Resonance Fluorescence and Resonance Raman Spectroscopy of Bromine and Iodine Vapor C. Frank Shaw, Ill University of Wisconsin-Milwaukee, Milwaukee, WI 53201
Resonance Raman (RR) spectroscopy and resonance fluorescence (RF) spectroscopy are two techniques for which the advent of lasers has generated renewed interest (2-11). In resonance Raman and resonance fluorescence, a molecule interacts with a photon which corresponds to an electronic transition. then re-emits liaht - which has changed - in energs -. by one or more vibrational and rotational quanta. Thus the soectrum of adiatomic eas - such as bromine or iodine in either process consists of an evenly spaced vibrational progression (overtones) as shown in Figure 1. 'rhe;e re( hnique; prohe the \,ihrational and rurarional enerr\' levels ofthe excited ~ n rdr w n d electronic states uignseo& molecules. The basic experimental results, can h e rationalized in terms of the molecular orbital, anharmonic oscillator, and rigid rotator quantum mechanical results of a diatomic molecule as developed in an undergraduate physical chemistrv course. Useful information about the s~ectroscopic constants and molecular properties of the molecule in various electronic states can be obtained by detailed analysis of the fine structure of the overtone bands. Although a theoretical understanding of RR and R F and the relationship between them is still heing developed, two competing interpretations of their relationship have been proposed and will he summa. rized briefly. Resonance Raman spectroscopy (5) is an inelastic scattering process in which the incident (laser) photon "excites" the molecule to a virtual state in the vibrational-rotational continuum of the excited state, accompanied by instantaneous re-emission of a Raman scattered photon, that has lost several quanta of energy because the molecule returns to a ground electronic, but vibrationally excited, state (Fig. 2a). The resonance fluorescence ~henomena(6) involves excitation to a discrete vibrational-rotational level of an excited electronic state, which after a finite time interval fluoresces, returning the molecule to a vibrationally excited level of the ground electronic state (Fig. 2b). The different modes of absorption and re-emission for RF and RR spectroscopy result in different spectral characteristics which are summarized in Table 1. Although the two techniques are experimentally distinct under most conditions, some workers, have suggested a common origin for them. However, there remain serious questions about their relationship, which are still heing investigated theoretically and experimentally E l l , 12,17). The selection rules for the R F and RR effects are very different from those for infrared and ordinary Raman spectroscopy, where only the fundamental vihratkmal tran>>iun (u" = O t:" = 11' is allowed t o i n the harnlunic nscillntnr approximation, and ovenonei and rumhination hands appear weakly usually less than 1'; of the fundamental intcnsity~due u, anharmonicitvefferts. In contrast. the o\.erronesof rhr RF and RR spectraare of comparable intensity to the fundamental, decreasing gradually for higher quantum numbers (Fig. 1).
-
'
Double primes are used to indicate the vibrational and rotational quantum numbers of the electronicground state; single primes, those of the electronic excited states.
Comparison of Resonance Raman and Resonance Fluorescence Eflects Resonance Fluorescence
Characteristic Excited state
Discrete vibrationalrotational quantum level Relatively long
Excited state lifetime Observed bands
Resonance Raman
Cont8nwm of excited state
(-lo-a set) Vibrational
Instantaneous decay ( < l o " sec) Vibrational overtones
OYerlOnes
Band intensities Fine structure
Irregular variation Doublets
Polarization
Depoiarized
Effect of increased gas pressure
intensity decreases (quenching) Intensity decreases iauenchind
Effect of foreign gases
Regular decrease with vibrational quantum number Q branch and rotational wings from each thermally populated vibrational State Totally symmetric vibrations are polarized intensity increases (concentration effect) Unaffected
RESONANCE FLUORESCENCE 514.5nn 8on4 slils
RESONANCE RAMIN 4 8 8 . 0 nrn 80.-8 slits
Figure 1. (a) RF spectrum of Br*: 700 mwans of 514.5 nm excitation; 8 cm-' slits: 25 cm-'Imin scan rate: 3000 cps full scale, 5 sec period. (b) RR spectrum of Ere: 500 mwanr of 488.0 cm-' excitation: 8 cm-' slits: 5 cm-'lmin scan rate: 300 cps full scale, 2 second perid.
