-one pairs of cross- terms and seven squared terms formed in this process would 57 be well beyond the programming capacity of a A9 step cal- culator. However, a program was written for use on a HP-67 calculator (22A steps) and is given in Appendix C along with the actual form of the equation obtainable from Equation 18 used to calculate the seven state excitation profile spectra. A calculated excitation profile spectrum taking account of five forbidden states and only one allowed state is shown in Figure 20; Table III lists the parameters and calculated points (the parameters were chosen to give a reasonable appearance). The energy chosen for the allowed state was that of the lowest energy visible absorption band, which should be near in energy to the ground vibra— tional level of the allowed excited electronic state. The important points to note about this calculated spectrum are first, it shows all the observed features in approxi- mately the correct relative intensities; and second, it fails to correctly reproduce the proper background increase in slope at higher energies. This can be corrected in two ways. One way would be to increase the value of a for the allowed state. However, this is equivalent to making the forbidden states more forbidden, thereby decreasing the intensity of the five features. The second way in- volves the following consideration. The second peak in the visible absorption spectrum appears at 22002 cm'l, only 1300 cm"1 higher in energy than the state being used in the calculation (which is ca. 1900 cm"1 higher than the Excitation Profile (Arbitrary Units) Figure 20. l 1, l 18,600 19,000 Frequency (cm—1) Six State Calculation Using “6 = 2000. 59 Table III. Parameters and Calculated Points of the Six State Excitation Profile Calculation al - 2 as - a7 = 2000 61 = 18,280 cm-1 02 . 3 r1 . r2 = r3 . r“ = r5 = 50 cm ’1 e2 = 18,380 cm‘l a3 - 1.5 r6 . r7 - 200 cm’1 83 . 18,600 cm‘1 “A - 2 56 == 20,700 cm-1 EA = 18,710 cm-1 as a 5 e7 8 10"9 cm-1 65 - 18,830 cm"1 ep IRI2 ep 19 Where We represents the electronic part of the wavefunction, TV represents the vibrational part of the wavefunction; and double prime, j, and prime refer to the initial, inter- mediate, and final states respectively. An examination of Equation 1A indicates that in order for a peak repre- senting a forbidden state to appear in the excitation pro- file spectrum the quantity “j must be different from zero for the forbidden state j. It is clear that if state j is an allowed state, then “j will be a large quantity. To see how 03 can be non-zero (but probably very small) for a forbidden state, j, it is necessary to consider the effects of vibronic symmetry. In general, when discussing whether a transition from the ground electronic state to some excited electronic state is allowed or forbidden one considers the integral: (vzxcited|ulyground>. 20 Here, the T's represent just the electronic wavefunctions and u is the dipole moment operator. If this integral is different from zero, the transition is said to be allowed for electric dipole radiation. If this integral equals 68 zero, the transition is said to be forbidden. For B-carotene, in Which C2h symmetry is assumed, it is easy to specify when the integral mppp be zero and when it may be dif- ferent from zero, because of the inversion operation in the group. The inversion operator requires that the wave- functions be distinguished by g (gerade) and u (ungerade) subscripts. Since the integrand must be totally symmetric in order for the integral to be non-zero, for an allowed transition one of the two wavefunctions must be g and the other u — because the dipole moment operator has u symmetry. As a first approximation Equation 20 is adequate for deciding if a transition is forbidden, but when considering very sensitive techniques or very weak transitions the full vibronic wavefunction (instead of just the electronic wave- function) must be used, as noted in Equation 21.20 excited ground > 21