Physical Chemistry Chemical Physics

Effect of through bond coupling and conformation on the photophysical properties of -bridged systems comprising a vinylnaphthalene donor and a dicyanovinyl acceptor

J. Kurzawa^a, S. Schneider^a, J. Büber^b, R. Gleiter^b and T. Clark*^c
aInstitut für Physikalische und Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
^bOrganisch-Chemisches Institut der Universität Heidelberg, Im Neuenheimer Feld 270, D-69120 Heidelberg, Germany
^cComputer-Chemie-Centrum, Universität Erlangen-Nürnberg, Nägelsbachstr. 25, D-91052 Erlangen, Germany. E-mail: Tim.Clark@chemie.uni-erlangen.de; Fax: +49-9131-8526565; Tel: +49-9131-8522948

The electron transfer kinetics of the donor–bridge–acceptor (D–B–A) compounds investigated is governed by three different effects: polarity of the solvent, change of conformation (especially rotation of the single bond of the vinylnaphthalene moiety) and the p-character of the bridge (bicyclooctane, norbornane, stellane). The expected increase of the rate of electron back transfer with increasing p-character of the bridge orbitals is only clearly seen in medium and very polar solvents (methylene chloride and acetonitrile). In less polar solvent (2-methyl-THF) the temperature dependence of the charge-transfer (CT) fluorescence of the system with the bicyclooctane bridge points to the existence of two emitting CT conformers. Semiempirical MO calculations with configuration interaction reveal that 2 or even 3 (norbornane bridge) local minima exist on the energy surface of the CT state. They differ mainly in the angle of rotation of the single bond mentioned above, but also by deformation of the bridge structure. In non-polar solvent (methylcyclohexane) the fluorescence behaviour becomes even more complex because emission from the CT state(s) and from the locally excited state overlap. The analysis points to an equilibrium between different rotamers on the energy surface of the lowest locally excited state, on the one hand, and of the CT state, on the other hand. Investigations of the compound with the stellane bridge are hampered by significant photodegradation in methylcyclohexane solution.

Much attention has been paid to electron donor–bridge–acceptor (D–B–A) systems during the last few decades, mainly for two reasons. Firstly, because the experimental results are well suited to testing the quality of theoretical models¹ and their predictions^2–5 (e.g. the variation of the rate for electron transfer with the distance R_DA between donor and acceptor) and secondly because of the desire to mimic the very effective photoinduced charge separation over large distances that occur in photosynthesis^6–8 or to construct molecular devices.^9–11

More recently, investigations of D–B–A systems with semi-flexible bridges have shown that conformational changes induced by the strong attractive Coulomb forces between the oppositely charged groups (harpooning mechanism) can result in remarkably strong alterations of the electronic properties of charge-transfer (CT) states.^12,13 These properties are also strongly dependent on solvent polarity whenever the distances for charge separation vary significantly with the change of conformation.^14,15

Furthermore, it was found that, even in such D–B–A systems where the bridge was considered to be very rigid in the electronic ground state (e.g. norbornane-type -systems), the conformation of the bridge in the CT state changed significantly in nonpolar environments.^14–17

Another important aspect besides the rigidity of the bridge is the strength of the electronic coupling mediated by it. If donor and acceptor are both -electronic systems, a simple model predicts that the through-bond interaction should increase with the p-character of the frontier orbitals of the bridge. Previous studies on 2,5-dimethylidenebicyclo[2.2.2]octane 1, 2,5-dimethylidenebicyclo[2.2.1]heptane 2 and 2,5-dimethylidenetricyclo[3.3.0.0]octane 3 ^3,7(Scheme 1) revealed a difference in the first two ionization energies of 0.2 (1), 0.3 (2) and 0.9 eV (3) by means of photoelectron spectroscopy.^18,19 This increase in the energy splitting is due to the higher through-bond coupling^20,21 between the two -fragments during ionization. This energy splitting can be traced back to the increase of p-character of the bridges of 1, 2 and 3. Assuming that the through-bond interaction^20,21 found for the ionization process is related to that in charge-separated states, we used the scaffolds of 1, 2 and 3 and connected one of the exo-methylene groups with two cyano-groups as acceptor. As donor groups, we used naphthalene, anthracene or pyrene. A comparison of the fluorescence spectra of these D–B–A systems with those of the corresponding donor-bridge systems showed that the driving force for photoinduced charge separation is only large enough to result in quenching of the fluorescence from the locally excited state(s) in solvents of medium or high polarity with naphthalene or pyrene as donor.²² Because of higher extinction coefficients at the preferred excitation wavelength (300 nm), we chose naphthalene as substituent to investigate the photophysical behavior of the model systems 4, 5 and 6 shown in Scheme 1 in detail.

	Scheme 1 Dienes of the bridge compounds (1, 2, 3) formerly investigated by means of photoelectron spectroscopy, investigated D–B–A systems (4, 5, 6) and reference (D–B) compounds (7, 8, 9).

A further advantage of this series of bridging elements is that the length of the bridge is essentially constant. Consequently, the synthesis of D–B–A systems employing these three bridges should allow an easy determination of the influence of the p-character of the -bonds on the rates for charge separation and recombination. In previous work exploring the harpooning mechanism, we found, however, that rotation around a single bond connecting the donor to the bridge can influence the excited state kinetics strongly.¹³ Arai et al. reported rotational isomerization of 2-vinylanthracene in the excited singlet state as early as 1989.²³ One can therefore surmise that, in the case of our model compounds 4, 5 and 6, the vinylnaphthalene group acts as a non-rigid donor group, thus giving rise to new phenomena in the behavior of both the locally excited and especially the charge-transfer state, which have not yet been studied in detail. Upon rotation of the single bond, the distance between donor and acceptor group varies to a large extent, thereby modifying the energy difference between locally excited and charge-transfer states, especially in non-polar solvents. We will demonstrate that the latter effect indeed gives rise to the population of structurally different CT states in solvents of sufficiently low polarity.

