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Resonance Raman studies of the 1La state of 1,2,3-trisubstituted benzene derivatives: Lack of an induced transition moment
Volume 148, number 6
CHEMICAL PHYSICS LETTERS
29 July 1988
RESONANCE RAMAN STUDIES OF THE ‘L, STATE OF 1,2,3-TRISUBSTITUTED BENZENE DERIVATIVES: LACK OF AN INDUCED TRANSITION MOMENT Shijian LI ’ and Bruce HUDSON Department ofChemistry and Chemical Physics Institute, University @-Oregon,Eugene, OR 97403, USA Received 11 April 1988; in final form 3 1 May 1988
Resonance Raman spectra of 1,2,3&chlorobenzene and 1,2,3-trimethylbenzene obtained with excitation in the region of the ‘L, electronic state exhibit the pattern of a vibronically induced transition similar to that observed for benzene and symmetric 1,3,%isubstituted derivatives in contrast to the allowed (B-type) pattern observed for monosubstituted and 1,Cdisubstituted species, This behavior is consistent with early ideas of War, Platt, Fiirster, Moffttt and Petruska of the perturbative vector nature of the allowed intensity component resulting from substituent effects in benzene derivatives. The present work represents the first quantitative demonstration of the applicability of these ideas to the ‘L, state of benzene derivatives.
1. Introduction Resonance Raman scattering under conditions of resonance with symmetry forbidden electronic transitions has proven to be a useful way to probe vibronic coupling [ l-4 1. Previous resonance Raman studies of benzene with excitation in the vicinity of the ‘B,,, excited state [ 1,2,5,6] reveal the expected C-type [ 7- 10] activity in the form of strong binary overtone and combinations of non-totally symmetric modes of eZgsymmetry, especially the 2~8 band at 3200 cm-‘. The fundamental transition of this ring mode near 1600 cm-’ is not seen in these spectra. Similar studies of derivatives ofbenzene [3,5,6] have shown that the small allowed electric dipole component of the ‘L, transition in the lower symmetry species results in B-type Raman intensity, specifically a strong transition of the fundamental band near 1600 cm-’ corresponding to the v8 motion of benzene. Because of the vibronic activity in this weakly allowed electronic transition, the combination band 288 also has a significant intensity in these derivatives. The relative intensity of the fundamental to the overtone band is a measure of the contribution ’ Present address: Department of Chemistry, Colorado State University, Fort Collins, CO 80523, USA.
of allowed intensity compared to that of vibronic intensity in the electronic transition of a particular benzene species. Thus the Raman spectra may be classified into “forbidden” or “allowed” type on the basis of the ratio of the intensity of the 3200to 1600 cm-’ vibrational transitions. Symmetric substitution at positions 1, 3 and 5 results in Dj,, symmetry for the benzene derivative and, as a result, the ‘L, transition is now forbidden by symmetry. The resulting resonance Raman spectra [ 3 ] show intensity in the 3200 cm- ’ band but not in the fundamental region, demonstrating the forbidden nature of this transition for this substitution pattern. The modes of the aromatic ring of us parentage are largely insensitive to substitution either in terms of frequency or form, remaining close to 1600 cm-l in all species. In the molecules with only twofold or lower symmetry, this degenerate e,, mode splits into symmetric and asymmetric non-degenerate modes. The splitting of these two modes is very small, however, and both components are expected to be vibronically active. This constancy of the “vgl’ modes of substituted benzenes permits comparison of vibronic Raman mechanisms through the benzene derivative series. In the present paper we extend these previous
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
581
Volume 148. number 6
CHEMICAL PHYSICS LETTERS
studies of methyl benzenes [ 31 to chloro species and consider the case of 1,2,3-trimethyl- and 1,2,3-trichloro-benzene. On symmetry grounds, these species should have as much allowed character as the corresponding monosubstituted benzenes. However, according to the “migration moment” theory developed by Sklar, Platt, Fiirster, Moffitt, Murrell and Petruska [ 1l- 16 1, there should be a vector cancellation in the intensity induced in benzene for this substitution pattern. Resonance Raman scattering provides a direct and unambiguous test of this prediction without the need to make assumptions concerning the independence of the vibronic and substituent-induced contributions.