Because of their simole structure and well understood quantum levels, the hacogen gases, especially bromine and iodine, which have intense visible absorptions, have been used extensively for developing and testing. rhe theoretical harei fur H H and R F sDectroscuDv ( 2 ,3.6-10). Hromine is a svmD-h) and, therefore, metrical diatomii m ~ l e c u l ~ i p o igroup nt has only one fundamental frequency (322 cm-1) and one-set of rotational energy levels, which means that the vibrational and rotational spectra have simple, easily interpreted features. Figure 3 shows the Morse potential curves (18) for the ground Volume 58
Number 4
April 1981
343
- -
F g.re 7 t r c ut on .m re-emm on of ognt n RF ilnd RR enoclr tal RF re-, MS lrom exc tauon lo a 0 screle Lmron L 61itle o RR re% ls from e r c !allon lntu the continuum of an excited state.
'no+"
(G+
GROUND
Fiaure 4.
STATE
E X C I T E D STATE
MO diaarams shawfnothe orbital occupations of '&+and3IIo,+
states of Br2.
+
*
%.+
states of Br, (atter Ref Figure 3. Morse potential curves for 'Z,+and 11). The ueflical arrows show me relationships of 514.5 and 488.0 nm exciting lines to the convergence limit of excited state. state, I&+, and second excited state, 3IIo,+, of Brz, which are involved in the RR and RF phenomena discussed below. Figure 4 shows the orbital occupation (molecular orhital schemes) for the two states. Each electronic state has associated with it a characteristic series of vihrational enerev levels. which are overtones of the fundamental frequency f& that electronic state. The spacing of the vihrational enerw levels. G ( u ) ,are not exact multi~les of the fundamental frequency, hut become progressively clker according to the relationship below, where w, is the harmonic frequency and wax, is the inharmonicity constant (typically less than 1%of we), u is the vibrational quantum number (0, 1 , 2 . . .), h is Planck's constant, and c is the speed of light:
As u increases, the spacing eventually becomes so small that a continuum of vibrational states is present. This point is referred to as the convergence limit. In BIZthe 3110,+ excited state lies at 15,891cm-' ahove the ground state. The green (514.5 nm) line of the argon ion laser, which has an energy of 19,429.5 cm-', excites a bromine molecule into one of the vibrational-rotational levels of the sou+ state giving rise to the RF spectrum. In contrast, the 344
Journal of Chemical Education
Figure 5.
Emitted Light
Cell lor RR and RF spectra of gases
higher energy 488.0 nm exciting line, 20,486.5 cm-1, is ahove the convergence limit of the 3&,+ state, 19,585 cm-', and causes a ";irtual excitation" in;; the continuum of vibrational-rotational levels thereby stimulating the RR effect (3,6). For molecular iodine, the convergence limit of the 3&,+ state is 20,162 cm-1 and laser wavelengths longer than 496.5 nm fall below it in the reeion of discrete vibronic states. and shorter wavelengths cause excitation into the continuum of states above the limit (8).The details of the excitation and re-emission processes of RR and RF are discussed. The RR and RF Experiments
Resonance Raman and Resonance Fluorescence Spectra can be recorded routinely on a conventional laser Raman spectrometer. The laser serves as an intense. coherent. narrow band width excitation source, and the high resolution spectrometer is necessarv to resolve the scattered lieht into the vihmtional l~andswith associated rotational fine structure. The light is ~~~~~~~~d wirh a sensitive ph~,tomulripliernil*. m d the resulting elecrronic signal is ampliiied and displavcd by conventional means. A sample of the gas to be examined is illuminated in a simple glasibr quartz cell. The main experimental limitation is that the path lengthof the scattered light throurrh the cell must he verv short to avoid reabsorntioihv othermolecules (Fig. 5). o he only differenceb&een thk experimental designs for RF and RR experiments is the re-
vihrational states of the molecule (19).Since only one vibrational state of the excited molecule is populated, a progression of bands differing by a vihrational quantum is observed. Another conseauenie is that the rotational selection rule for electronic transitions, A J = f 1 applies. If as is the case here. only one rotational level, J', is populated in the excited state, the molecules will return to the J" = J' 1and J' - 1rotational levels in the erouud state. As a result, the vihrational overtones can be r&lved into a doublet arising from rotational transitions to J' = J' 1and J' - 1 (Fig. 6 ) . Also the Franck-Cundon principle applies: the electronic transition from the excited to the ground state is vertical which means that it occurs much faster than a molecular vibration; thus, the molecule is "frozen" during the time the electron returns from the hieh enerev orbital to the around state.2 As a result, the probability ofthe molecule returning to any particular vihrational level of the ground state depends on the Franck-Condon overlap integrals for the excited state and ground state vihrational wavefunctions. For a molecule in the kth vihrational level of the excited state returning to the uth vibrational level of the around state, the integral, R , is given by eqn. 2, where il., and fi8 are the excited a i d ground state electronic functions and $k and $, are the excited and ground state vibrational functions, and is the transition dipole:
+
+
I
I
F R E Q U E N C Y (crn-l) Figure 6. The doublet structure of the Av" = 1 band in the high resolution RF spectrum of Br2. excited with 514.5 nm laser line. Used with permission from Reference 3.