The syntheses of the compounds under investigation have been described in detail elsewhere.²¹ The solvents used throughout this study were: methylcyclohexane (MCH, Aldrich, 99% spectrophotometric grade), CH₂Cl₂ (Merck, 99.9%, uvasol), methyltetrahydrofuran (MeTHF, Aldrich, 99+%) and acetonitrile (ACN, Ferrak, 99.8%, HPLC grade).

All solvents were tested for fluorescence from impurities and, if necessary, distilled repeatedly until no fluorescence could be detected.

Solutions were bubbled through with argon or dry nitrogen for about 20 min before fluorescence measurements.

UV/vis absorption spectra were recorded with a Perkin Elmer, Lambda 2 spectrometer. Room-temperature fluorescence spectra were monitored either with a Perkin Elmer, LS50B fluorimeter (wavelength resolution 2.5 nm, scan velocity 240 nm min^–1) or with a Fluoromax 30 (Jobin Yvon) (wavelength resolution 5 nm).

For low temperature fluorescence experiments, the sample was mounted on the cold finger of a closed-cycle refrigerator (CTI-Cryogenics). The sample temperature was measured by means of a temperature-sensitive resistor placed in the sample cuvette. Spectral correction of the detection systems was generally achieved by comparison with the output of a certified calibration lamp (FSA-PE-50E, Labsphere).

In time-resolved fluorescence experiments, the frequency-doubled output of a cavity-dumped Rhodamine 6G laser, synchronously pumped by a mode-locked NdYAG laser, was used for excitation around 300 nm. The spectrally resolved fluorescence was detected under magic angle conditions by a multi-channel plate photomultiplier (more details can be found in refs. 24 and 25).

The decay curves were recorded by means of the single-photon-timing technique employing electronic standard components. They were analyzed in the usual manner by iterative reconvolution of multiexponential decay laws employing least-squares fitting techniques involving both Marquardt and (for the final fit) the simplex algorithms.^26,27

Transient absorption was measured at the Rutherford Appleton Laboratory (Didcot, UK) employing a set-up described in detail elsewhere.^28,29 The excitation wavelength was around 300 nm. The transient absorption was monitored by a white-light continuum in the wavelength range 360 to 750 nm.

All calculations were performed with the program package VAMP 8.0 employing the standard AM1 Hamiltonian.^30,31 Properties of the electronic ground states were determined within the restricted Hartree–Fock approximation. Calculations of spectra used a CI expansion involving all single and pairwise double excitations within 20 active orbitals (PECI = 20). Geometry optimizations with configuration interaction (CI) used analytical gradients³² along with a CI expansion including all singly excited states and the doubly excited states in which an intact electron pair is promoted between the 3 highest occupied and 3 lowest unoccupied orbitals (PECI = 6).

Because the UV/vis absorption spectra of the three compounds investigated show a very small solvatochromic effect, only the spectra recorded in methylcyclohexane are shown in Fig. 1. The presence of the weak, but unstructured band with maximum around 300 nm is evidence that the -electronic system of naphthalene is enlarged by the conjugated double bond. The lack of vibronic structure may be indicative of structural heterogeneity in the electronic ground state connected with a torsion around the single bond. The extinction coefficient varies with the nature of the bridge. It increases with increasing ring strain. This points to an interaction of the donor -electronic system with the bridge orbitals.

	Fig. 1 UV/vis absorption spectra of compounds investigated in methylcyclohexane (MCH): 4(—), 5() and 6 (). For structures see Scheme 1.

The efficient quenching of the fluorescence from the locally excited (LE) state by very fast electron transfer is most clearly seen by a comparison of the emission spectra of the D–B–A systems in solvents of medium polarity with those of the corresponding donor–bridge (D–B) systems as reference (Fig. 2). The fluorescence of the D–B systems exhibits its maximum around 360 nm. The fairly large Stokes shift of about 6000 cm^–1 hints at significant geometrical relaxation in the emitting state, e.g. torsion around the single and/or double bond. In the D–B–A system, only moderately intense fluorescence from the CT state with a maximum around 475 nm can be seen.

	Fig. 2 Comparison of the fluorescence spectra obtained for the donor-bridge system (8) and the corresponding D–B–A system (5) in tetrahydrofuran at room temperature.

In non-polar solvents, the fluorescence spectrum of the D–B–A system closely resembles that of the corresponding D–B system, except that the red wavelength tail is more pronounced (not shown). Evidence for the presence of CT emission is found in the temperature-dependent changes of the spectra (see below). In very polar solvents, the emission from the LE state is completely quenched (as shown for solvents of medium polarity). However, the CT-fluorescence is also extremely weak with the effect that time-resolved fluorescence experiments could not be performed.

To obtain information about the formation and decay of the CT state in acetonitrile, we employed transient absorption spectroscopy with _ex 300 nm (first absorption band). The rise time of the induced optical density around 500 nm is so short that it cannot be resolved (_R < 4 ps). Therefore, we cannot decide whether the difference in p-character of the bridge is reflected in the rates for photoinduced electron transfer.

The decay of the transient absorption, on the other hand, differs strongly for the three compounds investigated (Fig. 3). The lifetimes deduced from a monoexponential fit are 800 ps for 4, 250 ps for 5 and 80 ps for 6. This reduction in lifetime parallels the increase in ring strain and is therefore in accord with expectations. Furthermore, no longer-lived component was found in the whole spectral range investigated in the course of the transient absorption. This implies that the CT states decayed fast and exclusively to the electronic ground state. The short lifetimes observed must be a consequence of fast radiationless charge recombination. They also provide a rationale why CT fluorescence in acetonitrile is negligible.

