The effect of torsion angle on the rate of intramolecular triplet energy transfer

Abstract

The magnitude of electronic coupling between the terminal chromophores shows a precise dependence on the dihedral angle around a bridging biphenyl group.

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Long-range, triplet energy transfer along a well-defined molecular-scale wire offers one of the more promising routes by which to construct miniaturized communications systems.¹ Furthermore, the super-exchange mechanism² seems to provide the best approach for achieving proper control of the flux of information transfer along a molecular axis. This mechanism involves through-bond electronic coupling, the strength of which depends markedly on the nature of the wire.³ It has long-been argued that the relevant electronic coupling matrix element, this being a direct measure of electronic communication between donor and acceptor units, should depend on the geometry of the connector. Proving this concept by experiment, however, has proved to be extremely difficult, although several notable attempts have been made.^4,5 In principle, it should be possible to regulate electron flow by controlling the central torsion angle of a bridging biphenyl group.⁶ We have previously used a variant on this approach to provide an estimate of how the efficacy of intervalence charge transfer depends on the geometry of the bridge.⁷ We now show that for a much expanded data set, the rate of triplet energy transfer depends precisely on the torsion angle of the lowest-energy conformation of the bridge.

Intramolecular triplet energy transfer between remote reactants connected through an organic spacer usually occurs via Dexter-type electron exchange.⁴ This process involves simultaneous transfer of an electron, through the bridging LUMO, and a positive hole, through the bridging HOMO, from donor to acceptor.⁴ Properties of the spacer, notably the length,⁸ connectivity⁹ and conductivity,¹⁰ combine to control the rate of energy transfer. For a spacer of fixed length and composition, it is likely that the rate will depend on the mutual orientation of subunits comprising the spacer,^3,4 especially for a poly(phenylene)-based bridge.¹⁰ In order to test this long-standing hypothesis, a set of ruthenium(II)/osmium(II) bis (2,2′:6′,2″-terpyridine) binuclear complexes was synthesized† (Fig. 1). The terminal metal complexes are linked by an ethynylene-substituted biphenyl bridge that itself is equipped with a constraining tether.¹¹ These terminals are well known to display intramolecular triplet energy transfer from Ru^II donor to Os^II acceptor.^8,10 Clearly, the strap is intended to function as a ratchet and fix the dihedral angle around the biphenyl unit.¹² This angle is further controlled by binding cations to the crown ether strap.¹³ The entire data set comprises 11 torsion angles, ranging from 37° to 130°. To prevent undue rotation, the system was studied in a glassy matrix.

Fig. 1 Structural formulae for the binuclear complexes studied here.

Illumination into the ruthenium(II) bis (2,2′:6′,2″-terpyridine) (Ru-terpy) terminal at 480 nm, where the corresponding Os-terpy unit absorbs ca. 40% of the incident photons, generates the excited triplet state. This species emits weakly at 660 nm in a butyronitrile glass. The emission quantum yield (Φ_LUM) and lifetime (τ_LUM) increase with decreasing temperature but both values remain much less than those measured for the analogous binuclear Ru-terpy complex.¹¹ The yield and lifetime measured for emission from the Os-terpy terminal at 770 nm remain similar to those recorded for reference compounds¹⁴ and following excitation at 650 nm where only Os-terpy absorbs. Thus, the presence of the Ru-terpy unit has no obvious effect on the photophysical properties of the Os-terpy terminal but emission from Ru-terpy is quenched. Comparison of Φ_LUM and τ_LUM recorded for the Ru-terpy units of the various Ru-Os compounds with those for the corresponding Ru–Ru complexes indicates that quenching lies in the range 55–95% at 150 K. Close examination of time-resolved emission profiles recorded for the Os-terpy units indicates that more than 50% of the emission grows-in on the time scale of a few hundred nanoseconds (Fig. 2). This confirms that quenching of the Ru-terpy emission is due to intramolecular triplet energy transfer. The triplet lifetimes were measured also by laser flash photolysis following excitation at 480 nm.

Fig. 2 Time-resolved luminescence decay profiles recorded following laser excitation of C1 in butyronitrile at 150 K. The decay records refer to emission from the Ru-terpy unit at 660 nm and emission from the corresponding Os-terpy unit at 760 nm. The sharp profile is the instrument response function (IRF).

The rate constant for intramolecular triplet energy transfer (k_TT) was derived‡ for each compound by comparing triplet lifetimes measured for the Ru-terpy terminal (τ_CMP) in the mixed-metal complex with that found for the corresponding Ru–Ru complex (τ_REF). All emission decay profiles were mono-exponential.

These first-order rate constants were measured over the temperature range 77–150 K where the solvent remains frozen in a glassy matrix. For each compound, the derived k_TT value was found to follow a modified Arrhenius behaviour of the type expressed by eqn (2).Here, k_F refers to an activationless rate constant for energy transfer whilst k_D is the rate constant for the activated process. The derived k_F values converge to a common rate constant of 2.2 ± 0.3 × 10⁶ s⁻¹. In contrast, the derived k_D values span a wide range and are clearly sensitive to the length of the tether (Table 1). The activation energy, ΔG^‡, remains independent of strap length and corresponds to an average value of 2.8 ± 0.4 kJ mol⁻¹.

