The A,,
Mary K. Campbell Mount Holyoke College South Hadley. MA 01075
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Bh, Transition of Benzene
A physical chemistry experiment
Benzene exhibits three bands i n the more readily accessible regions of t h e ultraviolet. T h e first is centered around 183n m 46.000. where r-. refers t o t h e molar absomw i t h a n r-.. tivity a t thewaveiength of m&imum absorption. T h e second 6900) a n d t h e third b a n d is centered around 203 n m (r,, around 256 n m (r,. 220) (1).This last band is symmetryforbidden between pure electronic states and becomes allowed because of interaction with normal modes of vibration which distort t h e carbon framework of t h e molecule (2). T h e actual manipulations involved i n this experiment are relatively straightforward, b u t t h e analysis of t h e results provides students with a n opportunity t o gain some insight into t h e apnlication of t w o important concepts. T h e group-theoretical . ana!y& of t h e vihronic coupling permits assignment of t h e more prominent peaks which appear i n regularly spaced progressions i n t h e 256 n m band (3),and, i n addition, shows t h e applicability of t h e Born-Oppenheimer approximation.
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is thus (as.)2 (elgI4= Alp,the totally symmetric state. The electron configuration for the first excited state is ( a d (el# (ea,). The aporooriate direct omduet for the first excited state . . erouo-theoretical .. . yives a reducible representauon whirh runtains symmetry oi rhrw meduciblc reprewnrations. tuo non-degrnrrotc and unr dcgrwratr. H:.. H,., and E l , i n order of inrreasingenrrg).The E p , itate has the symmetry of an x ory component of the electric dipole moment, where
Experimental Procedure Sinvr n m s j u portiun of the experiment is the nnnlws c,f the spectrnm, the rewlution in terms of w a ~ r l ~ n g isil r h lmitiny factor. T h r q,rctn~photcmet*rused chould prcfrr.lhly be m e fc,r which a wavelength seale expansion to four significant figures, i.e. f 0.1 nm, is possible. A Perkin-Elmer 350 UV-Visihle-NIR speetrophotometer was used in this case, and spectra were obtained in both the normal and exoanded seale modes. Fieure 1 shows a tvoical soectrum of
I with vapor in a stoppered, l-cm path length, rectangular quartz cell. Analysis of Results Electronic Transition The intensity of an electronic transition is given by the square of rmnsirion d ~ p n lmoment ~ u, defined by the integral u = -*.,(0,'r0,dr, u,hrreu is the pn,tmiccharge. 0, and 0. rhr wnvefuncrums iur the twc,elertnmir states invdved. i the diarancr hetween the center of gravity of the charges in the two electronic states and d r the volume element (4).As mentioned earlier. the transition ob-
I
250
WAVELENGTH nm Figure 1. Typical spectrum of benzene vapor. WAVENILIBER cm-'
priate point group by which they can be characterized determine whether the integral will vanish (2). At least some part of the integrand must belong to the totally symmetric irreducible representation if the integral is not to vanish. Benzene belongs to the DG,point group, havinr a sixfold axis. a oeroendicular twofold axis and an inversion
can be characterized as to their symmetry by appropriate irreducible representations of the group, and the usual convention is to use capital
letters for total electronic wavefunctions and lower ease letters for single-electron wavefunctions. The A and B representations are non-degenerate, and the E representations are douhly-degenerate; the subscripts g and u refer to symmetry or antisymmetry on inversion through the center. The electronic ground state of benzene belongs to the totally
wavefunctions have the following symmetries, in order ifincreasing energy: as,, el,, ea,, bzg as shown in Figure 3. According to the Pauli orinciole. . . . the a and h levels can each accommodate two electrons. and the degenerate e levels, four. The ground state electron configuration 756 1 Journal of Chemical Education
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I
I
260
250
WAVELENGTH nm Figure 2. Expanded scale specbum of benzene vapor.
&
E
2G
Table 1. Partial Character Table for the 4,Point Group Showlng lrreduclble Representations Involved In Benzene Tramnlonr 2G C2 3C2' 3C2" i 25, 2% 0
A,. B, E,, Em
I 1 2
1 -1 1 -1
1 1 -1 -1
2
GROUND STATE
1 -1 2 2
1 -1 0
0
1 1 2
0
0
2
1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -2 . 2
3ad
30,
1 -1 0 0
1 1 0 0
FIRST EXCITED STATE
Al.
E2.+ Bl"+BZ"
Figure 3. Energy level diagram fa benzene showing elecbon wnfiguratiansand Symmetries for the ground state and the first excited state.
the ry plane is defined as that of the benzene molecule. By the usual direct product rules, then, the integrand of the transition moment for the Ezustate contains the totally symmetric irreducible representation of the Dfh ~ O U.D the . condition for a non-vanishine.. inteeral .. and an alloued tmnsimn. On the other hand, neither the HI. nor the H.,, stare helongs tu the same irreducible rcpwsentatim asa component utrhc elrrtrlc mcmtnt, and the trcnsirion mmncnt integral (.8n~.ihed, with the electronic transition forbidden. ~
Vibrational Interactions The argument so far has implicitly assumed the validity of the Born-Oppenheimer approximation which has allowed separate treatment of the electronic wavefunctions of the ground and excited states, without considering nuclear coordinates. Strictly speaking, the total wavefunction involves vibrational energy levels as well as electronic. The symmetries of the normal modes of vibration must he included with the electronic factors in determining symmetry for the total wavefunction. A vibration of suitable symmetry characteristics. then.. can orovide a oerturbation such that the transition be. comes symmetry-alluwed. a here LS n degenerate. in-plane. \,ibration (,Isymmerrv E l , affecting the carhon skeleton. The direct prvduct b.'r,\A,,.H:,) grws rise to an A'>, m r d u r h l e representation, which does have the correct symmetry and is allowed.
Progressions and Assignment of Peaks With the imoortance of vihronie couulinein this transition established, it is no; posslhle tlr make speckc Gsrgnments uipetkv and 10 currelaw rhe ohaervrd pnlyrrssVms w t h vrhrati