	Fig. 3 Transient absorption recorded for 4(), 5() and 6() in acetonitrile. exc= 300 nm and det= 500 nm. Solid lines represent monoexponential fits.

In methylene chloride, the CT fluorescence yield is sufficient for fluorescence experiments. In the steady-state fluorescence spectra, lowering the temperature has two effects. First, the maximum of the CT fluorescence shifts towards longer wavelength (Fig. 4). Second, the intensity of the CT fluorescence decreases. Its bathochromic shift can be understood easily. Upon reduction of the solvent temperature, both the refractive index n and the dielectric constant increase (as long as the reorientation of the solvent dipoles is not frozen out). Since we have already shown that in polar solvents the nonradiative charge recombination is the predominant relaxation process, a reduction in the energetic splitting between the ground and CT states would enhance the rate for radiationless relaxation (energy gap law) and concomitantly decrease the fluorescence yield.

	Fig. 4 Normalised steady state emission spectra of compounds investigated in methylene chloride: (a)4(T= 202 K, 217 K, 241 K, 257 K, 280 K and 295 K); (b)5(T= 219 K, 229 K, 247 K, 266 K, 289 K and 300 K); (c)6(T= 230 K, 239 K, 247 K, 261 K, 273 K, 296 K and 300 K). Arrows indicate changes upon decrease of temperature.

By making use of published data on the temperature dependence of n and ,^33,34 we can calculate the temperature-dependent values for the polarity parameter f = (_r – 1)/(2_r + 1) – (n² – 1)/(4n² + 2) and construct a Lippert–Mataga plot^35,36 (Fig. 5a), which can be used to derive an estimate of the dipole moment of the CT state (see below).

	Fig. 5 Lippert–Mataga plots derived from the temperature-dependent shift of the CT fluorescence band of 4(), 5() and 6(): (a) methylene chloride and (b) 2-methyltetrahydrofuran.

In general, fitting the fluorescence-decay curves monitored at the wavelengths of the CT fluorescence maxima requires two exponentials. The first with a very short lifetime and low amplitude is necessary to obtain a ² close to 1, but is obviously without physical relevance. The lifetime of the second, dominant component increases steadily with sample temperature (see Table 1) as can be expected, because the intensity of steady-state CT fluorescence also increases with increasing temperature. The ordering of the lifetimes (at all temperatures) corresponds to that obtained with acetonitrile as solvent: _CT (4) > _CT (5) > _CT (6). The ratio between the three lifetimes is, however, different from that measured in the polar solvent. The inverse of the lifetimes can be used to construct an Arrhenius plot (Fig. 6). The formal activation energies, E_A, are: –2.1 kJ mol^–1 (4), –3.6 kJ mol^–1 (5) and –7.7 kJ mol^–1 (6). The latter compound exhibits both a higher rate for relaxation to the ground state and a higher absolute value for the activation energy.

4
T/K	2/ns	A2
199	3.14	2470
217	3.65	3162
240	4.04	3005
258	4.34	3121
280	4.69	3644
295	4.88	4493
309	4.97	2742
5
T/K	2/ns	A2
219	2.69	669
228	3.05	401
247	3.35	368
266	3.71	440
277	3.99	436
289	4.29	731
300	4.51	580
6
T/K	2/ns	3/ns	A2	A3
227	0.30	2.15	554	8
240	0.39	14.64	783	4
247	0.43	8.61	767	4
261	0.50	6.65	1974	9
273	0.56	1.94	1544	25
285	0.69	4.65	1443	4
296	0.80	—	1070	—
300	0.83	—	1224	—

	Fig. 6 Arrhenius plots of the inverse CT fluorescence lifetimes measured for 4(), 5() and 6(): (a) methylene chloride and (b) 2-methyltetrahydrofuran.

In 2-methyltetrahydrofuran, the temperature-induced shifts of the fluorescence maxima (Fig. 7) and the changes in fluorescence intensity of 5 and 6 are qualitatively similar to those described for methylene chloride solvent. However, the behavior of 4 is different in that a decrease of the temperature results in an increase of the steady-state intensity of the CT fluorescence.

	Fig. 7 Normalised steady state fluorescence spectra of D–B–A systems investigated in 2-methyltetrahydrofuran: (a)4(T= 170 K, 199 K, 219 K, 238 K and 271 K); (b)5(T= 194 K, 218 K, 239 K, 260 K and 295 K), (c)6(T= 220 K, 237 K, 246 K, 261 K, 272 K, 293 K). Arrows indicate shifts upon decrease of temperature.

Analysis of the fluorescence decay curves recorded at different temperatures confirms this distinctive behavior. In contrast to the measurements in CH₂Cl₂, three-exponentials were sometimes needed for a proper fit (see Table 2). The fast component of low amplitude is ignored for the reasons given above. The amplitude of the second component ( 0.8 ns) varies strongly from one measurement to the next. Its significance is still unclear to us. The third and major component exhibits a decay time that varies continuously with temperature. The Arrhenius plots of the inverse lifetimes show a qualitatively similar behavior for 5 (E_A = –1.2 kJ mol^–1) and 6 (E_A = –2.7 kJ mol^–1) as in CH₂Cl₂ (Fig. 6b). However, the plot for 4 exhibits a negative slope (i.e. means a positive activation energy, E_A = 1.3 kJ mol^–1). This implies that, in the case of 4 in 2-methyltetrahydrofuran, a thermally activated process contributes significantly to the deactivation of the CT state.