2. Experimental The experimental methods used to obtain resonance Raman spectra in the ultraviolet region have been described elsewhere [ 8,9,17- 19 1. The proca dure used for the generation of radiation in this region is stimulated Raman shifting in hydrogen gas of the harmonic frequencies of a Q-switched, flashlamp-pumped Nd : YAG laser. The 223 and 209 nm radiation used in the studies reported here was obtained as the fourth anti-Stokes shift from the 355 nm harmonic of the Nd : YAG laser and the seventh anti-Stokes shift of the 532 nm harmonic, respeo tively. Small peaks occur in the Raman spectra at 4155 cm- ’ due to residual radiation at the next Raman shifted frequency. In some spectra lines at 1557 and 2332 cm-’ due to O2 and N2 respectively can be seen. Other stray 1Ineswith variable intensity originating in the stimulated Raman shifter include a pure rotational interval of 587 cm-’ and a series of lines at 235, 470, 705, etc. cm-‘. These are due to stimulated Raman scattering involving vibrationally excited hydrogen [ 6,201. All samples were obtained from Aldrich Chemical Company and were used without further purification. Vapor samples were obtained by flowing a stream of nitrogen gas through a liquid sample of the substituted benzene in question. This required an elevated temperature for the chlorobenzenes. A heated sample tube system with an external sheath flow of heated nitrogen was especially designed for this purpose [61. 582
29 July 1988
3. Results Resonance Raman spectra of the substituted benzene derivatives in question are shown in figs. 1 and 2. The chlorobenzene spectra were obtained with 223 (or 2 18) nm radiation; the methyl-substituted benzene spectra were obtained with 209 nm radiation. These wavelengths correspond roughly to the peaks of the ‘L, transition of the trisubstituted species of each type. The major experimental observation of this work is that the 1,2,3_trisubstituted benzene species have resonance Raman spectra that are much more similar to the symmetric 1,3,5-trisubstituted species than to the mono- and p-d&substituted species. SpeciIitally, the p-disubstituted species show strong intensity in the fundamental vs region ( 1600 cm-‘) while the trisubstituted species, whether symmetric or not, are dominated by the overtone of this transition. This means that the electronic transition in this region has the property of being dominated by the vibronic
I
I
I
I
Fig. 1. Resonance Raman spectra of methyl-substituted benzenes obtained with 209 nm radiation.
CHEMICAL PHYSICS LETTERS
Volume 148, number 6
29 July 1988
first-order terms in the displacements away from the equilibrium,
The resulting terms are designated the “allowed” component of the transition and the “vibronically induced” or simply “vibronic” component. A forbidden transition is, by definition, one for which the leading term vanishes. Application of this approach to the Kramers-Heisenberg perturbation expression for the Raman process results in potential contributions to the scattering process that may be grouped in three terms designated as A, El and C-type contributions,
2me llav&
Me
Fig. 2. Resonance Raman spectra of chloro-substituted benzenes obtained with 218 nm radiation (monochlorobenzene) or 223 nm radiation (di- and tri-substituted derivatives).
contribution to the electric dipole matrix element rather than by the allowed component induced by the asymmetric substitution.
