J. Phys. Chem. 1986, 90, 6710-6711
6770
FEATURE ARTICLE Proxlmlty Effect In Molecular Photophyslcs: Dynamlcal Consequences of Pseudo-Jahn-Teller I nteractlon Edward C. Lim Department of Chemistry, Wayne State University, Detroit, Michigan 48202 (Received: July 7, 1986)
We present here photophysical properties of nitrogen-heterocyclicand aromatic carbonyl compounds that can be attributed to vibronic coupling between nearby nn* and nn* states (proximity effect).
Nitrogen-heterocyclic and aromatic carbonyl compounds often exhibit luminescence (fluorescence and/or phosphorescence) that is strongly dependent upon temperature, the nature of the solvent, chemical substitution, and the position of the deuterium substitution.’ Many of these complexities can be traced to the vibropic interaction between close-lying nn* and nn* states, which leads to a large increase in the nonradiative decay rate of the lowest excited state. This phenomenon, which we have termed proximity effect, has been a subject of extensive studies in recent years, and there is now compelling evidence that the photophysical behavior of the lowest excited state in these molecules is strongly influenced by the proximity effect. The purpose of this Feature Article is to elaborate on this conclusion by presenting emission properties of nitrogen-heterocyclic and aromatic carbonyl compounds that can be attributed to the manifestation of the proximity effect. The paper is divided into two parts. In section I we describe a simple theoretical model of the proximity effect and the results of the model calculations. The predictions of the theoretical analyses are then compared with the experimental results in section 11.
I. Theoretical Considerations Two theoretical frameworks exist for understanding the influence of the n a * i n * vibronic coupling on radiationless trans i t i o n ~ . ~The , ~ first operates within the Franck-Condon principle, whereby the out-of-plane bending mode that adiabatically couples the close-lying nn* and *A* states acts as an efficient accepting mode for the radiationless transition,2 by virtue of its frequency shift and displacement (pseudo-Jahn-Teller e f f e ~ t ) . In ~ ~this ~ mechanism, vibrational coordinate dependence of adiabatic electronic wavefunction is neglected by invoking the Condon approximation, so that the vibronically active mode enters the matrix element of the radiationless transition only via the Franck-Condon factor. Strictly speaking, the Condon approximation is not valid for radiationless transition since the transition matrix elements do not usually separate into an integral over the promoting modes and an overlap integral over the accepting modes. The second is a non-Condon mechanism that incorporates the dependence of the adiabatic electronic wavefunction on the coordinates of the vibronically active modes. This dependence indirectly affects the matrix element of the radiationless transition (1) Lim, E. C. In Excited States, Lim, E. C., Ed.; Academic: New York, 1977; Vol. 3, p 305 and references therein. (2) Wassam, W. A., Jr.; Lim, E. C. J. Chem. Phys. 1978,68,433; J . Mol. Struct. 1978, 47, 1129. (3) Siebrand, W.; Zgierski, M. Z. J. Chem. Phys. 1981, 75, 1230 and
earlier papers of this series. (4) Moffitt, W.; Liehr, A. D. Phys. Rev. 1957, 106, 1195. Liehr, A. D. 2.Naturforsch. 1961, 16, 641. ( 5 ) Hochstrasser, R. M.; Marzzacco, C. A. In Molecular Luminescence; Lim, E. C., Ed.; Benjamin: New York, 1969; p 631.
0022-3654/86/2090-6770$01.50/0
from the lowest excited state, induced by another non-totally symmetric mode (inducing mode).’ The non-Condon mechanism can lead to an enhancement of radiationless transition even in systems where vibronic coupling is too weak to produce a large frequency shift in the out-of-plane bending mode.3 Because the Condon mechanism2 (albeit its shortcoming) allows simple physical insight into the role of the vibronic coupling in the radiationless processes, only this model will be described here in some detail. Two-State Vibronic Coupling. To see how the close proximity of nn* and nn* states can lead to a rapid radiationless transition via the Condon mechanism, we start with two electronic states Im(q,Qo))and In(q,Qo))which are eigenfunctions of the electronic Hamiltonian ( H e )
He(q,Qo) = TJq) + U(q,Qo)
(1)
Here, Terepresents the kinetic energy operator for electrons (with coordinate q) and U represents the potential energy of interaction between the electrons, and between the electrons and the nuclei, at the equilibrium nuclear configuration Qo. The corresponding potential energy surfaces are taken to be simple harmonic potentials
and
E,’O’(Qp) = E,’O’(Qo) + (1 /2)kpJo)Qp’
(3)
where kpm(0)and kpJO)denote the force constants for the mode Qp which induces lm(q,Qo))- In(q,Qo))vibronic coupling. Expanding the potential energy of interaction in a power series in QP
WQ,) =
(4) one obtains
as the dominant interaction term ieft out in the crude adiabatic electronic Hamiltonian (eq 1). Thus, the term [aU(q,Q,)/ aQp]@Qpcan induce coupling of the state Im(q,Qo))with the state In(q,Qo)). In planar aromatic molecules, the mode Qpthat couples nn* and nn* states is an out-of-plane bending mode as n and 7r orbitals are symmetric and antisymmetric with respect to reflection through the molecular plane, and the operator aU(q,Qp)/dQp 0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 26, 1986 6771
Feature Article
I QP
Figure 1. Schematic representation of the potential energy distortion resulting from the vibronic interaction between two close-lying excited states.