4
T/K	2/ns	3/ns	A2	A3
170	0.83	9.35	74	1956
199	0.76	8.27	–150	1876
219	—	7.73	—	1887
238	0.78	7.36	47	1015
258	—	6.92	—	1060
271	—	6.70	—	1092
294	0.41	6.30	207	1321
5
T/K	2/ns	3/ns	A2	A3
176	0.85	7.42	4018	3029
194	—	8.26	—	2453
218	—	8.85	—	2685
239	—	9.38	—	2292
260	—	9.83	—	2298
288	—	10.11	—	2553
6
T/K	2/ns	3/ns	A2	A3
208	0.86	1.78	–74	1272
222	0.34	1.94	36	1179
236	0.89	2.11	–112	1618
246	0.63	2.23	–190	2251
261	0.84	2.44	–27	2081
273	0.08	2.63	–243	1885
293	0.04	2.79	–195	1825

The Lippert–Mataga plots constructed in a similar manner as described above from the temperature-dependent values of n and ^34,37 provide, at first glance, no hint for a different nature of the fluorescing CT states. The slopes, which represent a rough measure for the dipole moment of the CT state, are about the same for 4 and 5; the slope obtained for 6 is somewhat steeper in both solvents employed (Fig. 5b).

The fluorescence spectra of the D–B–A systems in non-polar solvent are very similar to those of the corresponding D–B systems. Therefore, one can question whether photoinduced electron transfer occurs at all, e.g. for energetic reasons (CT states are higher in energy than the corresponding LE states). Lowering the temperature (297 K 207 K) results in a bathochromic shift of the emission maximum by about 25 nm (Fig. 8). At the same time, the relative intensity of the long-wavelength emission is increased. Since the increase of the polarity parameter f of methylcyclohexane upon lowering of the temperature is fairly small, the bathochromic shift cannot be explained as a consequence of an increase in solvent polarity, as in the case of the solvents of medium polarity. An alternative explanation could be that the spectrum recorded at room temperature represents essentially fluorescence from a locally excited state. Upon lowering the temperature, the relative intensity of the CT fluorescence increases and finally dominates the spectral distribution at low temperature. This implies that the location of the fluorescence maximum observed at low temperature characterizes the energy of the CT state. The energetic splitting between the LE and CT states is, under this assumption, less than 1000 cm^–1 (or 0.125 eV). Consequently, there could be thermally induced back electron transfer from the CT to the lowest LE state and/or an equilibrium could be established between these two states.

	Fig. 8 Normalised steady state fluorescence spectra of D–B–A systems investigated in methylcyclohexane: (a)4(T= 207 K, 216 K, 231 K, 247 K, 262 K and 297 K); (b)5(T= 192 K, 222 K, 238 K, 252 K, 275 K and 295 K), (c)6(T= 224 K, 235 K, 255 K, 280 K, and 295 K). Arrows indicate changes upon decrease of temperature.

A proper fit of the fluorescence-decay curves generally needs three exponentials, as in the case of the solvents of medium polarity. The lifetimes of the second and third, physically relevant, components determined for various temperatures are summarized in Tables 3 and 4. However, in contrast to the more polar solvents, no steady variation of the decay times in one direction is found, except perhaps for ₂ in the case of 5. We cannot exclude that such a unique trend would be found if more exponentials were included in the fitting procedure. However, fitting decay curves with more components with similar lifetimes is always subject to large errors and/or ambiguities.

T/K	1/ns	2/ns	3/ns	A1	A2	A3
295	0.08	0.99	1.68	–152	651	249
277	0.87	1.91	3.95	–190	1148	171
252	0.10	2.29	6.64	–333	—	926
238	0.37	5.69	10.90	–124	–26	1080
222	0.43	5.51	14.10	–180	–44	1132
192	0.14	5.25	15.54	–561	–83	1008

T/K	1/ns	2/ns	3/ns	A1	A2	A3
297	0.36	1.38	3.08	847	1390	321
263	0.04	1.38	4.98	–1052	795	896
247	0.15	2.69	7.16	–548	1213	1077
232	0.17	5.23	8.60	–319	719	635
216	0.23	2.15	8.17	–8	–127	1613
206	0.38	2.58	9.58	154	–97	2141

Independently of the problem of a correct fitting of the recorded decay curves, the data shown in Tables 3 and 4 suggest a more complex photophysical behavior in non-polar solvents. Such a situation is known from previous studies of donor–acceptor systems and could be related to structural heterogeneity. Variations in the distance across which the charge is transferred generally only exert a significant effect on the energetic ordering of the CT versus the LE state(s), and concomitantly on the rates of the competing deactivation processes,¹⁴ in non-polar solvents.

However, in the compounds investigated, one must not only pay attention to the energy of the CT state, but also to that of the lowest LE state. The latter can vary with a torsion around the single and/or double bond. As a consequence, the photophysical properties of vinyl-substituted arenes, and especially those of stilbene, vary strongly with solvent viscosity and temperature.^38–40 In accordance with this line of argument, we have studied the temperature dependence of the fluorescence of the D–B reference compounds. As for the above systems, reduction of the solvent temperature results in a dramatic increase of the steady-state fluorescence intensity of 8 in methylcyclohexane (Fig. 9). The lifetimes derived for the two major components in the fluorescence decay of 8 show a steady decrease with increasing temperature (Table 5) and provide, by comparison with the behavior of trans-stilbene, evidence for the presence of a thermally activated deactivation channel for the emitting excited state. The ratio of the amplitudes of the second and third component varies with detection wavelength (the range is given in the sixth column of Table 5) and shows no systematic trend with temperature.