4. Discussion The vibronic theory of Raman scattering, developed by Albrecht [ 71, is particularly useful when applied to molecules such as benzene that are highly symmetric and which do not suffer large changes in geometry upon electronic excitation. In cases such as this the expansion of the electric dipole matrix element between two electronic states as a power series in the ground state normal coordinates is expected to converge rapidly and the spectroscopic consequences of inclusion of higher terms are easy to identify for comparison with experiment. Specifically, it is often useful to limit the expansion of the dipole matrix elements to the equilibrium (zero-order) and
The important difference between these terms is that they contribute to distinct vibrational transitions. This is due to symmetry constraints on the electronic integrals M$ and 6Mic and to the fact that the A term involves vibrational overlap integrals while the B and C terms involve integrals of the form ( i IQ Ij). In the harmonic approximation, integrals of this type obey the selection rule j=i+ 1. The result of these considerations is the following set of approximate rules: A terms from allowed electronic transitions result in a series of fundamental, overtone and combination transitions of totally symmetric modes; B terms from vibronic activity in allowed electronic transitions result in fundamental transitions of non-totally symmetric vibrations; C terms resulting from forbidden or allowed electronic transitions result in binary overtones and combinations of non-totally symmetric modes. In the case of B and C terms the particular nontotally symmetric modes that will gain activity from 583
Volume 148, number 6
CHEMICAL PHYSICS LETTERS
a given excited electronic state involved in a forbidden transition are determined by the fact that these modes must induce intensity in the transition in question. This information often indicates the symmetry of an excited electronic state. The validity of the above approximate rules in particular circumstances can be ascertained by examination of the resonance Raman spectrum for specific transitions that are expected to have no intensity. For example, linear vibronic coupling within the harmonic approximation will only result in intensity in the binary combinations and overtones of non-totally symmetric modes (e.g., 2vs, 29 and v8+ v9 for the B,, state of benzene). Breakdown of the harmonic approximation for the non-totally symmetric mode in the excited electronic state (resulting in a double minimum potential) will produce intensity in bands such as 4 v8 and 3 v8+ v9 due to terms such as, ~OlQ~13>~~31Q814>~~O10~9 x (O]O), and (OlQsl3>8(313>8(OlhlI)~ X ( 1 I 1)+ The absence of intensity in such bands confirms the validity of the linear vibronic and harmonic approximations. Resonance with a forbidden electronic transition (where Mie =O) result in enhancement of C-term activity and the appearance of binary overtones and combinations of the mode responsible for “promoting” this transition. There may, be more than one mode with promoting activity; if so this will result in combination transitions between these modes. The other modes observed under these conditions will be fundamentals and overtones of totally symmetric modes; these gain activity on the basis of the degree of displacement of the excited state along these normal coordinates and from the fact that the C term includes terms in which the promoting mode increases in quantum level by one in the upward transition and decreases by one (to the original value) in the downward transition. This pattern of C-term domination of the Raman process is clearly demonstrated in the spectra observed for benzene with excitation in the 220 to 180 nm region [ 21. Here resonance is with the transition to the state of B1, symmetry; the primary promoting modes vg and v9 have e29symmetry RSdting in vibronic symmetry of E,, corresponding to the allowed in-plane electronic transition. Only binary overtones and combinations of v8 and v9 are observed con584
29 July 1988
firming the validity of the linear vibronic coupling and harmonic potential approximations. Conversely, these resonance Raman studies of benzene [ 2 ] have confirmed the assignment of the x 2 10 nm electronic transition as being of B,, electronic symmetry. The observed depolarization ratio of the 2 vE band of 0.41 kO.05 is in good agreement with the value of 7/ 16 (0.44) expected on the basis of C-type vibronic coupling intensity. Alternative intensity mechanisms involving an A-type mechanism and an allowed transition result in depolarization ratios of either l/3 or l/8 (clearly in disagreement with the observed value ) . B-term Raman intensity of fundamental transitions of non-totally symmetric modes is most important under conditions of resonance with weakly allowed electronic transitions where the vibronically induced intensity is comparable in magnitude to the allowed component. This is the situation in substituted benzene molecules [ 3,561. It is useful in this context to consider the effect of substitution as a perturbation to the electronic structure of the benzene aromatic system so that a particular group induces a small allowed component to a forbidden electronic transition. The overall effect of these “migration moments” will be additive according to this viewpoint [ 1 l-161. The relative intensity of the A or B term to C term contributions to activity in these modes is a measure of the degree of induction of allowed intensity in the ‘L, transition of these derivatives of low symmetry, It has been clearly shown that fluoro substitution has a much smaller effect than methyl or chloro substitution [ii] and, as can be seen by comparison of figs. 1 and 2, chloro substitution has a larger effect than methyl substitution in induction of an allowed component. The 1,3,5-trisubstituted compounds have sufficient symmetry that the ‘L, electronic transition in this region is forbidden; the resulting Raman spectra are consistent with this prediction of group theory. (Resonance with the allowed electronic transition of 1,3,Strichlorobenzene reveals intensity in the fundamental transition of the mode of vg parentage. This must be due to B-term activity in this degenerate E state transition.) Perhaps the most interesting observation is that 1,2,3&isubstituted chloro and methyl species have resonance Raman spectra that are dominated by vibronic activity, i.e.
