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A Kekulé-Crossing Model for the “Anomalous” Behavior of the B2u

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A Kekulé-Crossing Model for the “Anomalous” Behavior of the B2u VOLUME 29 NUMBER 5 ® MAY 1996 Registered in U.S. Patent and Trademark Office; Copyright 1996 by the American Chemical Society A Kekule´-Crossing Model for the “Anomalous” Behavior of the b2u Modes of Aromatic Hydrocarbons in the Lowest 1 Excited B2u State SASON SHAIK,*,1a SHMUEL ZILBERG,1b AND YEHUDA HAAS*,1b Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Received October 13, 1995 I. Introduction As shall be shown the model is general enough and can form a basis for thinking about delocalized ground This Account presents a model that provides a lucid states and their twin excited states made of the out- physical basis for the apparently unusual behavior of of-phase combination of the same set of Kekule´ 1 Kekule´-type vibrational modes in the 1 B2u excited structures. state of benzene and other aromatic hydrocarbons. The The frequency up-shift of the Kekule´-type b2u modes 1 model, called the Kekule´-crossing model, is based on in the 1 B2u electronically excited state of several 1 the idea that the electronic ground state (1 A1g) and aromatic hydrocarbons (benzene, naphthalene, an- 1 the first B2u excited state may be considered to a thracene, and some of their derivatives2-4) is well reasonable approximation as twin states, arising from documented and appears to be a general phenomenon. in- and out-of-phase combinations of the same Kekule´ For instance, the frequency of the skeletal mode 1 in 1 -1 Publication Date (Web): May 14, 1996 | doi: 10.1021/ar950206i structures. The Kekule´-crossing model is used to the 1 B2u state of benzene (the ν14 mode, 1570 cm ) account for other properties of these systems, and the is 261 cm-1 higher than that of the same mode in the 1 2 observed spectroscopic “anomaly” in fact provides the ground 1 A1g state. How is it possible that the mode first experimental proof of the dominance of these that disrupts the ground state’s aromaticity possesses structures in determining the physical and chemical a higher frequency in the excited state? It is interest- Downloaded by HEBREW UNIV OF JERUSALEM on September 1, 2015 | http://pubs.acs.org properties of benzene and other aromatic molecules. ing to note that the assignment of this mode presented unexpected difficulties in the early days of the vibra- Sason Shaik received his B.Sc. and M.Sc. from Bar-Ilan University and his Ph.D. tional spectroscopy of benzene. A straightforward from the University of Washington, where he was a Fulbright Scholar (1974−1978). After spending one postdoctoral year at Cornell, he joined the staff of the Ben Gurion force field (Urey-Bradley type) predicted that the University in 1980, and in 1992 moved to the Hebrew University. He is an applied ground state mode should have a frequency of about quantum chemist interested in the construction of unified concepts for problems of 1600 cm-1,5 and after the firm establishment of the bonding, structure, and reactivity. Current interests include organic electron transfer -1 reactivity, the role of electronic delocalization in ground and excited states, two-state lower value (1309 cm ), it was necessary to add a reactivity patterns of transition metal catalysis, and examination of the perfectly special “Kekule´ term” to the force field6 in order to resonating state as a model for the transition state. reproduce the low experimental frequency value. The Shmuel Zilberg completed his M.Sc. (1977) and Ph.D. (1983) studies at the state University of Moscow. He came to Israel in 1991, and is now a research associate (1) (a) Department of Organic Chemistry and the Fritz Haber Center at The Hebrew University of Jerusalem. He is a theoretical chemist, interested mainly for Molecular Dynamics. (b) Department of Physical Chemistry and the in the properties and reactivities of molecules in their ground and excited states, the Farkas Center for Light Induced Processes. design and preparation of novel compounds, and the application of computers to (2) (a) Hochstrasser, R. M.; Wesel, J. E. Chem. Phys. Lett. 1974, 24, quantum chemistry. 1. (b) Wunsch, L.; Metz, F.; Neusser, H. J.; Schlag, E. W. J. Chem. Phys. Yehuda Haas completed his undergraduate and graduate studies at The Hebrew 1976, 66, 386. (c) Friedrich, D. M.; McClain, W. M. Chem. Phys. Lett. University of Jerusalem, obtaining the Ph.D. degree in 1971. After a stay at the 1975, 32, 541. Weizmann Institute and at the University of California, Berkeley, he joined the faculty (3) (a) Mikami, N.; Ito, M. Chem. Phys. 1977, 23, 141. (b) Hochstrasser, of the Hebrew University in 1975. He is an experimentalist, interested mainly in the R. M.; Sung, H. N.; Wesel, J. E. Chem. Phys. Lett. 1974, 24, 168. properties and reactivities of electronically excited states, in the mechanisms of their (4) Haas, Y.; Zilberg, S. J. Am. Chem. Soc. 1995, 117, 5387. reactions, and in the possibility of controlling their reactions by environmental (5) Califano, S.; Crawford, B. Spectrochim. Acta 1960, 16, 889. manipulations. (6) Scherer, J. R.; Overend, J. Spectrochim. Acta 1961, 17, 719. 