	Fig. 9 Steady state emission spectra of 8 in methylcyclohexane (T= 213 K, 236 K, 252 K, 276 K and 295 K). Arrow indicates decrease of temperature.

T/K	2/ns	3/ns	A1	A2	A2/A3
295	0.13	0.65	3959	3164	1.06–1.25
276	0.20	1.29	1403	1219	1.15–1.33
252	0.56	2.61	527	1091	0.48–0.40
236	1.26	3.10	403	1872	0.16–0.26
213	1.69	2.99	–568	2424	–0.26–(–0.21)

For the fastest component, the derived amplitudes are always negative, indicating a delayed onset of the fluorescence. The associated rise time ₁ is close to the time-resolution of the experiment. Therefore, we cannot make a definite assignment of the 60 ps rise time without further information.

The most likely source for structural heterogeneity in the electronic ground state is a rotation of the single bond connecting naphthalene to the double bond (angle ). Accordingly, we have calculated the heat of formation employing the standard AM1 Hamiltonian.^30,31 The geometry of the system was optimized for different fixed values of angle . In the case of 5 (Fig. 10, bottom), the variation of the heat of formation, H_f, is less than 4 kJ mol^–1 for a variation of between 70° and 150° and 210° and 290°, respectively. This implies that in solution at room temperature a broad range of angles is most likely realized. For all three compounds investigated, two local minima are found, one for 125°, the other for 230° (see Table 6). By using the Boltzmann equation, a first estimate of the ratio of the two rotamers with minimal energy can be made (see Table 6). This ratio is close to 11 with a slight excess of rotamer 2. Since the barrier between these two conformations is only about 10 kJ mol^–1, the equilibrium between the two should be established quickly.

	Fig. 10 Influence of torsional angle on the distance between donor and acceptor group, RDA, and the heat of formation (Hf) in the electronic groundstate. All calculations for 5 with AM1 Hamiltonian in vacuo.

		4	5	6
Rotamer 1	/°	120	130	130
	RDA/pm	679	675	792
	Hf/kJ mol–1	493.53	593.91	812.34
	µ/D	4.62	4.56	4.83
Rotamer 2	/°	240	230	220
	RDA/pm	745	743	802
	Hf/kJ mol –1	493.29	593.62	812.08
	µ/D	4.78	4.72	4.86
TS	Hf/kJ mol–1	505.26	602.25	824.47
= 180°	µ/D	4.81	4.72	4.93
	fR1fR2	4852	4753	4753
Extreme parameters	(RDAmin)/°	50	60	320
	RDAmin/pm	609	594	706
	(RDAmin)/°	200	200	180
	RDAmin/pm	780	761	829

More interesting is, however, how the distance between donor and acceptor changes with the variation of the torsional angle . For the sake of simplicity we assume that, after photoinduced electron transfer, the positive net charge is located on C₁₀ of naphthalene and the negative net charge on the carbon carrying the two cyano groups as substituents. With this definition of R_DA, the shortest distance is found for = 60°, the largest for 200° (Fig. 10, top).

Important for further considerations is that the distance R_DA is about 75 pm different for the two conformations representing nearly isoenergetic local minima on the energy surface of the ground state. If we assume photoinduced electron transfer to occur rapidly in the ground-state conformation then, at least in non-polar solvents, the Coulomb interaction will be different in the primarily formed CT state (Franck–Condon state geometry) and concomitantly provide the driving force for geometrical relaxation (harpooning mechanism).

The program package VAMP 8.0 includes an algorithm for geometry optimization of electronically excited states. It was therefore tempting to use this feature for the CT state of our D–B–A systems and to test whether indeed several local minima on the excited state energy hypersurface connected to specific values of the dihedral angle exist.

In the case of 5, the procedure described (with PECI = 6) yields three distinctly different conformations for the CT state (Fig. 11). The angles computed for these three conformers (Table 7) are quite different from those determined for the two most stable ground-state conformations (Table 6). This means that a significant rotation around the single bond is required to reach the three conformations. The differences between the calculated values of the angle , which provides a measure for the distortion of the norbornane bridge, show that the deformation of the bridge varies with the Coulombic force between the two charged groups. The calculated dipole moments of the three conformers do not reflect the variation of the distance R_DA defined above. In conformer 1, this distance is shorter than that of conformer 3 by about a factor of 0.77, but the calculated dipole moment is larger by a factor of 1.25. This discrepancy points to a distribution of the net charges across the whole donor and acceptor species, respectively. It is visualized in the molecular electrostatic potentials displayed in Fig. 11 for 5.

	Fig. 11 Geometries and electrostatic potentials of three CT conformations of 5. All geometries represent local energy minima (in vacuo) in the calculation performed with analytical CI gradients (PECI = 6). Calculated parameters are compared in Table 7.

	4	5	6
/°		36	27
RDA/pm		488	717
Hf/kJ mol–1		1081.2	1336.6
µ/D		24	28
/°		101	135
/°	157	165
RDA/pm	657	706
Hf/kJ mol–1	973.49	1119.3
µ/D	17	31
/°	112	108
/°			193
RDA/pm			824
Hf/kJ mol–1			1321.1
µ/D			28
/°			135
/°	326	321
RDA/pm	590	634
Hf/kJ mol–1	984.38	1089.4
µ/D	19	19
/°	106	104

For the other two D–B–A systems investigated, only two local minima were found on the energy hypersurface of the CT state (Table 7). In case of 4, the correlated geometries resemble those of conformer 1 and conformer 3 of 5. In the case of 6, the angles are closer to 0° and 180°, respectively. This can be understood on the basis of the symmetry of the stellane bridge.