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CHEMICAL PHYSICS LETTERS
the electronic state near 2 10 nm appears to be of forbidden character. This behavior is not expected on the basis of group theoretical arguments but is a consequence of the perturbational character of these substituent effects (so that their influence is additive) and the hexagonal nature of benzene [ 6,11- 16 1. This theory may be schematically outlined as follows. We first assume that the effects of the individual substituents are additive. For a given single substitution the induced allowed transition moment must be either radial or tangential at the point of substitution because of the reflection symmetry of the mono-substituted benzene. For the ‘L, transition the induced transition moments are expected to be radial. The vector sense of the induced perturbation is arbitrary since it depends on the choice of the phase of the wavefunctions involved in the transition. Whatever this phase choice, the result of a perturbation at another position will not have a fixed vector sense. For example, with para substitution the induced components for an Alg+Blu transition will be radially outward for one and radially inward for the other resulting in the same overall vector sense and additive contributions to the overall moment. For 1,2,3 substitution the induced moments, if radial, are alternatively inward, outward and inward resulting in no net intensity because of the sixfold symmetry of the aromatic ring. The vector cancellation of the contributions to the overall transition in these systems was originally proposed by Sklar, Platt, Moffltt, FGrster and Petruska [ 1l- 16 ] and used by them to interpret absorption spectra; the resonance Raman technique provides a more sensitive, more generally applicable and less ambiguous method for the detailed analysis of these subtle changes in electronic structure. In the present case, these ideas concerning the perturbative nature of induced intensity have been extensively tested by evaluation of absorption intensity data for the ‘Lb ( ‘BZU)transition of benzene derivatives and a consistent picture has been established [ 16 1. However, the same analysis cannot be applied to the ‘L, transition because the perturbation-induced intensity is too small a fraction of the vibronically induced intensity and because of overlap with the allowed transition at higher energy [ 16 1, The present Raman experiments, therefore, provide the first
29 July 1988
demonstration of the validity of these ideas for this second excited state of benzene.
Acknowledgement We wish to thank Leland Mayne, Roseanne Sension and Richard Brudzynski for assistance during the course of this work. This work was supported by NSF grant CHE85-11799.
References [l] L.D. Zieglerand B. Hudson, J. Chem. Phys. 74 (1981) 982. [ 21 D.P. Gerrity, L.D. Ziegler, P.B. Kelly, R.A. Desiderio and B. Hudson, J. Chem. Phys. 83 (1985) 3209.
[ 31 L.D. Ziegler and B. Hudson, J. Chem. Phys. 79 ( 1983) 1134. [ 41 R.R. Chadwick, D.P. Genity and B. Hudson, Chem. Phys. Letters 115 (1985) 24. [ 51 S. Li and B. Hudson, in: Proceedings of the Tenth International Conference on Raman Spectroscopy, eds. W.L. Peticolas and B. Hudson (University of Oregon, Eugene, 1986) p. 17.26. [ 61 S. Li, Thesis, University of Oregon, Eugene ( 1987). [ 71 J. Tang and AC. Albrecht, in: Raman spectroscopy, Vol. 2, ed. H.A. Szymanski (Plenum Press, New York, 1970) p. 33. [8] B. Hudson and R.J. Sension, in: Vibrational spectra and structure, Vol. 