L. W. Johnson and K. Wong' York College of the City University of New ~ o i k Jamaica. NY 11451
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Polarized Electronic Absorption Spectrum at 300°K and 77OK
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A physical chemistry laboratory experiment
Most modern physical chemistry courses contain a section on the fundame%& of electronic spectroscopy. A central topic of this discussion is the transition moment. Its component integrals along the x, y, and t axes are the basis of "selection rules" and of symmetry identification of excited electronic states using.. nolarized light. The theorv concernine this subject is well developed; however, there do not appear to he anv underzraduate level experiments which illustrate the lxh&ation properties of thv [;ansition m,gmcnt.Thii ,.an hc i~ttrihuted10 thf. prd)lrms which nre i~iuallve n r o ~ ~ n t t . n d in obtaining polarized spectra (e.g., growing'large crystals which have the appropriate optical density and can be oriented easilv: electronic hands in an easilv accessible rezion of the spectrum). The experiment described below utilizes a crystal system which eliminates most of the usual problems and demonstrates not only the polarization properties of the transition moment, hut also vibronic activity in an excited state, cryogenic techniques, crystal site split&g and the use of mixed crystals.
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A.
Theory and Background
The experimental intensity of an absorption hand is generally expressed in terms of the molar extinction coefficient 4").This is related to the oscillator strength ( f )hy: f = 4.32 X 10V j t(v)du; u is the wave number. The oscillator strength is in turn related to a quantity of theoretical importance, the transition moment (Mhl): 8&cm i:hlMhllY f=-3hr2
where Gh is the degeneracy of the higher state, ;is the average wave number of the hand, c is the speed of light, h is the Planck's constant, m is the electron mass, and e is the charge. T h e square of the transition moment can he expanded as, /Mht12=~
T h e ground and excited state wave function transform as ~ ( w I and ) r(*h), respectively; the electric dipole moment operator transforms as r ( o p ) . It is this metliod of analysis which will he used on the electronic soectrum studied here. The species under investigation in this experiment is the Dermaneailate ion. Theoretical work on MnOa- heean in 1952 when \ i d f i h e r g and Hdmhol7 I I 1 pul~liiht'dtheir claw(.. stmi-rmpiriral molrwl;~rrwhital cnlr~~lation to i n t ~ r r ~ w itst electronic spectrum. Since then, the permanganate ion has played a central role in the development and calibration of a long series of quantum mechanical computational schemes (2). The complimentary experimental investigation started with Teltow's ( 3 )work in 1938; however, this was not followed by more definitive experiments until 1967 (4). At oresent. theorv and exneriment aeree on the maim features of the ion's electronir spectrum. The symmetry of the isolated MnOa- ion is tetrahedral (TA).The hiehest filled molecular orhital has t 1 symmetry and the lowest unfilled one has e symmetry. The ground state configuration is (core) (t1)Ye)"and has Al symmetry; the first excited state configuration is (core) ( t ~ ) ~ ( e -and ) ' gives rise to T I and T2 singlet states and T I and T2 triplet states (tl X e = TI + T2); only the singlet states will he considered here. Thus there are two transitions ( T I A and T? A 1). Since the components of the electric dipole moment operator transform as the x , y, and z vectors, in the Td point group this operator transforms-as T,. The two corresponding transition moments are ('Z'~,lMl*n,) and (.3rr21MI*a,).Todeterminewhether these are nonzero, write the direct product of the integrands
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TI X T ? ( x y z )X A , = A 2 + b: t TI + T 2
( i ' h l f i l ~ ~ )l (~* h~ l =f i r l i ' ~ ) 1 2
+ I(i'hIM).I*i)l't
TPXT~(X.YZ)XA~=A,+E+T,+T~
I(i'hIfin;,I*i)l?
where Yh and 'Z'l represent the wave functions of the higher and lower states, respectively. For electronic transitions, M is the electric dipole moment operator: M = 2e;F;. Fi is the position vector of each nucleus and electron in the molecule, I and e is the charge. If all three components (x, y, z) of M ~are zero the transition is forbidden and its intensity is zero. If only the z part is nonzero the transition is only allowed for light with its electric vector polarized parallel to the z axis; if only the x and y components are nonzero the transit,ion is allowed for light with its electric vector in the xy plane. The first transition is said to be z polarized and the second xy polarized. I t is not usually necessary to evaluate transition moment integrals to determine if a transition is allowed. By using simple group theory, it is possihle to ascertain if one or more of the transition moment's component integrals (x, y, or z) is nonzero, and, consequently, if the transition is allowed and how it is polarized. The basic rule is that an integral will he nonzero if the direct product of the integral contains the totally symmetric representation of the particular m i n t
'National Science Foundation-Undergraduate Research Partiepant. Summer 1977.