Figure 7. Illustration of the Franck-Condonprinciple for a hypothetical molecule: transitions are most probable between vibrational states having a similar distribution of bond lengths. Thus, from me v = 0 level, excitation to k = 1 is most probable, and from v = 1. to k = 0 and k = 2.
lationship of the exciting laser line to the electronic absorption bands of the molecule. Resonance Fluorescence The resonance fluorescence spectrum of bromine consists of a series of evenly spaced bands which correspond to vibrational overtones of the Brz stretching frequency (322 cn-'), as shown in Figure la. The spectrum is presented as a shift in wavenumbers from the exciting frequency (in this case, 19,429.5 cm-'1, although the spectrometer actually measures the absolute frequency of the fluorescent light. Because there is a net absor~tionof enerev bv- the bromine. the fluorescent light is red-shifted from the exciting line. ~ h d fluorescent emission is so intense that it can be observed with the naked eye. The bromine is excited into a discrete vibrational-rotational sratr of its ,'lloU7electronic stale, which ha6 been estimated in the literature to have rotational and vibratimal quantum 19 16).The Iar'le IWIUQS 01 thrsc numl~era..J' = 15 and I,' quantuknnmbers illustrate the importanclof rotational and vibrational states in accountine for the total enerev of a chemical system. The lifetime i f this excited state$ long compared to the time scales of molecular vibrations. -10-'3 to 10-lP see, and molecular rotations, lo-" to 10-'2sec, and the virtual excited state of the RR experiment, altboueh i t is still very short on an absolute basis, appro&natel; 10-8 sec. The finite lifetime of this excited state has several direct consequences for the experimentally observed spectrum. First. since the ahsorption and re-emission are independent in time, the emission of light, as the molecule relaxes to the ground electronic state, obeys the rules for electronic transitions, which permit the molecule to relax into any of the excited
--
-
R = J+,(r,R) &(r,R) dr,~,, S$a(R) v U R ) drnve~ (2) The first inteeral in e m . 2 is constant for a eiven electronic state returning& the ground state, and o n l i t h e second int e ~ r ainvolvine l the nuclear coordinates, which is called the ~rinck-Condo; factor, changes for the various vihrational states. Simply stated, the Franck-Condon principle indicates that the intensity will he greatest when the excited and ground state vihrational functions have closest correspondece in distributions of internuclear distances. Figure 7 schematically illustrates the principle. It is the magnitude of these overlap integrals which account for the irreeular intensitv. oatterns u . in the R F spectrum of bromine as the molecule returns to various vibrationallv excited levels of the around electronic state(Au" = 1 >A;,' = 4 > Au" = 3 > AU"= 2 > Au" = 5 tll. 'The time interval hetween the ahsrrhanrr and emi-rim id lirht in HF also exl~lainsthr d ~ ~ ~ ~ ~ rc tkf the ~ dhnndr. f i ~ :Sinre l l t i e excited molec>le is freelyktating much faster than the time between absorption and fluorescence, the excited molecules are randomlymiented by the time they fluoresce. Even though the exciting light was coherent (plane polarized), the fluorescent light is depolarized (randomly oriented). Resonance fluorescence is observed only in the gas phase, because neiehborine molecules in solids and solutions will absorb the energy of the excited molecule, providing anonradiative Dath for loss of enerw. ... That is, the nonradiative processes fur deartivsting the mtdecnle #)(curmu Ii fuarer in the cundens~drlhase 1h.m lhr re.cmi.;iiun r , i thr lieht. 'l'hir quenching of thk fluorescence also occurs if either thebromine or a foreign concentrations. As the - pas - is ureseut at significant . pressure in the sample cell is increased the resonance fluorescence is promessively quenched and at higher pressures (21, the weaker-~a&anphenbmena is
-
cedes it. "Sods and liquids do fluoresce, but not resonantly, as gases do. Conventional fluorescence spectra of liquids and solids are much broader, corresponding to electronic transitions, in contrast to the narrower resonance fluorescenceof gases which have widths comparable to vibrational bands. However, at very low temperatures using h e r excitation vibrational structure can be observed with crystalline solids. Volume 58 Number 4
April 1981
345
Under high resolution the structure of any overtone corresponds to multiple Q(AJ = 0) and S ( A J = +2) branches arising from fundamental and hot (thermally populated) vibrational levels of molecules in the ground electronic state (91, Figure 8. The O(AJ = -2) branch is apparently too diffuse to he detected. Transitions arise from the hot vihrational levels hecause there will always be an appropriate continuum state for which the energy difference corresponds to the exciting laser freauencv (8). .I he pdarizatism of the I~andinlsu currhponds t o !hat e x iwcted fur the nmmal Rmanefiect. That i-, . onis. the to~alls Bymmetric modes are expected to be polarized according to the usual Raman selection rules and the same result holds for resonance Raman spectroscopy. The RR effect is intrinsically much weaker than the RF effect. ~~, and is obscured under conditions where both effects nre uccurring. Hcwe\.~r,the RF can t,c. quencl~cdnr h~gheryns ure>iures.or when the nit~leculeis in irhtion. The thwrrriml basis for the two phenomenais still evolving (1,4,8,10,11-17). Recent exoerimental(2. . . 17) . and theoretical results (1.8.10. . . 21) suggesting a continuous transition from the resonance fluorescence effect to resonance Raman effect have riven rise . to a considerable debate (1,8,11-15,25).