17, ed. J.R. Durig (Elsevier, Amsterdam, 1988), to be published. [9] B. Hudson, P.B. Kelly, L.D. Ziegler, R.A. Desiderio, D.P. Gerrity, W. Hess and R. Bates, in: Advances in laser spectroscopy, Vol. 3, eds. B.A. Garetz and J.R. Lombardi (Wiley, New York, 1986) p. I. [lo] L.D. Ziegler and B. Hudson, in: Excited states, Vol. 5, ed. E.C. Lim (Academic Press, New York, 1982) p. 4 1. [ 111 A.L. Sklar, J. Chem. Phys. 10 (1942) 135. [ 121 A.L. Sklar, Rev. Mod. Phys. 14 (1942) 232. [ 131 J.R. Platt, J. Chem. Whys.19 (1951) 263. [ 141 Th. Fiirster, Z. Naturforsch. 2a (1947) 149. [ 151 W. Mofitt, J. Chem. Phys. 22 ( 1954) 320. [ 161 J. Petruska, J. Chem. Phys. 34 ( 196 1) 1111, 1120. [ 171 B. Hudson, Spectroscopy 1 (1986) 22. [ 181 R. Sension, L.C. Mayne and B. Hudson, J. Am. Chem. Sot. 109 (1987) 5036. [ 191 P.B. Kelly, A. Ruggiero, S. Li, G. Harhay, G.D. Strahanand B. Hudson, in: Proceedings of the Tenth International Conference on Raman Spectroscopy, eds. W.L. Peticolas and B. Hudson (University of Oregon, Eugene, 1986) p. 20. I 1. [20] T.R. Loree, R.C. Sze, D.L. Barker and P.B. Scott, IEEE J. Quantum Electron. QE- I5 ( 1979) 337; M.-M. Audibert and J. Lukasik, Opt. Commun. 21 (1977) 137.
CHEMICAL PHYSICS LETTERS
29 July 1988
RESONANCE RAMAN STUDIES OF THE ‘L, STATE OF 1,2,3-TRISUBSTITUTED BENZENE DERIVATIVES: LACK OF AN INDUCED TRANSITION MOMENT Shijian LI ’ and Bruce HUDSON Department ofChemistry and Chemical Physics Institute, University @-Oregon,Eugene, OR 97403, USA Received 11 April 1988; in final form 3 1 May 1988
Resonance Raman spectra of 1,2,3&chlorobenzene and 1,2,3-trimethylbenzene obtained with excitation in the region of the ‘L, electronic state exhibit the pattern of a vibronically induced transition similar to that observed for benzene and symmetric 1,3,%isubstituted derivatives in contrast to the allowed (B-type) pattern observed for monosubstituted and 1,Cdisubstituted species, This behavior is consistent with early ideas of War, Platt, Fiirster, Moffttt and Petruska of the perturbative vector nature of the allowed intensity component resulting from substituent effects in benzene derivatives. The present work represents the first quantitative demonstration of the applicability of these ideas to the ‘L, state of benzene derivatives.
1. Introduction Resonance Raman scattering under conditions of resonance with symmetry forbidden electronic transitions has proven to be a useful way to probe vibronic coupling [ l-4 1. Previous resonance Raman studies of benzene with excitation in the vicinity of the ‘B,,, excited state [ 1,2,5,6] reveal the expected C-type [ 7- 10] activity in the form of strong binary overtone and combinations of non-totally symmetric modes of eZgsymmetry, especially the 2~8 band at 3200 cm-‘. The fundamental transition of this ring mode near 1600 cm-’ is not seen in these spectra. Similar studies of derivatives ofbenzene [3,5,6] have shown that the small allowed electric dipole component of the ‘L, transition in the lower symmetry species results in B-type Raman intensity, specifically a strong transition of the fundamental band near 1600 cm-’ corresponding to the v8 motion of benzene. Because of the vibronic activity in this weakly allowed electronic transition, the combination band 288 also has a significant intensity in these derivatives. The relative intensity of the fundamental to the overtone band is a measure of the contribution ’ Present address: Department of Chemistry, Colorado State University, Fort Collins, CO 80523, USA.