transforms as Qp. Since vibronic coupling mixes Im(q,Qo))and In(q,Qo)) we write the adiabatic Born-Oppenheimer (ABO) electronic states as
In(q,Qp)) = an(Qp)ln(q,Qd)+ bn(Qp)Im(q,Qo))
(6)
and
Im(q,Qp))= am(Qp)ln(q,Qo))+ bm(Qp)lm(q,Qo)) (7) Making use of eq 2-7 and implementing the variation method, we solve for the A B 0 potential energy surfaces. The results are5v6
L
and
where Umn@) is given by
If 2[kPm(O) - kp,’O)]> IUmn@)Iz/AEmn and the term in the square bracket of eq 9 is negative, the lower energy surface assumes a double m i n i m ~ m .However, ~ if the term in the bracket is positive, the quartic (Q‘) and higher order terms, not written out in (8) and (9), are simply anharmonic corrections to the harmonic surfaces. It should be noted from eq 8 and 9 that the force constant (and therefore the frequency) of the vibronically active out-of-plane bending mode decreases in the lower electronic state, while that in the upper electronic state increases as a result of the vibronic intera~tion.~ The potential energy distortion resulting from the vibronic interaction is schematically illustrated in Figure 1. The magnitude of the frequency decrease in the lower electronic state can be quite large as illustrated by the fact that the vloa(blg)mode, which is active in lB,,,(n~*) - ‘B2,(mr*) vibronic coupling in pyrazine (1,Cdiazabenzene), undergoes a substantial reduction in its frequency (383 cm-l) in the lB,,,(n~*)state relative to that (919 cm-’) in the ground electronic state (So). FranckCondon analysisEof the fluorescence and absorption spectra of gaseous pyrazine shows that the greatly reduced frequency of the vloa(bls)mode is almost entirely due to vibronic coupling between S1(1B3,,,n?r*)and S2(IBk,m*), which are separated by about 7000 cm-I. The large reduction in frequency is accompanied by strong anharmonicity, consistent with the importance of the quartic and higher order terms in eq 9. The potential energy distortion (frequency change) and displacement (geometry change) along the vibronically active out(6) Duben, A. J.; Goodman, L.; Koyanagi, M. In Excited Srates; Lim, E. C., Ed.; Academic: New York, 1974; Vol. 1, p 295. (7) Kanamaru, N.; Lim, E. C. J. Chem. Phys. 1976,65,4055. ( 8 ) Suzuka, I., Mikami, N.; Ito, M . J. Mol. Spectrosc. 1974, 52, 21. Kiamogawa, K.; Ito, M. Ibid. 1976, 60, 277.
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Figure 2. Threestate model for radiationless transition, consisting of two excited electronic states, Im)and In), coupled through a single vibroni-
cally active mode, and a third electronic state, IO), to which the state In) decays nonradiatively. of-plane bending modes and the anharmonicities associated with these vibrations have important effects on the nonradiative decay rate of the lowest excited state, as discussed in the next section. nT*-m* Vibronic Coupling and Radiationless Transitions: Franck-Condon Factors. Radiationless transition involves conversion of electronic energy belonging to the upper electronic state to vibrational energies of the lower electronic state. Nonradiative decay rate can be expressed in the Golden-rule form by k,, = (27r/h)PF,where V represents the electronic matrix elements (involving spin-orbit coupling for intersystem crossing and nuclear kinetic energy for internal conversion) and F is the density-of-states weighted Franck-Condon f a ~ t o r . ~The magnitude of the Franck-Condon factor depends sensitively on the frequency shift as well as the displacement of the energy accepting modes. For a distorted, but undisplaced, harmonic oscillator, the FranckCondon factor for In) 10) radiationless transition can be written as9
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where
Thus, the modes that suffer large frequency increases in going from the initial electronic state ( n ) to the final electronic state (0) of the radiationless transition are expected to contribute most to the Franckxondon factors. Since the out-of-plane modes active in the nr*-m* vibronic coupling have lower frequencies in the excited electronic state than in the ground state (vide supra), these vibrations should be important accepting modes for radiationless decay of the lowest excited state. This conclusion becomes especially obvious when the anharmonicity associated with the vibronically active out-of-plane bending modes is included in the consideration of the Franck-Condon factors.I0 To investigate the effect of nA*-mr* vibronic coupling on radiationless decay rates more quantitatively, we have used the three-state model consisting of two excited electronic states, Im) and In), coupled through a single vibronically active mode p , and a third electronic state, IO), to which the lower of the two vibronically coupled states can decay nonradiatively (Figure 2). The results of the numerical (9) See, for a review: Henry, B. R.; Siebrand, W. In Organic Molecular Phorophysics; Birks, J. B., Ed.; Wiley-Interscience: London, 1973; Vol. 1, p 153. (10) Wassam, W. A., Jr.; Lim, E. C., unpublished results.