0001-4842/96/0129-0211$12.00/0 © 1996 American Chemical Society 212 Acc. Chem. Res., Vol. 29, No. 5, 1996 Shaik et al. physical nature of this term was left unexplained, but In this Account we show that the Kekule´-crossing turns out to arise naturally from the proposed model. model may be applied to other polyaromatic hydro- It should be noted that this mode’s frequency poses carbons, and that this generalization allows the serious difficulties, even to the very sophisticated prediction of the expected behavior of the Kekule´-type quantum mechanical calculations.7 modes for all the acene series. II. Kekule´-Crossing Model The model, applied to benzene, was discussed in detail elsewhere,11,12 so only a brief survey of the main assumptions and results follows. It is easily shown, on the basis of symmetry transformations of the In naphthalene, the Kekule´-type mode 2 is annu- Kekule´ structures, that the 1A ground electronic lenic in type and undergoes a frequency exaltation of 1g state of benzene and the 11B excited state may both 189 cm-1 in the 11B state relative to the ground 2u 2u be considered as combinations of the two Kekule´ state.3a In anthracene there exist two Kekule´-type structures K (5) and K (6). Thus, since the D point modes, one (3) in which the benzene-like vibration is l r 6h group symmetry operations, inversion (i), 180° rotation localized in the central ring and has been shown (c ), and reflection through a plane perpendicular to recently to undergo an up-shift of 231 cm-1.8-10 The 2 the molecular plane (σ ), interconvert K and K ,it b modes in the B states can be observed only by v l r 2u 2u follows that their positive combination 7 transforms two-photon absorption, making their observation some- as the totally symmetric representation of the group what difficult; the second anthracene mode (4) has not (A ), while their negative combination 8 transforms been definitely assigned yet. It is calculated to be 1g exalted by 96 cm-1.10 This phenomenon of frequency up-shift of the b2u modes is in contrast with the usual pattern of fre- quency decrease which is observed upon electronic excitation. The weakening of π bonding which attends as B2u. Extensive valence bond (VB) calculations an excitation of an electron from a bonding to an following the pioneering study of Da Silva et al.13 show antibonding orbital is intuitively expected to reduce that these two structures give a good quantitative 11 the force constant of the associated normal modes and description of the states around the D6h geometry. thereby, provided the reduced masses remain un- At distorted D3h geometries, one needs ionic struc- changed, to lead to smaller vibrational frequencies. tures. However, the relative steepness of the ground Indeed, this expected trend is the observed behavior and excited state potentials is still determined by the in many aromatic molecules (see ref 10 and references two Kekule´ structures. Consequently, presentation of therein). Furthermore, the frequency up-shift is the physical origins of the phenomenon requires only 1 specific to the 1 B2u state and, to the best of our the Kekule´ structures. This is the main goal of our Publication Date (Web): May 14, 1996 | doi: 10.1021/ar950206i knowledge, is not observed in other excited singlet treatment which seeks a qualitative physical insight states of benzene, naphthalene, and anthracene. We rather than an accurate calculation of the frequencies. are thus dealing here with a mode- and state- selective Figure 1 shows a schematic representation of the phenomenon. As discussed in a recent ab initio modes for the case of benzene. It is based on the VB- modeling,11 the phenomenon originates in the simul- calculated11 energy of the two Kekule´ structures as a Downloaded by HEBREW UNIV OF JERUSALEM on September 1, 2015 | http://pubs.acs.org 1 1 taneous genesis of the 1 A1g and 1 B2u electronic states function of motion along the b2u coordinate that from the avoided crossing of the Kekule´ structures interchanges the two Kekule´ structures. The energy along the b2u coordinate, hereafter referred to as the of Kl is seen to be minimal at the geometry in which Kekule´-crossing model. the three double and three single bonds have their According to this Kekule´-crossing model, the ben- standard equilibrium values. Stretching of the double zene case can be explained by the avoided crossing bonds and simultaneously contracting the single bonds, 11 mechanism of Shaik and Hiberty, assuming that the by motion along the b2u coordinate, increases the 1 1 ground 1 A1g and first excited B2u states of the energy of Kl which becomes a highly strained excited molecules may be described as arising primarily from structure.
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