Evidence for excited electronic state interference in resonance raman scattering

Volume 50, number i

CH~~fICAL

IWYSICS LET-1 EKS

15 August 1977

EVIDENCE FOR EXCITED ELECTRONIC STATE INTERFERENCE JN RESONANCE RAMAN SCATTERING I?_BAIERL, W. KIEFER Sektion

IYtysik dcr Uttiversiriit Iliihtchett. O-8000 Munich 40, FRG

I’_F. WILLIAMS Depamnen t of l%_Wricol C3gineerivl~, Texas “Iecir Univrrsiry, Luitbock. Texas 79409. USA

and D.L. ROUSSEAtJ &II Laboratories, Muway I-fill; New Jersey 07974, USA Received 28

Apr111977

Ti:c: complex rcsommcc Raman spcctia of molecular bromine have been .malyrcd quantitatively and a clear dcmonrtration of interfcrencc in the Ranun intensity from the L@IIQ+~) nnd 1 111, excited s:stes has been found.

As the theoretical understanding of resonance Raman scatfering is progressing, complexities in the spectral distribution of the scattered light arc becoming more and more evident. In particular it is becoming apparent that in systems of physical, chemical and biological interest the Raman excitation prome need not coincide with the absorption line shape [l]. It was pointed out by Friedman and Hochstrasser [2] that one cause of such a problem is interference effects when more than one excited state may contribute to the Raman intensity. Since then in complex systems such effects have often been cited as occurring. Most recently an investigation of matrix isolated Br, by Friedman et al. [1] has demonstrated very clearly that there is no obvious relation between absorption data and Raman excitation profile data. Interference effects were cited as a possible explanation of these results. Probably the clearest demonstration of interference effects has been reported in the resonance Raman spectra of some semiconductors [3]. Here it appears that the amplitude to scatter via the resonant electronic state may interfere with the amplitude to scatter via all other nonresonant states. However, in these

cases, the complicated electronic and vibronic structure of the semiconductors precluded fundamental calculations of the interference effects. Because of tbc importance of interference effects in understanding both fundamental and applied aspects of resonant Raman scattering, we have invcstigatcd the resonance Raman scattering behavior of gaseous molecular bromine_ The spectroscopic properties of this molecule are very well understood and it is known that two electronic states contribute to the absorption band in the visible region. In addition there is a great deal of sharp structure in its Raman spectrum_ Consequently, it is ideally suited to study the importance of interference effects. In tliis preliminary Iettcr we report a quantitative analysis of the complex resonance Raman scattering data [4] of Rr,, above the excited state dlssociatlon limit, in which clear interference effects arc strikingly demonstrated. This represents the first report of interference effects in a system simple enough that fundamental quantitative calculations could be made. These results indicate the need for great care when attempting to interpret resonance Raman data. 57

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CfiEhiICAL

PHYSfCS

Quantitative calculations of diatornic Jralogens Irave been reparted in the past. iJsing secund order perturbation theory WiJliams and Rousseau [5,6] cdculated resonance Raman spectra of gaseous iodine, camparcd their results with experi~nentaI~y observed spectra, and obtained good agreement. In their preliminary work tJley could describe the highly structured scattering with a calculation that included contributions from the B(3J10+u) state only with complete neglect ofcontributions from the * II l,r repulsive state. In a recent calculation WilIiams et al. [7] have included contributions from thts repulsive state and have ~~fuded to some * interference effects. Recently Baierl and Kicfcr [4] have reported the results of a com~re~effsive vi&~tion~r--rotational analysis of the ~csonance Raman spectra of isotopitally pure 81 J3r2 and 7gBr2 as well as natural bromine. Just as observed in I:, [S-S] striking changes in ~JIC overall bandshape of the fundamental
(W where

Here JIVOJec-O is the electronic matrix element for the transition from the ground state to the electronic excited state e evaluated at tJle equiljbri~lm internucIear separation, v” and vi correspond to vibrational wave58

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15 Auglist 1977

functions of the ground electronic state and ve to vibrational w~vefunct~~ns of tJrc excited state, e, and p(v,) is the density of excited vibrational states. The quantity b,dJ is a factor resulting from the rotational matrix elements. It depends on the polarizatian of the incident and scattered light, p and u, on the rotational quantum numbers J and m J, on the component of the excited state electronic angular momenturn along the internucIcnr axis, and on whether the transition is an S, Q, or 0 branch. TJre matrix elements (u’Jve) and (v, 1~“) arc simply Franck-Condon overlap amplitudes. If we assume that only ihe B and the f R,, state make contributions to the Raman intensity we may then write out tJre Raman intensity, f al 2, as