.
~~~
FREQUENCY SHIFT lcm-91 Figure 8. The S and Q branches of the Av" = 3 Vansition in the high resolution resonam R a m Spearurn of i, excited wim 457.9 nm laser line. The numbers in parenthesesrefw to me lower and upper vibrational levels (8 and v'l involved in the transitions.Redrawn from the data in Ref. ( 8 ) .
Resonance Raman Spectroscopy
The resonance Raman effect (5) is a special case of Raman spectroscopy (20) in which the exciting line corresponds to an electronic transition of the molecule. In the gas phase resonance fluorescence, which is much more intense, may obscure the Raman scattering if both processes are occurring. However, when the incident light is of correct energy to excite the molecule to the continuum, resonance fluorescence does not take place and RR scattering may he observed. The origin of the RR effect may be understood in terms of Albrecht's theoretical treatment which oredicts that when the excitinrfrequency, uo, approaches an allowed electronic absorption hand., u,,. ,b. the Raman intensitv will be enhanced.. as orevi. ously described in this Journal i5):
For our purposes it suffices to note that the intensity of the fundamental hand depends on the square of the expression, ) . subscripts of ueUak refer to the uth l/(v,,, k - vo I P ~ " The . and k t5 ,vibrational states of the ground, g, and excited, e , electronic states involved in the virtual excitation. The damnine factor., ir,,,. which is related to the width of the electronic transition, prevents the expression from becoming u,,, .b. the denominator becomes infinite. As un- auoroaches .. very small, and the intensity correspondingly increases by several orders of magnitude. Theoretical explanations for the occurrence of the very intense gas phase RR overtone hands and their gradual decrease in intensity have been developed by Kobinata and by Nafie, Stein, and Peticolas (7,101. Following the treatment of Kobinata (lo), the intensity of the nth overtone, I,,,is given by the following equation where v, and u, are the ground and excited state fundamental vibrational frequencies, respectively, and other terms have the same meaning as above:
+
.
I,
4
("0
-
- n~~)'n!(vo~rJ2)"
+
346
+
Journal of Chemical Education
~
~
~
Spectroscopic Data from RR and RF4
A surwrisineamount of information can he extracted from the spectroscopic data obtained by RR and RF, using the ouantam mechanical results for electronic, vibrational, and rotational energy levels of a diatomic oscillator to interpret it. First one can calculate the harmonic frequency, we, and the anharmonicity constant, x,w,. From eqn. 1, the energy differences for a transition from the ground vibrational state (u" = 0)to the u t h excited vibrational level is found to be Fo,. = G(u) - G(0) = uu. - ( u 2 + u ) x , w , (5) Equation (5) can he solved for u" = 1,2, and 3 toobtain w, 322 em-' and x,w, 1.45 em-', which agree with the literature values of 321.8 and 1.12 cm-' for Brz ( 6 ) . The rotational quantum number of the excited state electronic-vibrational-rotational state populated in the R F experiment can he calculated from the splitting of the doublet observed at high resolution (2 cm-I). The selection rules for an electronic transition require that AJ = +I. Thus, the rotational states to which the molecule relaxes during fluorescence will have gained ur lost unr rotarionJ qunntbm and it' the extitud srote had the rutntimal quantum numl~erJ ' , rhe ~obier\.t-drloulder arrresuonds ro rhe mraricmdl sratc..JW = J' 1and J' - 1. In the rigid rotator approximation, the energy of a rotational quantum level is given as
--
--
+
F(J) = BJ(J + I) (6) where B is h/8a3cIB and IB is prZ. Replacing J by J' 1and J' - 1corresponding to the energy difference of the doublet, one obtains
+
AiJ,+lJ-l = F(J'
+ 1)- F(J' - 1) = B(4J' -2)
(7)
The value of B for the ground vihrational state is given as 0.0809 bv Herzbere (22). Solvine the eauation with the experimen& value or^" gives J' vzues of ~pproximately1618, in reasonable agreement with the literature value of 15. The vibrational level from which the excitation occurs can be estimated as follows: the photons of the 514.5 nm laser source have an energy of 19,429.5cm-'. The electronic state, 3110u+ to which excitation occurs is 15,891cm-' (22), and the -
The term, (uo - nu,)4, and the progressively smaller product, II l/[(uo - uegb pue)2 PJ, although partially offset by (uo2reU/2)"n!,contribute to the steadily decreasing intensity of the overtones with increasing values of n as shown in Figure I h for bromine gas.