of allowed intensity compared to that of vibronic intensity in the electronic transition of a particular benzene species. Thus the Raman spectra may be classified into “forbidden” or “allowed” type on the basis of the ratio of the intensity of the 3200to 1600 cm-’ vibrational transitions. Symmetric substitution at positions 1, 3 and 5 results in Dj,, symmetry for the benzene derivative and, as a result, the ‘L, transition is now forbidden by symmetry. The resulting resonance Raman spectra [ 3 ] show intensity in the 3200 cm- ’ band but not in the fundamental region, demonstrating the forbidden nature of this transition for this substitution pattern. The modes of the aromatic ring of us parentage are largely insensitive to substitution either in terms of frequency or form, remaining close to 1600 cm-l in all species. In the molecules with only twofold or lower symmetry, this degenerate e,, mode splits into symmetric and asymmetric non-degenerate modes. The splitting of these two modes is very small, however, and both components are expected to be vibronically active. This constancy of the “vgl’ modes of substituted benzenes permits comparison of vibronic Raman mechanisms through the benzene derivative series. In the present paper we extend these previous
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
581
Volume 148. number 6
CHEMICAL PHYSICS LETTERS
studies of methyl benzenes [ 31 to chloro species and consider the case of 1,2,3-trimethyl- and 1,2,3-trichloro-benzene. On symmetry grounds, these species should have as much allowed character as the corresponding monosubstituted benzenes. However, according to the “migration moment” theory developed by Sklar, Platt, Fiirster, Moffitt, Murrell and Petruska [ 1l- 16 1, there should be a vector cancellation in the intensity induced in benzene for this substitution pattern. Resonance Raman scattering provides a direct and unambiguous test of this prediction without the need to make assumptions concerning the independence of the vibronic and substituent-induced contributions.
2. Experimental The experimental methods used to obtain resonance Raman spectra in the ultraviolet region have been described elsewhere [ 8,9,17- 19 1. The proca dure used for the generation of radiation in this region is stimulated Raman shifting in hydrogen gas of the harmonic frequencies of a Q-switched, flashlamp-pumped Nd : YAG laser. The 223 and 209 nm radiation used in the studies reported here was obtained as the fourth anti-Stokes shift from the 355 nm harmonic of the Nd : YAG laser and the seventh anti-Stokes shift of the 532 nm harmonic, respeo tively. Small peaks occur in the Raman spectra at 4155 cm- ’ due to residual radiation at the next Raman shifted frequency. In some spectra lines at 1557 and 2332 cm-’ due to O2 and N2 respectively can be seen. Other stray 1Ineswith variable intensity originating in the stimulated Raman shifter include a pure rotational interval of 587 cm-’ and a series of lines at 235, 470, 705, etc. cm-‘. These are due to stimulated Raman scattering involving vibrationally excited hydrogen [ 6,201. All samples were obtained from Aldrich Chemical Company and were used without further purification. Vapor samples were obtained by flowing a stream of nitrogen gas through a liquid sample of the substituted benzene in question. This required an elevated temperature for the chlorobenzenes. A heated sample tube system with an external sheath flow of heated nitrogen was especially designed for this purpose [61. 582
29 July 1988
3. Results Resonance Raman spectra of the substituted benzene derivatives in question are shown in figs. 1 and 2. The chlorobenzene spectra were obtained with 223 (or 2 18) nm radiation; the methyl-substituted benzene spectra were obtained with 209 nm radiation. These wavelengths correspond roughly to the peaks of the ‘L, transition of the trisubstituted species of each type. The major experimental observation of this work is that the 1,2,3_trisubstituted benzene species have resonance Raman spectra that are much more similar to the symmetric 1,3,5-trisubstituted species than to the mono- and p-d&substituted species. SpeciIitally, the p-disubstituted species show strong intensity in the fundamental vs region ( 1600 cm-‘) while the trisubstituted species, whether symmetric or not, are dominated by the overtone of this transition. This means that the electronic transition in this region has the property of being dominated by the vibronic
I
I
I
I
Fig. 1. Resonance Raman spectra of methyl-substituted benzenes obtained with 209 nm radiation.