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Only the second direct product contains A,, and therefore only this transition (T2 Al) is allowed. Since all three vectors (x, y, and z ) transform as Tz, the transition is allowed for light polarized in any of these directions. It is in fact. this first electronic hand which is the suhiect of the experiment. In aqueous solution it is centered a t ahout 520 nm. has an ..c, of 2500. and even exhihits vihronic activitv a t room temperature ! ~ i g :1 ) . The basic problem here is to
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Figure 1.
Absorption spectrum of LiMnO,
in Ha0 at 300DK
Volume 56. Number 4. April 1979 / 275
experimentally determint, it this ahsorption of the permanranate ion is the result of an T , A I transition. 'l'u du thia. the ion must be fixed in space and a polarized spectrum obtained. This is usually accomplished by growing a crystal of the material to be investigated. However, the 520 nm absorption has such a large extinction coefficient that a crystal of a pure permanganate salt would have to be extremely thin to provide a useful optical density. Therefore a mixed crystal is made: LiMnOA.3H~0/LiClOa.3H?O. - . . .. The M n O c ion fits sul,.ititutionally intu the perrhlorntc vryiwl lattrc; CIO;, has no ahsorotion bands in the, v~sil~le or near U V rerion, and provides'an excellent matrix for diluting and herding the Mn04- ions. T h e lithium perchlorate crystal also offers another important advantage; the crystal sites where the Mn04ions sit have Cs, symmetry. This means that in the crystal the permanganate ion experiences a symmetry reduction: T d C:i,. The effect of the crystal Csuenvironment is to split the tetrahedral ion's T z state into two components ( E and Al) and push them apart by about 500 cm-I. Under these symmetry condi~ionsthe transition moments have two general forms: (AIIMIA1) and (ElMIA]); in the CR. point group the electric dipole moment operator transforms as Al(z) and E(xy). The direct products for the possible transition moments are:
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A, X A,(*) X A ,
= A,
(1)
A , X E(xy) X A , = E EXA,(z)XA,=E
(2)
(3)
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EXE(xy)XA, = A , + A z + E (4) These show that the Al A I transition is only allowed for z polarized light and the E Al transition is only allowed for light polarized in the xy plane. Consequently, if the 520 nm band is produced by a Tz A, transition in the tetrahedral ion, in the CR,crystal site it will be split into two components, one polarized parallel to the z axis and one in the xy plane; the two absorption origins, 0,0 bands, are separated by 500 cm-1 in the crystal.
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Figure 2.
Absorption spectrum of the mixed crystal at 300°K. Unpolarized.
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Not only are the two transitions ( E A1 and A1 -Al) clearlv identifiable from their oolarization and seoarated 0.0 bands; but also they each have Aistinctive vibrational patterns. The transition to the Al state has a strong progression of the ion's symmetric stretching frequency. In the ground state (5) this vibration has a frequency of 840 cm-'; in the Al excited state it is reduced to -770 cm-'. This is expected because of the shift of an electron into an anti bond in^ orbital and resultant weakening of the bonds. The transitcon to the E state shows a somewhat more complex doublet pattern. The strong bands are again due to symmetric breathing frequency of the ion but each is followed by a lower frequency vibration of about 330 cm-'. This is interpreted most easily by noting that the Mn04- ion's t a vibrational modes are split in the CQu symmetry into a1 and e components; it is assumed that the 330 cm-I bands result from the ground state t z vibration of 407 cm-'. Experimental The key element of this experiment is the mixed crystal. It is a LiMnOrRH~O/LiC1O~:lHYO system;the Mn04- ion fits substantially into the Clod- lattice in virtually any concentration. Crystals are easily grown by evaporation of aqueous solutions. To obtain the appropriate concentration of permanganate, the initial solution should be in the proportion of 25t: LiCIOc3Hz0 to0.03-0.06g LiMnOr3H.O in just enough H20 tu make a solution. The solution is covered with porous material and stored in a dark cabinet for 3-6 weeks; during this time it should be handled as little as possible. (Both lithium salts can beobtained from Afla Inorganic or ICN-K & K Laboratories).Crystals which are about 1-2 mm wide and about 6 7 mm long are large enough for use. The crystals are hexagonal and easily oriented morphologically since the molecular 2 ( e : , ) axis is parallel to the c (long)axis of the crystal. To mount the crystal, cut a small rectangle (13 mm X 25 mm) of thin cardboard and make a slit in its center which hasslightly larger dimensions than the crystal to be studied. Fir the ends of the
Figure 4. Absorption spectrum of the mixed crystal at 300°K. The electric Vector is perpendicular to the crystal's c-axis.