Lim
6772 The Journal of Physical Chemistry, Vol. 90, No. 26, 1986 d -.
*.
,_-
n *'
nu'
'.'.
'I*'
A
n II'
,I
0
*.
n I' C D Figure 4. Effects of electron-donatingsubstituent, or protic solvent, on energy-level disposition of nr* and rr* states. Figure 3. Barrier width for radiationless transition, for cases in which
the vibronic coupling is weak (left), strong (right), and very strong (center). investigations based on the known or estimated spectroscopic parameters show that for a sufficiently large interaction strength and sufficiently small energy separation between the interacting states the vibronically active out-of-plane bending mode could become the dominant accepting mode for the radiationless transition.2v" The radiationless decay rate was found to increase dramatically with vibrational excitation of the out-of-plane bending modes in the lower of the two vibronically coupled states." In the event that the lower excited state In) adopts a doubleminimum potential, a large change in geometry between In) and 10) was found to render the out-of-plane vibration an even better accepting mode and thereby enhance the rate of the radiationless transition compared to that expected in the absence of structural distortion.I2 Vibrational Effects on (SI So)/(Sl T l )Branching Ratio. A particularly interesting conclusion to come out of the theoretical studies is that for the single-minimum case the proximity effect on radiationless transition, as well as the effects of vibrational excitation thereon, is greater for larger In) -10) electronic energy Since the SI (lowest excited singlet)-So (ground singlet) electronic energy gap is much greater than the SI-T1 (lowest triplet) gap, it follows that the proximity effect will have a much greater influence on SI So internal conversion than on SI TI intersystem crossing. Thus, the (SI So)/(Sl TI) branching ratio in the radiationless transition is predicted to be greatly enhanced by optical excitation of the out-of-plane bending modes in SI under collision-free conditions of a low-pressure gas phase or by thermal population of the same modes (in SI) in a condensed phase.2 The photophysical behavior a t high temperatures is therefore expected to be strongly influenced by SI So internal conversion if the proximity effect plays an important role. Vibronic Interaction and "Barrier Width"for Radiationless Transition. The foregoing conclusions, based on the results of by the the model calculations, can be qualitatively rationali~ed'~ so-called barrier width,14which represents the horizontal distance (Le., the distance along the constant energy line) between the wall of the initial state potential energy surface and the wall of the , ~ bamer ~ final state surface. As shown by Ross and ~ w o r k e r sthe width is inversely related (albeit crudely) to the magnitude of the Franck-Condon factors associated with the radiationless transition. In Figure 3 we compare the barrier widths for cases in which the vibronic coupling is weak (left), strong (right), and very strong (center). Note that the barrier width is smaller the stronger the vibronic interactions, consistent with the increasing FranckCondon factors. Furthermore, the barrier width decreases with
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-
-
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-+
(11) (12) (13) (14)
Wassam, W. A., Jr.; Lim, E. C. J . Chem. Phys. 1978, 69, 2175. Wassam, W. A., Jr.; Lim, E. C. Chem. Phys. 1979, 38, 217. Wassam, W. A., Jr.; Lim, E. C. Chem. Phys. Leff. 1978, 56, 419. Byme, J. P.;McCoy, E. F.; Ross, I. G . Ausf.J. Chem. 196!4,19,1589.
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TABLE I: T1(nr*) S, RadiaDeeay Rates of Pyrazine and Two of Ita Methyl Derivatives in MethylcyclohexaneClass at 77 K compd aF aP T ~ ms , k,," s-l k,,," s-' pyrazine 0.30 18.5 16.2 37.9
2-methylpyrazine