CHEMICAL PHYSICS LETTERS
Volume 148, number 6
29 July 1988
first-order terms in the displacements away from the equilibrium,
The resulting terms are designated the “allowed” component of the transition and the “vibronically induced” or simply “vibronic” component. A forbidden transition is, by definition, one for which the leading term vanishes. Application of this approach to the Kramers-Heisenberg perturbation expression for the Raman process results in potential contributions to the scattering process that may be grouped in three terms designated as A, El and C-type contributions,
2me llav&
Me
Fig. 2. Resonance Raman spectra of chloro-substituted benzenes obtained with 218 nm radiation (monochlorobenzene) or 223 nm radiation (di- and tri-substituted derivatives).
contribution to the electric dipole matrix element rather than by the allowed component induced by the asymmetric substitution.
4. Discussion The vibronic theory of Raman scattering, developed by Albrecht [ 71, is particularly useful when applied to molecules such as benzene that are highly symmetric and which do not suffer large changes in geometry upon electronic excitation. In cases such as this the expansion of the electric dipole matrix element between two electronic states as a power series in the ground state normal coordinates is expected to converge rapidly and the spectroscopic consequences of inclusion of higher terms are easy to identify for comparison with experiment. Specifically, it is often useful to limit the expansion of the dipole matrix elements to the equilibrium (zero-order) and
The important difference between these terms is that they contribute to distinct vibrational transitions. This is due to symmetry constraints on the electronic integrals M$ and 6Mic and to the fact that the A term involves vibrational overlap integrals while the B and C terms involve integrals of the form ( i IQ Ij). In the harmonic approximation, integrals of this type obey the selection rule j=i+ 1. The result of these considerations is the following set of approximate rules: A terms from allowed electronic transitions result in a series of fundamental, overtone and combination transitions of totally symmetric modes; B terms from vibronic activity in allowed electronic transitions result in fundamental transitions of non-totally symmetric vibrations; C terms resulting from forbidden or allowed electronic transitions result in binary overtones and combinations of non-totally symmetric modes. In the case of B and C terms the particular nontotally symmetric modes that will gain activity from 583
Volume 148, number 6
CHEMICAL PHYSICS LETTERS
a given excited electronic state involved in a forbidden transition are determined by the fact that these modes must induce intensity in the transition in question. This information often indicates the symmetry of an excited electronic state. The validity of the above approximate rules in particular circumstances can be ascertained by examination of the resonance Raman spectrum for specific transitions that are expected to have no intensity. For example, linear vibronic coupling within the harmonic approximation will only result in intensity in the binary combinations and overtones of non-totally symmetric modes (e.g., 2vs, 29 and v8+ v9 for the B,, state of benzene). Breakdown of the harmonic approximation for the non-totally symmetric mode in the excited electronic state (resulting in a double minimum potential) will produce intensity in bands such as 4 v8 and 3 v8+ v9 due to terms such as, ~OlQ~13>~~31Q814>~~O10~9 x (O]O), and (OlQsl3>8(313>8(OlhlI)~ X ( 1 I 1)+ The absence of intensity in such bands confirms the validity of the linear vibronic and harmonic approximations. Resonance with a forbidden electronic transition (where Mie =O) result in enhancement of C-term activity and the appearance of binary overtones and combinations of the mode responsible for “promoting” this transition. There may, be more than one mode with promoting activity; if so this will result in combination transitions between these modes. The other modes observed under these conditions will be fundamentals and overtones of totally symmetric modes; these gain activity on the basis of the degree of displacement of the excited state along these normal coordinates and from the fact that the C term includes terms in which the promoting mode increases in quantum level by one in the upward transition and decreases by one (to the original value) in the downward transition. This pattern of C-term domination of the Raman process is clearly demonstrated in the spectra observed for benzene with excitation in the 220 to 180 nm region [ 21. Here resonance is with the transition to the state of B1, symmetry; the primary promoting modes vg and v9 have e29symmetry RSdting in vibronic symmetry of E,, corresponding to the allowed in-plane electronic transition. Only binary overtones and combinations of v8 and v9 are observed con584
29 July 1988