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Figure 3. Absorption spectrum of the mixed crystal at 300DK.The electric vecto~is parallel to the crystal's caxis.
276 1 Journal of Chemical Education
Figure 5 .
Absorption spectrum of the mixed crystal at 77'K Unpolarized.
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Figure 6. Absorption spectrum of lhe mixed crystal at 77% The electric vector is parallel to the crystal's c-axis.
If the experiment is only t o be conducted a t room temperature, then the mounting is finished and it need m l y he positioned in the spectrometer's light path. To ohtain spectraat 77O K, aDewarmrrunt must be made. An alligator clip attached t o a glass md which has been fitted thmugh a stymfoam Dewar top works well. T h e card holding the crystal is placed in the clip's teeth and lowered t o the level of the Dewar's optical window. Since the electronic band under investigation is a t -520 nm an inexpensive Pyrex Dewar which has an unsilvered 2-3 cm optical hand will suffice. (When the Dewar is ordered the dimensions ol'the spectrometer's sample compartment should he considered, especially with regard to the position of the unsilvered band on the Dewar:. the cost of the Dewar should h e about 550from either Kontcrr hlarrm o r I'oprr. Pulnrilcd qpwtra can be olrrained using a pulnriring sheet. t.1 sheet van hc pun:has*;l frgm F:schrrSc,entriic for almut %I. I f t h r sprrtrn are to b~ meaiurrd h a duohlr heam instrument (e.g. Cary 14 or Beckmann Acta VI), it may he helpful touse neutral density filters in t h e reference h e a d After the room temperature spectra have been measured, the crystal is coaled t o 77°K. Before putting liquid nitrogen into the Dewar, it is important t h a t the Dewar be carefully cleaned and dried. Initially, put only 3 4 cm of liquid nitrogen in the Dewar. Quickly place the crystal mount and Dewar top in position, but with the crystal pulled about three quarters the way up the Dewar; the crystal is then lowered very slowly t o t h e optical band to prevent it from cracking a s i t goes from 300PK to 77°K. Once the system has maled, lift the top slightly and fill the Dewar two thirds full. T h e Dewar can now be placed in the spectrometer and the crystal aligned in t h e light path. A "dentist" type mirror is often useful in the alignment.
Figure 7.
AbsMptiM spechum of lhe mixed crystal at 77'K. The electric vector is perpendicular to the cryslal's c-axis.
obtained a t 77°K (Figs. 5-7). First, the student should run a spectrum of an aqueous M n 0 4 solution (Fig. 1). From this, the exact maximum extinction coefficient can be determined and the progression in the single vibrational frequency measured. T h e student should then ohtain an unoolarized soectrum of s sindecrvstsl in the Dewar at room .. . tv!c.pt.raturc IFM.2,. Thi, slim. hlm n t r 1.8 l m w w t ~ o ~ l l l n~ ri l h n I ~ n . n gtIw,rpt;al 1,) t l ~ e ~ ~ , * t ~ t r ~w~ ~ t ~t > h c~ ttlw ~otrul ~ t u n~i ~l r u g r n k u r t h c r ~ n ~rn~hen r~~ , m . p m t~ hd-* q w . 1 r~C~n 31 that the cw\tal envimnment is having an effect un the ion. In aqueous solution the ahsorption in this region corresponds t o a single transition (T2 A,); in the mixed crystal the absorption in this region a m e s p a n d s to two superposed transitions (Al - A l and E A,) and is thus less resolved. Finallv the student should fill the Dewar with the liouid niz A i, w d i h r ts,., p t h r w r d trurtn .md . h r ; l ~ none w ~ p d ~ r ~IF,:. i p w t r s (FIX%. B itnd -,. 'l'hr pls,~tim>.,I the 0.1,hand5 ih