TJle R’s correspond to the real parts of cq. (lb) and the I’s to the imaginary parts. Note that if scattering events occurring via each intermediate state, B and lu, were physically distinguishable f14], only the first two terms (corresponding to the sum of pr~b~~b~ities) woufd bc present. The third, interference, term is required because these events are fundamentally indistinguishable in tfre experinlent. Jn this light, we have performed a preliminary numerical calculation on isotopically pure 7gBrz sin&r to that de~crJbcd for X2 in refs, [S&l. In a f&ion similar to that of the iodine work, wavcfunctions for tJlc bounded X state were calculated by solving the radiai Schriidinger equation, the c~~rrespond~g FranckCondon overlap integrals were evahiated, and the complex transition amplitudes, Xe in eq. (I), were obtained for both intermediate electronic states. To avoid recalculating the wavefunctions for each J value., the weak J dependence of the Franck-Condon factors was approximated by shifting the J = 0 potential curves by the appropriate rotationaf energy [5,6]. TJre potential curves for the B and the X states were constructed by applying the Rydbeg-Klein-Rees method and using computer programs developed by Zare [ 151, the molecular constants of 7qBr2 being taken from Barrow et all. 1163. Since the sllape of the ‘if,, repulsive state potenti~ function was not wellknown, we chose to USCthe potential given by Bayliss

Volun~c 50. mrmbcr 1

CIIEBIICAL PIiYSlCS LLMERS

To dcterminc the intensity of a given spectral fcature, the appropriate Ial 2 must bc summed over all values of tnJ Doing so [7] results in the rotational factors,S=, given by Placzek and Teller [17,18] _The simulated spectra were produced by calculating the transition probabilities of all rotational-vibrational transitions originating from rotational levels up to J = 400 and from vibrational Icve!s up to u” = 9, by introducing the appropriate vibrational-rotational population factors, by assigning each transition a frequency from the known spectroscopic constants of 79Br2, and finally by convoluting this result with a 0.75 cm-l experimentally determined slit function. For dctcrmining the population factors it was ncccssary to know the sample temperature in the laser beams under experimental conditions (laser power: 1 W, Br2 pressure: 90 torr). This was done in the usual manner 15-81 from the intensity distributions in the pure rotational Raman spectrum of N2 added to bromine [4_1.Vducs between 650 K (501.7 nrn) and 750 K (457.9 nm) were measured. In fig. 1 the observed spectra and calculated spectra for three different cases arc shown for both 488.0 nm and 457.9 nm excitation. The two lower traces for each excitation frequency represent calculated spectra where only the labeled transition (either I3 +- X or lu + X) contributes to the RR intensity. The second trace from above was obtained by including both electronic

15 August 1977

states in the summation. The absolute intensity of these spectra was scaled to the intensity of the experimentally observed spectra. The spectra arising from contributions of the pure B + X or 1 II lu + X transitions alone arc scaled relative to the combined spectra. No other adjustable parameters were used in these calculations. It is iinportant to note that the amplitudes for a transition to occur via the two electronic states nlust

be added, and not ihc probabilities. In order to emphasize this point we compare in fig. 2 spectra calculated with (top) and without (bottom) the intcrfcrence term resulting from adding the amplitude before squaring. From the figure, it is quite clear that the interference term cannot be neglected. Comparing the calculated spectra with the observed spectra for all exciting wavclcngths there are some small relative intensity differences. The most cvidcnt dis-

x=45r9-

CALCL’L4TED WITHOUT INTERkERENCE

TERM

CALCULATED

I

ix

CALCULATtD B-X ONLY

CIKULATLD B-X ONLY

L_%LL_L--_L_--TII 330

320

310

500 FREWENCY

330 320 km-‘1

_--YQ-

=k’

Fig. 1. Experimentally observed and theoretically calculated resonance Raman spectrum of “8~ vapor for AU = 1 with 488.0 and 457.9 nm excitation frequencies. The lines are Q branch transitions uld the initia1 and fiial vibrational quanturn numbers are assigned to the observed peaks. For calculated spectra see text.

