Vibrational Spectra of Mn04- Isolated in KBr Crystals An Illustration of Pure Td Symmetry in the Solid State

H. Hagemannl, Y. Ravi Sekhar, and H. Bill2 Universite de Geneve, 30. quai E. Ansermet. CH 1211 Geneva 4. Switzerland

In introductory lectures of group theory in vibrational can thus be directly used (without cutting) as the referential spectroscopy, carbon tetrachloride is commonly used as an axes for the polarized Raman measurements. (5) Finally, the example of a tetrahedral molecule (I). However, the polar- first electronic hand of charge transfer character of Mu04- ization of the Raman lines are subject to motional averaging (21, which complicates a straightforward demonstration of the symmetry properties of the molecule. We felt the need CRYSTAL ANALI~ER for a solid state example which can clearly illustrate the rigorous application of IR and Raman selection rules in a pure Td symmetry. o K

In this note, we present the vibrational spectra of MnOa- o w matrix isolated in KBr. Mn04-ion has been subject to sever- UI

al spectroscopic studies earlier ( 3 5 ) both in solutions and in 0 0

different crystalline environments. The choice of this partic- ular system is based on the following criteria: (1) Single crystals of KBr doped with MnOa- can easily he grown with the glassware available in any chemistry laboratory (see ex- POWIZATIDI

oerimental section). The crvstals are stable under normal conditions and canbe handfed without any special care. (2) The host matrix KBr. which is often used to make oellets for IR spectra, does not absorb in the spectral domain bf M ~ o ~ - x d ion. (3) Unlike the other Td molecules, there is little Fermi resonance interference. (4) The orientation of the crystals is RERRWTEL IXES

straightforward since they grow in the form of cubes with INC~DENT LUKR

natural (100) faces. The Mn04- ion substitutes for a Br- Figure 1. Schematic representation of the Raman experiment (specnometer anion and as shown in Figure 1, the macroscopic crystal axes with 90' configuration) described in the ten, me figure depicts the laboratory

axes and Me polarization geamehies used. Also shown is the structure of the KBr:MnO: cw~tal. The Raman tensor elements are ex~ressed as. for exam- . .

' Present address: Un versity 01 California. Berkeley, CA 94720. p e q x xl,, where z = d rec! on ol ncsnence and y = alrection of obrervat on Author 10 whom correspondence shou d be addressed. The polar zao ry tensor component is ix.r) = r..,

456 Journal of Chemical Education

lies around 510 nm. Thus the Raman intensities of the verv diluted Mn04- are greatly enhanced through a resonant Raman effect (6 ) when one uses the visible exciting lines of the Argon ion laser (514.5 and 488 nm).

Theory Raman effect occurs because of a change in magnitude or

direction of the electronic polarizability during the molecu- lar motion, while infrared absorption occurs because of a change in magnitude or direction of the electric dipole mo- ment during ths motion. The magnitude of the induced dipole moment P is given by

where is the electric vector of the incident radiation of frequency v and rr the polarizahility. If a changes during the vihration i with freauencv v;. Pwill change with the freauen- rirs v + r , nnd z, - v as wellas with frcqurncy v. Thr scattered light will thus cont in the Frequencies u i u, inaddition to". heref fore, the Raman recordis obtained by spectral analy- sis of the light scattered from the sample illuminated by a laser source (Fig. 1); it has the form of the intensity I of the scattered light versus the displacement of the frequency from the incident laser frequency. Each Raman vihrational hand is characterized by its frequency, intensity, linewidth, and depolarization ratio. The first three parameters are oh- tained directly from the experimental spectra. To measure the depolarization ratio, one has to record the spectra with the analyzer parallel and perpendicular, respectively, to the incident electric field vector. This means, for instance, that when the incident electric field (Ej,) is parallel to P, one has to record spectra with the analyzer parallel to P,, (I1 = intensity of the given line) and P,, ( I I = intensity of the same line). The ratio (IlllI,) is the depolarization ratio. When the sample is a single crystal, it is possible to choose the orientations of the sample axes with respect to the inci- dent beam so as to measure individual elements of the polar- izability tensor. Group theory relates the point symmetry of the svstem at hand to these elements (7) enahline one to characterize the m&cular vihrat~ons. In an unqmmetrical niolec11Ie like .\lnO,-. a ~er iodir chanae of the ~olari7abililv takes place during ail the normal vihiations. Therefore, ail normal frequencies are Raman active and appear in the Raman spectrum. The selection rule for hoth IR and Raman spectra is Aui = It1 for each normal vihration ui.