firming the validity of the linear vibronic coupling and harmonic potential approximations. Conversely, these resonance Raman studies of benzene [ 2 ] have confirmed the assignment of the x 2 10 nm electronic transition as being of B,, electronic symmetry. The observed depolarization ratio of the 2 vE band of 0.41 kO.05 is in good agreement with the value of 7/ 16 (0.44) expected on the basis of C-type vibronic coupling intensity. Alternative intensity mechanisms involving an A-type mechanism and an allowed transition result in depolarization ratios of either l/3 or l/8 (clearly in disagreement with the observed value ) . B-term Raman intensity of fundamental transitions of non-totally symmetric modes is most important under conditions of resonance with weakly allowed electronic transitions where the vibronically induced intensity is comparable in magnitude to the allowed component. This is the situation in substituted benzene molecules [ 3,561. It is useful in this context to consider the effect of substitution as a perturbation to the electronic structure of the benzene aromatic system so that a particular group induces a small allowed component to a forbidden electronic transition. The overall effect of these “migration moments” will be additive according to this viewpoint [ 1 l-161. The relative intensity of the A or B term to C term contributions to activity in these modes is a measure of the degree of induction of allowed intensity in the ‘L, transition of these derivatives of low symmetry, It has been clearly shown that fluoro substitution has a much smaller effect than methyl or chloro substitution [ii] and, as can be seen by comparison of figs. 1 and 2, chloro substitution has a larger effect than methyl substitution in induction of an allowed component. The 1,3,5-trisubstituted compounds have sufficient symmetry that the ‘L, electronic transition in this region is forbidden; the resulting Raman spectra are consistent with this prediction of group theory. (Resonance with the allowed electronic transition of 1,3,Strichlorobenzene reveals intensity in the fundamental transition of the mode of vg parentage. This must be due to B-term activity in this degenerate E state transition.) Perhaps the most interesting observation is that 1,2,3&isubstituted chloro and methyl species have resonance Raman spectra that are dominated by vibronic activity, i.e.
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CHEMICAL PHYSICS LETTERS
the electronic state near 2 10 nm appears to be of forbidden character. This behavior is not expected on the basis of group theoretical arguments but is a consequence of the perturbational character of these substituent effects (so that their influence is additive) and the hexagonal nature of benzene [ 6,11- 16 1. This theory may be schematically outlined as follows. We first assume that the effects of the individual substituents are additive. For a given single substitution the induced allowed transition moment must be either radial or tangential at the point of substitution because of the reflection symmetry of the mono-substituted benzene. For the ‘L, transition the induced transition moments are expected to be radial. The vector sense of the induced perturbation is arbitrary since it depends on the choice of the phase of the wavefunctions involved in the transition. Whatever this phase choice, the result of a perturbation at another position will not have a fixed vector sense. For example, with para substitution the induced components for an Alg+Blu transition will be radially outward for one and radially inward for the other resulting in the same overall vector sense and additive contributions to the overall moment. For 1,2,3 substitution the induced moments, if radial, are alternatively inward, outward and inward resulting in no net intensity because of the sixfold symmetry of the aromatic ring. The vector cancellation of the contributions to the overall transition in these systems was originally proposed by Sklar, Platt, Moffltt, FGrster and Petruska [ 1l- 16 ] and used by them to interpret absorption spectra; the resonance Raman technique provides a more sensitive, more generally applicable and less ambiguous method for the detailed analysis of these subtle changes in electronic structure. In the present case, these ideas concerning the perturbative nature of induced intensity have been extensively tested by evaluation of absorption intensity data for the ‘Lb ( ‘BZU)transition of benzene derivatives and a consistent picture has been established [ 16 1. However, the same analysis cannot be applied to the ‘L, transition because the perturbation-induced intensity is too small a fraction of the vibronically induced intensity and because of overlap with the allowed transition at higher energy [ 16 1, The present Raman experiments, therefore, provide the first
29 July 1988
demonstration of the validity of these ideas for this second excited state of benzene.
Acknowledgement We wish to thank Leland Mayne, Roseanne Sension and Richard Brudzynski for assistance during the course of this work. This work was supported by NSF grant CHE85-11799.
References [l] L.D. Zieglerand B. Hudson, J. Chem. Phys. 74 (1981) 982. [ 21 D.P. Gerrity, L.D. Ziegler, P.B. Kelly, R.A. Desiderio and B. Hudson, J. Chem. Phys. 83 (1985) 3209.
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