~
-
-
-
The RF and RR spectra of Br2 comprise an excellent advanced, optional physical chemistry experiment for interested students. It exnoses them to concepts similar to those illustrated in the classical HC1 infrared spectrum and allows them to use state-of-the-artinstrumentation, while it introduces them to a topic of modern theoretical interest.
additional energy of the exciting photons must correspond to the vibrational state of the excited molecule. The quantum number, u', can he estimated using eqn. 1and the literature values for w, (169.7cm-l) and ,yew, (1.9cm-') of the "lou+ state as tabulated by Herzherg (221, a value for u' of 38 is ohtained. This calculation ignoring higher order corrections is in good agreement with the literature estimate of u' = 39 (6). The harmonic frequencies for the I&.+ (ground) and 3110,+ (excited) states can be used to calculate force constants. and hence the curvature of the potential wells, for each electronic state. usine the eauation (which aodied onlv to diatomic .. molecules), f = 4rr2,2u12fi/N (8) where fi = reduced mass (glmole), c = speed of light (cmlsec), w, = harmonic vibrational frequency (em-'), f = force constant (Nlm), and N = Avogadro's Number. The constants in eqn. 8. 4n2cLIN.havea value of 5.892 X loL5kg-cm2-mole/ g-8ec" The calculated force constants, 244 Nlm for the ground state and 67.7 Nlm for the excited state, can be related to the curvature of the potential wells in ~ i g u r 3. e These numerical values clearlv"emphasize the theoretical meanine of the force . constant: aZE a2E /=-=-
aQZ
arBrBIZ
(9)
E is the potential energy and r is the internuclear distance (bond stretching coordinate). The molecular orbital scheme of Figure 4 indicates that an electron has been promoted to a more antihonding level in the 3&,+ state. Thus, its potential well is shallower, resulting in the smaller force constant. Time-Resolved Spectroscopy An important advance during the past decade has been the develonment of time-resolved snectroscoov. . " ,T R S (8. . , 17). .. which itilizes a pulsed laser sourEe and very fast light detection and amplification svstems to measure Raman and fluorescent emiision as a function of time following excitation of the sample by a pulsed laser source. Using a mode-locked. cavity d k p e d laser, which utilizes a c o u s t ~ ~ o ~ t icoupling cal techniques, very short (less than a nanosecond) hut extremelv i~ can he rrp(~titivt4~ gmeruted, since a large intm>el , ~ ipulses I'ractiun or the rndiahn in the ln;er cavity is releainl in a very short time span. In a conventional or continuous-wave laser: a small amount of the radiation in the cavity (1-2%) is continuously bled through an "imperfect" mirror: while in the pulsed laser, a burstbf intense light travelling in the laser cavity is periodically "dumped" to the exterior (23). Time resolved RF and RR spectra are obtained by monitoring the light emitted a t a single frequency as a function of time after the sample is excited by the laser pulse. The details of the sophisticated electronics required to carry out such measurements are beyond the scope of this article and can he found in the literature (24). However, the basic principle of the system is straightforward: the numbers of photons reaching the detector a t given time intervals after the laser is pulsed are accumulated in a multichannel analyzer (each channel corresponding to a different time interval). After a predetermined number of laser pulses. the data are disnlaved displayed in Figure 9D. Time-resolved soectroscoov has been used to examine the
it shbnld be possible to explore the two phenomena by this method. Figure 9 shows the TRS of molecular iodine (redrawn from the data of Ref. (8)),when the laser is in exact resonance with
TIME
(",.11nnd argon l,+sers,p+.rm~tting hurh l