The intensity of the-scattered light depends on the in- duced dipole moment P which can he represented by inte- grals of the type

S *, P'*" d~ (2)

where P is a vector with the components

x , y, z are the axes of the coordinate system in the molecule fixed in space while a,,, ~u,,, . . . are called the components of the polarizahility tensor a. a is a symmetric tensor and thus a,, = a,,; a,, = a,, and a,, = a,. The time-independent part of eq 2 is given by

[PI""' = J +,ia.+" dr (4)

where is the amplitude of p. The intensity of-a Raman n - m transition is proportional to the square of_[P]"m. From eqs 3 and 4 we can obtain the components of [PI""' as

[el"" = S~rU,,J.,J.kdr+ 5 a,,+,&dr+G'S =,,J.,&dr

( 5 )

E:, I$, and @are the components of the amplitude of the incident light wave. The integrals

are the matrix elements of the six components of the polariz- +ility tensor. The diagonal matrix elements (n = m) of a or PO correspond to Rayleigh scattering, whereas the off-diago- nal elements (i.e., transitions n - m induced by the incident light wave) correspond to Raman scattering. Thus, from eq 5, a Raman transition n - m is allowed if a t least one of the six quantities [a,,]""', [a,]nm. . . is different from zero. If we now consider the vibrational Raman spectrum, $, and J., will he the vihrational eigenfunctions J.,. and $,a of the upper and lower states. Then, a Raman transition is allowed he- tween two vihrational levels u' and u" only when at least one of the six products a,,$,,$,-, a,$,&, etc., is totally sym- metric, that is, remains unchanged for all the symmetry operations pertaining to the molecule. This will happen only when the product (+,,J.,s) has the same species as at least one of the six components a,,, a,, . . .of the polarizahility tensor. Thus we see that there is a direct relationship between the Raman intensity and the symmetry properties of the mole- cule.

Further, in normal Raman spectroscopy (NRS), the excit- ing frequency lies in the region where the molecule has no electronic absorption hand while in resonant Raman spec- troscopy (RRS), it falls within the electronic hand. Thus, in NRS, the Raman intensity is relatively independent of the exciting frequency while in RRS there may he an enhance- ment of the Raman lines. I t follows, therefore, that MnO4- which has an electronic hand around 510 nm (9) is indeed subject to a RRS. Several articles in this Journal (10, 11) have treated the subject of RRS.

Results and Analysls Figure 2 shows a survey Raman spectrum of Mn04- in a

KBr crystal a t room temperature. The infrared spectrum shows a single sharp absorption line at 926 cm-'. The four normal modes expected in a tetrahedral XY4 molecule trans- form as A,, E, 2T2, respectively. Inspection of the character table of the Td group shows that only the modes transform- ing as T2 are IR and Raman active. Therefore, the line a t 927 cm-1 transforms as T2 since i t is observed in hoth IR and

Figure 2. Unpolarized survey Rsman spectrum of Mn04-doped in a KBr crystal at room temperature. h.,, = 514.5 nm. laser power on the crystal = 0.23 W. Spectral resolution = 5 cm-'. The inset presents an expanded spectrum in the region 770-880 cm-', which clearly shows the two weak lines at 813 and 832 cm-'.

Volume 64 Number 5 May 1987 457

Figure 3. Polarized Raman spectrum of M n O l doped in a KBr crystal at room temperature (L,. = 514.5 nm). Upper curve: polarization geometry dxx)y. Lower curve: polarlmtion geometry axz)y A. Laser power an the crystal 0.2 W. 50ecfral resolution 0.5 cm-'. 6. Laser mwer on the C W S I ~ 0.15 W. spectral resolAon 2 cm-' The onlens ly at tne lower CJwe ls electron cally amp tea by a factor of 5 ~ 8 t h respect 10 the wper C U W ~

Raman spectra. Polarized Raman spectra (Fig. 3) confirm this assignment. Indeed the nondiagonal elements of the Raman tensor XY, YZ, and XZ, transform as T2 according to the character table. The Raman line observed at 407 cm-I has the same polarization behavior as the line at 927 cm-'. This T? mode should. in ~rinciole. be seen in the IR soectra also (I$. But owing to the 10; concentration of ~ n 0 ~ - in KBr crystals, the line at 407 cm-I doesnot show UD clearlvin the IR-spectra. The two remaining bands at 367 and 848 cm-' observed in the Z(XX)Y polarization pertain toE or A1 symmetry according to group theory (examine the Td group table in conjunction with Fig. 3).

The precise assignments~of the observed transitions is obtained by an additional Raman measurement. Using the 514.5 nm line of the Argon ion laser, the resonant Raman spectrum of Mn04- in KBr reveals two intense band pro- gressions, namely 848, 2 X 848, 3 X 848 em-', etc., and 927, 927 + 848, 927 + 2 X 848 cm-', etc. In resonant Raman spectra, it is common to observe harmonic progressions of the totally symmetric mode (10). The 848 cm-' line is thus assigned to the totally symmetric mode (ul) and, according- ly, the line a t 367 cm-I to the E mode (vz ) . As the force constants of stretching modes are qualitatively expected to be stronger than those of bending modes, the T2 mode at 927 cm-' may be assigned to us and the other a t 407 em-' to q , where we use the notation followed bv Nakamntn (2). .- ,