If one restricts the comparison to the most stable conformer of each system, one finds a clear hierarchy of the calculated dipole moments: µ(4) = 17 D < µ(5) = 24 D < µ(6) = 28 D. This sequence may still be found in non-polar solvents. In more polar solvents, the conformer of 5 with the highest calculated dipole moment (µ = 31 D) could be stabilized so much more that it becomes the most stable.

Since we have shown in the previous section that the energy hypersurface of the CT state can have several local minima with geometries different from those of the most stable ground-state conformers, it is worthwhile to investigate whether structural relaxation can occur as early as in the locally excited state, either before electron transfer occurs or in competition with it.

Geometry optimization of the lowest excited LE state for fixed values of the angle (rotation around the double bond) yields as the most stable conformers for 5 those with = 0° and = 180°. Separated from these by a barrier on the order of 25–33 kJ mol^–1, we find another local minimum on the energy hypersurface for 90° (H_f 8 kJ mol^–1). The analysis of the molecular electrostatic potential provides a rationale for this finding. In the latter conformation, a charge separation occurs across the double bond as has been discussed in the past for various derivatives of ethylene,^41–44 and especially for stilbene, by Hamaguchi et al.⁴⁵ (exchange polarisation model). The direction of the charge transfer is opposite to that expected in the ground state because of the accepting properties of the cyanovinylene group and the donor properties of the naphthalene moiety.

In stilbenes, electronic excitation results in a weakening of the central double bond and a concomitant strengthening of the single bond to the phenyl rings. Because a similar effect can be expected for the single bond in vinylnaphthalene, it is worthwhile to study the course of the energy hypersurface(s) along this internal coordinate. The geometry-optimisation procedure applied to the lowest singlet state predicts a rather strange looking potential curve exhibiting several local minima. The appearance of these can best be understood if not only the S₁, but also the S₂ state, which in naphthalene lies close by, is considered (Fig. 12).

	Fig. 12 Calculated heat of formation of 5, Hf, in the first () and second () locally excited singlet state (bottom), and oscillator strength f for the transition into these states (top). CI-calculations including 10 highest occupied and 10 lowest unoccupied MOs (PECI = 20); AM1 Hamiltonian in vacuo.

To facilitate the computational effort (and the graphical presentation), the geometry of 5 was optimised in the electronic ground state for different fixed angles . For these geometries, the excitation energies were calculated in the CI approximation employing a large set of configurations (PECI = 20). The potential energy curves shown in Fig. 12 were constructed by combining the heat of formation in the ground state and the corresponding Franck–Condon excitation energies. Although the energies given are not those of the excited-state-optimized geometry, they nevertheless reproduce the essential features of the correctly calculated energy hypersurface. The reason for the complex dependence of the energy of the lowest excited singlet state on the single bond torsion is found in the crossing of the L_a and L_b states of naphthalene because of a torsion-dependent interaction with the vinyl group (for = 90° and 270°, the two -electronic systems are essentially decoupled). Excitation into the S₁ Franck–Condon state ( 130° or 230°) leads into a (local) minimum of the S₁ potential curve. The barrier to the second (local) minimum conformation with 180° is probably low enough that a population equilibration between the three distinct conformations is reached even during the short excited-state lifetime.

The course of the oscillator strength f for a transition from the ground state to the two lowest excited states as a function of confirms this explanation. In the decoupled system ( 90°), the transition to the S₁ state is essentially forbidden. This means that photon absorption occurs preferentially to the S₂ state. If the torsional angle approaches 180°, the oscillator strength for excitation to the lowest excited state increases to a maximum value because the nature of the electronic state has changed. This implies that the rate for fluorescence from the lowest excited state is increased dramatically when the planar conformation ( = 180°) is adopted. In other words, if the two types of conformers (LE1 with = 130° or 230° and LE2 with = 180°) are populated in equilibrium, the fluorescence that can be detected could originate preferentially from the planar conformer. A deviation from this expectation will occur only if the rate for photoinduced electron transfer is several orders of magnitude larger in the planar than in the twisted (ground-state) conformation.

Because the variation of the steric interaction between the naphthalene moiety and the bridge upon changing the torsional angle depends on the spatial extension of the bridge, the potential curves describing the two lowest excited states will be somewhat different for the three compounds investigated. However, the general features that give rise to the complex photophysical behavior in non-polar solvents remain the same.

Because the two conformers with 130° and 230° are very similar in their energetic and optical properties, we can lump them together as conformer G (ground-state-optimized geometry) in a simplified kinetic model (Scheme 2). As second species E, we define the conformer(s) with 180° (excited-state-optimized geometry). Because the difference in energy of the corresponding locally excited states, LEG and LEE, is small as is supposedly the barrier, a kinetic scheme must include forward and backward reactions between these two species. Based on the results of the semiempirical MO calculations, we postulate that the intrinsic lifetimes of the two species are significantly different.

	Scheme 2 Schematic presentation of different conformers in ground and first excited singlet state and relaxation rates taken into consideration when evaluating the fluorescence data for 8.

In the electronic ground state, the system exists preferentially in conformation G. This implies the LEG Franck–Condon state would be preferentially formed via photon absorption to the S₁ state. If excitation occurs into the S₂ state, which has a higher oscillator strength, not only the LEG but also the LEE state could be populated as consequence of internal conversion.

In the kinetic scheme chosen, the decay of both the LEG and LEE states follows a biexponential with the lifetimes ₁ and ₂:

(1)

However, not only the rates k_f and k_b are temperature dependent, but also the rates k_G and k_E for deactivation to the respective electronic ground states. In contrast to k_f and k_b, the temperature dependence is most likely more complex and can be determined on a trial and error basis only. Important criteria are that all mathematically possible solutions that give a negative value for one of the four rates are physically meaningless. Similarly, if one constructs decay-associated spectra on the basis of the deduced solutions for the four rates, the fluorescence intensities must not be negative at any of the observation wavelengths.