I I

I 330

I 320 FREQUENCY

I

I

310

300

km-‘)

Fig. 2. Theoretically caIcuIated resonance Raman spectrum of the fundamental vibrational region cr!’7’13r2. Upper s~ectrum: czdculation includes interference terms. Lower spcctrum: calculation without interference terms. The lower spcctrum W.LSscaled to have approximately upper spectrum.

the same height a\ the

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Volume

50, niimbcr

C~I~~¶ICAL

1

PHYSICS

crepancy is found for the 501.7 nm excitation line energy is about 350 cm-l above the dissociation limit. For this wavelength contributions to the scattering from the B state discrete levels which were neglected in our c~cula~jons are expected to become important. Other sources of error are the assumption that the electronic transition moments are independent of internuclear separation, our selection of the I If,, state potential function, or the approximations used in dc‘aling with the rotational energies. An improved calculation in which the discrete state contribution wiI1 be included is in progress. It is then hoped that the 1 ll lU potential function* can be assessed with similar accuracy, from the Raman data, as that reported by Wili~r~~s et al. [7] for molecular iodine. Because the rclatfve electronic transition moment is so much stronger in BrZ than it is in I2 we believe we should have even greater sensitivity (better than 0.1 A) than that reported for 1,. The data and analysis presented here represent the first quantitative dcn~onstrati~n of interference in the whose

Rarnnn

intensity

between

excited

electronic

states.

it

confirms prior theoretical predictions of the importance of such effects and supports proposals that interference effects are present in complex molecules. It also points to the need for careful quantitative analysis of Kaman spectra when physical, chemical or biological information is sought. Financial support for PB and WK from the Bundesm~isterium fi3r ~orsc~lung und Technologie is h~g~y acknowledged. PB and WK also thank the Leibniz * Since tfie cOnq3lOtion

Of our calculation new re5UltS for the excited state potential functions have been reported [ 121. Upon mclu\ion of the bound state% m our calculations, a comparkon witit tlte potentsal reported by LeRoy et al. will be made.

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15 August 1977

Rechenzcntrum, Munich, for grants of computer time. We finally thank J. Bran~~er for his interest in this work and I<. Ntmann and G. Strey for discussions.

References 1.I ] J.&i. Friedman,

D.L. Rousseau and V.E. Bondybey, Phys. Rev. f,ettcrs 37 (1976) 1610. PI J.hf. I:riedmatt and R.M. Hochstrasser, Chem. Phys. IAters 32 (1975) 414. J.M. R&ton, R.L. Wadsack and R.K. Chang, Phys. Rev. 131 Lcttcrs 25 (1970) 814; T.C. Damen and J.F. Scott, Solid State Commun. 9 (1971) 383; J-L. Lewis, R.L. W,tds&ck and R-K. Chang, Procerdings of the. Intcrnittiottiil Conference on Light Scattering m Solids, Paris, 1971, ed. M. Balkztnskti (Flanin~arion,

Paris, 1971) p. 41. f4l 1’.Baicrl and W. Ktefer, J. Raman Spcctry. 3 (1975) 353. 151 P.1:. Williams and D-L. Rousseau, Phys. Rev. Letters 30 (1973) 951. and P-F. Wlliiams, J. Chem. Phys. 64 161 D-L. K~USSXIU (1976) 3519. Chcnt. [71 P-1‘. W~lharns, A. Fcrn;indez and D.L. Rousscat, Phys. Letters 47 (1977) 150. @I W. Holzer, WI’. Murphy and H.J. Ucmstein, J. Chetn. Phys. 52 (1970) 399. PI W. Kiefer and H.J. Bcrnstcin, J. Mol. Spectry. 43 (1972) 366. llO1 hf. BrtUt, 0. Scltnepp and P. Stephens, Chem. Phys. Letters 26 (1974) 549. 1111 N.S. Bayliss, Proc. Roy Sot. A158 (1937) 551. [I21 R.J. LeRoy, R.G. MacDonald and G. Burns, J. Chem. Phys. 65 (1976) 1485. 1131 AC. Albrecht, J. Chcm. Phys. 34 (1961) 1476. [141 R.P. l~cyrtmcin and H.R. Ilibbs, Quantum mechanics and path integrals (McGraw-Hill, New York, 1965). [f51 R.N. Zare, 5. Chem. Phys. 40 (1964) 1934. [I61 RX. Barrow, TX. Clzrrk, J.A. Coxon and K.K. Yee, J. hfol. Spectry. 51 (1974) 428. [I 71 G. Pktczek and E. Teller, Z. Physik 81 (1933) 209. 1181 G. Her&erg, Molecu~r spectra and mobculv structure, Vol. 1 (Van Nostrand, Prinmton, 1950) p. 128.