A careful inspection of the Raman spectrum shows two additional verv weak lines at 813 and 832 cm-I (inset in Fie. 1). One of them a t 832 cm-I is likely to arise from the iI mode of MnOd- containine one oxveen-18 ion. Stridlv "- speaking, this molecule has Crigonal symmetry (C3J. But, :t is known ( 1 ) that at this level of analysis the molecule can

still be assumed to be cubic. Then, as this mode is nondegen- erate, a simple model calculation is appropriate. It relates the frequencies pertaining to the two species: Mn04- with four 160 and Mn04- with three 160 and one 160. Indeed, the frequency ratio '8v116u is proportional to

four times the mass of 160

(three times the mass of 160 + mass of one

Aoolvine this factor to the 848 cm-' line. one calculates the .. . frequency to he about 835 cm-'. Experimentally one ob- serves 832 cm-I. A second argument in favor of this identifi- cation is based on their intensities. Indeed, the relative in- tensity of the 832 cm-' line is approximately 0.7% while 0.8% would he expected considering the natural abundance of '80 (0.2%). The other line a t 813 cm-l corresponds to the first harmonic of "4 at 407 cm-' within the expkrimenta~ error in frequency reading of ahout 0.5cm-1.

Finally, in the foregoing discussion, we have assumed that all the Mn04- ions in the crystal are orientated in the same manner. This assumption seems valid in the present case because the polarization results clearly show the 100% ex- tinction of A, and E lines in the z(xz)v eeometw and 2T1 " .. lines in the z ( x x ~ ~ geometry. In other words, any reorienta- tional proces5 of MttOI. ions is vrobahls not within the time scale of a Raman meisuremedt. his-point has been dis- cussed in more detail in ref 5. If the symmetry of MnOa- (with four 160 atoms) is postulated to be lower than Td, one would expect to observe splittings of the degenerate E and TZ modes. Figure 2 shows that all the four observed modes have approximately the same linewidth, and measurements at hieh resolution and low temneratures reveal no solittine. ~ d d k o n a l l y , we observe no breakdown of the selection rules. Thus, the pure Td symmetry of Mn04- is established. Experimental

Single crystals of KBr doped with Mn04- have been grown by slow evaporation of aqueous solutions at room temperature. Pro analysi grade KBr and KMn04 powders were used. The solution contains typically 0.5% by weight of KMn04 with respect to KBr. Transparent and homoge- neously colored crystals were selected for the measurements. The concentration of Mn04- incorporated in the crystals is estimated to be less than 0.05 mol %.

All the spectra have been obtained a t room temperature. IR sDectra were recorded usine a Perkin-Elmer 597 soec- trometer with crystals of about 2-4 mm thickness. aha an spectra have been obtained with our laboratory-assembled Raman spectrometer (Fig. 1) consisting of a spectra Physics argon ion laser, a Spexmonochromator, and a photon-count- ing system. The power on the crystal never exceeded 0.3 W, and the crystals showed no damage due to laser irradiation. The resonant Raman effect of Mn04- in KBr causes rela- tively different enhancements of the internal modes de- Dendine on the excitine laser line. We found that the 514.5 bm ex&ing line is the-best suited for this experiment, be- cause the E mode is not easilv observed usine other excitine - lines owing to its weak intensity.

We would be pleased to provide copies of the original spectra to those not having a Raman spectrometer. Literature Cited 1. H e r ~ b e q , G. Mdaeulor Spertro and Molecular Structure. 11. Infrored and Romon

S p ~ e t r a ofPolyolomie Molecules: Van Nostrand Reinhold: New York. 1945: p 310. 2. Nskamoto K. lnfrorsd and omo on Spscrro of ~norgonir and Coordimrion com-

pounds; Wiley: New York, 1978. 3. Kiefer. W.; Bernstein, H. J. Mol. Phys 1972.23.835 (and referencnthercin). 4. C1ark.R.J. H.;Dines,T. J. J . Chem. Soc.ForodayTrons.2 1382.78.723. 5. Rsvi SeXhsr,Y.:Bill, H. Mol.Phys. 1985.54757. 6. Marimova. T. I.: Reshetnyak, N. B. SolidStole Comrnun. 1980.33.933, 7. Cotton. F. A. Chemicol Applirofiona o1Gmup Theory; Wiley-Inferscience: New York,

,a", 8. Long, D. A. Ramon Spectroscopy; McCraw-Hill: New York, 1977. 9. Wrohleski, J. T.: Long, G. J. J Chem. Edue. 1977.54 75.

lo. Strommen, D. P.;Nakamoto,K. J. C h a m E d u c 1977,51,474. 11. Hoskins. L.C. J. Chem Educ 1984.61.460. 12. Miller, F.A.: Carl~on, G. L.;Bentioy, F, F.; Jones, W. H.Spectroehim. Aelo 1960.16.

13s.

458 Journal of Chemical Education