One possible solution for the temperature-dependent rates k_G, k_E, k_f and k_b is shown in Table 8 and graphically illustrated in Fig. 13. (Note that the results also depend on the population ratio of LEE and LEG at time zero.) Except perhaps for the rate constant k_G, one finds an Arrhenius-type behaviour for temperatures above about 235 K. For k_G, such a behavior is found only above about 250 K. This difference, together with the smaller slope, as manifested in the temperature-dependent ratio k_E/k_G, could indicate that the LEE state can relax, in addition, via the thermally activated rotation around the vinylic double bond. A possible explanation for this difference in behavior can be found in the fact that the MOs involved in the CI-description of the LEG state in the ground-state conformation are exclusively localized on the naphthalene moiety. In the excited-state-optimized geometry, the HOMO and LUMO involved in the CI-description of the LEE state involve the AOs on the vinyl group. As a consequence of this, the molecular electrostatic potential discussed above indicates a charge shift from the vinyl group to the naphthalene moiety. Furthermore, the -bond order of the vinyl double bond is reduced and, consequently, a rotation facilitated. The slopes found in the Arrhenius plots of k_G and k_E correspond to a barrier about 10 times higher than that predicted by the quantum chemical calculations. (E_A 27 kJ mol^–1 for k_f and E_A 29 kJ mol^–1 for k_b). This implies that, at sufficiently low temperature, the change of conformation from LEG to LEE could give rise to a measurable delay in the onset of the fluorescence of the LEE state.

	Fig. 13 Temperature dependence of the rates kG(), kE(), kf() and kb()(for definition see Scheme 2) derived from the fluorescence lifetimes measured for 8 in methylcyclohexane.

T/K	kE/kG	LEGt = 0	kG/108 s–1	kf/108 s–1	kE/108 s–1	kb/108 s–1	E/G det = 385 nm
213	1.9	0.98	2.90	0.51	5.51	0.16	1.92
236	2.7	0.81	2.82	0.45	7.60	0.16	1.93
252	5.4	0.75	3.20	0.65	17.3	0.25	1.90
276	8.1	0.58	5.90	1.93	47.8	0.81	1.94
295	8.3	0.43	8.01	8.58	66.5	3.80	1.94

The second D–B system investigated, 9, also exhibits a rising fluorescence component at low temperature. We therefore hypothesize that the kinetic scheme developed for 8 also applies to 9.

The quantum chemical calculations for the D–B–A systems investigated suggest that in these systems we must also consider the existence of two different local minima on the energy hypersurface of the LE state. This implies that different relaxation pathways leading to the most stable CT state may exist. Since the time resolution of the fluorescence experiment is not sufficient to resolve these, we must restrict our discussion to the deactivation of the relaxed CT state(s).

Since the evaluation of the dipole moments from the slopes obtained from the Lippert–Mataga plots is considerably simplified by the assumption that the dipole moment of the system in the electronic ground state is zero, this approximation is often applied. However, in the case of our systems, the quantum chemical calculations predict a dipole moment in the ground state of about 4.8 D. We therefore also evaluated our experimental data by using the expression given by Mulder and Párkányi but with the neglection of polarizability terms.⁴⁶

(2)

	Methylene chloride			2-Methyltetrahydrofuran
	4	5	6	4	5	6
max,vac(CT)/cm–1	42800	37200	47700	35800	39800	53100
slope/cm–1	–69895	–57397	–90119	–49994	–64669	–109682
3/3	90	87	88	90	87	88
µ(CT)/D	25	22	28	21	24	31

The results of both types of evaluation are summarized in Tables 9 and 10. Generally, the values derived for the dipole moments in the CT state of 4, 5 and 6 are similar, but there are a few differences which could be important for the development of a proper model. Therefore, we concentrate the discussion on the more appropriate evaluation employing eqn. (2).

	Methylene chloride			2-Methyltetrahydrofuran
	4	5	6	4	5	6
µ(GS)/D	4.8	4.7	4.9	4.8	4.7	4.9
/°	34	37	7	34	37	7
max,vac(CT)/cm–1	39900	39300	47200	35800	39700	48900
µ(CT)/D	26	25	30	23	25	31

The first thing to note upon inspection of Table 10 is that the estimated dipole moments for 5 and 6 are essentially the same, whereas the estimated dipole moment of 4 is smaller by about 3 D in the less polar MeTHF. Furthermore, the estimated value for the emission maximum in vacuo, _max,vac(CT), is reduced by about 4000 cm^–1 for the same D–B–A system. The apparent reduction of the (averaged) dipole moment and of _max,vac(CT) in less polar solvent can be taken as evidence that in non-polar solvents a conformation is stabilised that exhibits a lower dipole moment. The results of quantum chemical calculations support this assumption. We obtained two different geometries for 4 with a difference in dipole moment of about 2 D (Table 7). The energetic stabilization in solvents like MeTHF and CH₂Cl₂ should be more pronounced for the conformer with the higher dipole moment (µ = 19 D), which is the less stable conformer in vacuo. Therefore, it is probable that an equilibrium between the two conformers can be established in solvents of proper (medium) polarity. Evidence for this hypothesis can be seen in the temperature dependence of the CT fluorescence of 4 in MeTHF. The activation energy derived from the Arrhenius plot (Fig. 6, bottom) then corresponds to the energy difference of the two CT conformers. Also in accordance with such a model is the presence of a second component in the decay curve.

For substance 5, the relaxed CT state in solvents of medium polarity should also take up the geometry with the highest dipole moment (µ = 31 D, Table 7). The remaining two conformers are not expected to represent populated energetic minima in MeTHF and CH₂Cl₂. In the case of 6, the two optimized CT geometries have the same dipole moment, nearly the same energy and energy difference to the electronic ground state. Thus, the two conformers cannot be differentiated by the evaluating the Lippert–Mataga plots.

The data presented in Table 10 allow us to estimate the location of the CT-fluorescence maximum in MCH if the electronic and geometric structure of the CT state is the same as in the more polar solvents. Because the calculated energies (Table 11) are higher than those of the corresponding LE states, one must conclude that exactly the same CT state as found in the more polar solvents cannot be formed by an exothermic process in MCH. If a CT-state is formed, it must have a smaller dipole moment such that less energy is needed for charge separation. This conclusion also implies that LE and CT states could be nearly isoenergetic and thermally induced electron back transfer must be considered when analyzing the experimental data concerning the CT state. For 4 and 5 we made an attempt to deconvolute the temperature-dependent fluorescence spectra into two components. The first component represents the fluorescence from the locally excited state (its spectral distribution is given by that of the room temperature fluorescence of the reference compound D–B), the second the fluorescence from the CT state. The intensity of the latter (Fig. 14) increases at lower temperature because the thermally activated decay path via the LE state becomes less effective. In the case of 5, the spectral distribution of the thus calculated CT fluorescence is essentially independent of temperature. This is in accord with the fact that the polarity parameter of MCH does not change significantly upon lowering the temperature. In contrast, the CT-fluorescence of 4 shifts towards higher wavenumbers for lower temperatures. This finding can be rationalized if the short-wavelength emission originates from the lower energetic CT-conformer, which is formed via electron transfer from the relaxed LE state. At higher temperatures, an additional deactivation channel is opened, namely transition to a second CT-conformer, whose fluorescence occurs at slightly longer wavelength (see Table 11). The MO calculations (Table 7) suggest the existence of 2 or 3 different rotamers in the charge-separated state. From the calculated energies one can, however, not deduce why a dual emission is observed for 4 but not for the other two compounds. We assume that the stabilization of the two CT conformers by the solvent is similar in magnitude because they possess similar dipole moments. In contrast, the dipole moments of 5 in the three proposed relaxed conformations differ significantly. Therefore, the energetic splitting could be large enough to restrict emission to one conformer at all temperatures, even in non-polar solvents.

	Fig. 14 Calculated CT emission spectra of 4(a, T= 207 K, 216 K, 232 K, 247 K, 297 K) and 5(b, T= 192 K, 222 K, 252 K, 275 K, 295 K) in methylcyclohexane. Arrows indicate changes upon decrease of temperature.

	4	5	6
max,est(CT)/cm–1	32540	32270	37100
max,exp(CT)/cm–1	24600	24300	25600
max,exp(CT)/cm–1	26800	—	—

The calculations also predict that the conformers for which the torsional angle lies between about 120° and 240° possess the lowest energy in the S₁-state. If one assumes that electron transfer occurring in these conformers leads to a relaxed CT state with similar geometry, then the preferentially formed CT state would actually be the one with the lower calculated energy (Table 7). For the second CT conformer to be populated around room temperature, the energy difference must be smaller than about 3RT. The difference calculated for the isolated molecules is much larger but one must keep in mind that the semiempirical CI technique tends to overestimate the energy required for formation of CT states. Furthermore, the second CT conformer should be stabilized more in solvents because of its higher dipole moment.

The postulate that the higher energetic second CT conformer ( = 326°) exhibits a longer wavelength fluorescence is surprising at first glance. One must, however, keep in mind that the energy of 4 in the electronic ground state is much higher for the twisted ( = 326°) than for the nearly planar conformer with 180° (see analogous result for 5 in Fig. 10).

Previous experiments showed that compounds that contain the stellane bridge are fairly photolabile, especially in non-polar solvents. Since, at least in part, strongly fluorescing species are formed, it is difficult or even impossible to evaluate the fluorescence experiments for 6 in MCH in a unique way.

The results reported in this contribution confirm the conclusions presented in previous work, namely that in D–B–A systems that possess a single bond, torsion around this bond is most likely the preferred coordinate for structural relaxation in a charge-separated state. This is more true the larger the relative distance and orientation is changed upon a variation of the angle of torsion. The driving force for structural relaxation is the Coulombic interaction between the charged donor and acceptor groups (harpooning mechanism). Therefore, the effect is most pronounced in non-polar solvents. Since, in addition, the reaction enthalpy for the formation of the CT state, G_et, is small in non-polar solvents, the reaction scheme describing charge separation and recombination is rather complex (See Scheme 3). In very polar solvents, the compounds investigated exhibit the usual sequence of excitation into an LE state and fast charge separation followed by slower charge recombination. In ACN, the rates for charge recombination reflect the variation of the electronic coupling with the p-character of the bridge orbitals. In solvents of medium polarity, the population of structurally different relaxed CT states manifests itself in a temperature-dependent spectral distribution of the CT fluorescence and a non-monoexponential decay law. Since back-electron transfer leading to formation of the electronic ground state is not the only decay channel, the effect of bridge-dependent electronic coupling only shows up clearly at low temperatures, when thermally activated alternation decay channels are frozen out.

	Scheme 3 Schematic presentation of the relevant decay paths for the locally excited and CT states of the D–B–A compounds (4, 5, 6) in solvents of different polarity. CT1 is the extended charge separated conformer and therefore CT2 that one with the shorter D–A distance. We assume that the equilibrium between the two locally excited states LEE and LEG, observed for the D–B systems, is only relevant in non-polar solvents for the D–B–A compounds, because electron transfer is very fast in the two other cases.