Table 1 The effect of torsion angle on the efficiency of triplet energy transfer in a glassy butyronitrile matrix

Cmpd	Angle/° ^a	10^−6kF/s^−1^b	10^−7kD/s^−1^b	ΔG^‡/kJ mol^−1^c	V DA/cm^−1^d
a Central torsion angle calculated by MDS for the lowest-energy conformation. b From eqn (2). c From eqn (4). d From eqn (5).
C1	37	2.1	15.5	3.05	0.31
C2	55	1.8	5.0	2.93	0.17
C3	67	2.0	2.1	2.45	0.11
C4	94	2.1	0.30	2.86	0.04
CE4	122	2.0	1.5	2.78	0.09
CE5	125	1.7	4.0	3.00	0.16
CE5 + Na	83	1.8	0.49	2.90	0.05
CE5 + K	113	1.6	2.6	2.45	0.13
CE6	130	1.9	8.8	2.75	0.22
CE6 + Na	58	2.0	2.8	3.02	0.13
CE6 + K	62	1.9	4.1	2.75	0.15

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The activationless step, corresponding to k_F, can be attributed to Förster-type dipole–dipole energy transfer.¹⁵ The calculated rate constant, determined using spectroscopic properties measured for the Ru–Ru complexes, is 2.5 × 10⁶ s⁻¹, which is in good agreement with the averaged k_F value. As such, the activated process, corresponding to k_D, can be assigned to Dexter-type electron exchange.^4,5 This involves long-range, through-bond interactions and, therefore, is expected to depend on the geometry of the bridge. The activation energy for Dexter-type electron exchange corresponds to eqn. (3).¹⁶

Here, ΔE_TT (=1430 cm⁻¹) is the difference in triplet energies between Ru-terpy and Os-terpy chromophores and λ_TT (=670 cm⁻¹) is the total reorganization energy accompanying deactivation of the two triplet excited states. This value can be calculated from a Franck–Condon analysis of the respective emission spectra.¹⁷ The derived values are independent of strap length and give rise to an averaged activation energy for electron exchange of 2.6 ± 0.2 kJ mol⁻¹. This is in excellent agreement with the experimental ΔG^‡ values, thereby confirming that triplet energy transfer involves a mixture of Förster and Dexter mechanisms. Except at very low temperature, Dexter electron exchange dominates.

The variation in k_D must be associated, in some way, with the geometry of the biphenyl bridge. Molecular dynamics simulations made in a reservoir of acetonitrile molecules showed the torsion angle around the central biphenyl group to be sensitive to the length of the strap (Table 1). Although there is considerable fluctuation about the mean value at high temperature, it was found that the strap constrains the geometry around the biphenyl group and imposes a preferred dihedral angle on the lowest-energy conformation. We suppose that the lowest-energy structure will predominate in the glassy matrix and that the measured k_D value refers to electron exchange across that particular geometry. Additional angular variations are possible for the crown ether derived straps by incorporating selected cations into the central cavity.¹³

On the premise that k_D refers to electron exchange across a certain torsion angle, we can relate the kinetic data to the electronic coupling matrix element (V_DA) for long-range interaction between donor and acceptor. This can be done by way of eqn (4), which allows determination of V_DA from the intercept of the appropriate Arrhenius-type expression⁴ (Fig. 3).

The derived coupling elements are collected in Table 1, together with the activation energies ΔG^‡, and vary over an eightfold range for the various bridges. Small torsion angles give higher coupling whilst there is a clear minimum in V_DA as the phenylene rings become orthogonal. Coupling does not decrease to zero but follows the form of eqn (5) where ϑ refers to the torsion angle (Fig. 4). A non-linear, least-squares fit to the derived values indicates that V_DA at 0° has a value of 0.400 ± 0.005 cm⁻¹ but this falls to only 0.046 ± 0.002 cm⁻¹ at 90°.

V_DA = V₀ cos²ϑ + V_N (5)

The term V_N in eqn (5) describes the extent of the inherent electronic coupling when the phenylene rings are orthogonal. The derived value (V_N = 0.046 cm⁻¹) is about 12% that found for a coplanar arrangement of the bridge. This inherent coupling could be associated with internal rotation of the biphenyl unit giving rise to a multitude of conformers at any given moment. However, given that the molecule is resident in a glassy matrix this structural variation should be kept modest. The experimental conditions (e.g., low temperature and electron exchange occurring in the Marcus “inverted” region), however, do favour nuclear tunnelling.¹⁸ This latter process involves tunnelling through the barrier separating donor from acceptor. Presumably, this barrier is presented by a single σ bond. In this case, electron exchange is promoted by specific vibrations associated with the reactants or the surrounding solvent and the rate will be weakly temperature dependent.

Fig. 3 Arrhenius-type plot constructed for intramolecular triplet energy transfer in C1 and C4 dissolved in a glassy butyronitrile matrix. The solid line drawn through the data points corresponds to a non-linear, least-squares fit to eqn (4).

Fig. 4 Effect of torsion angle on the size of the electronic coupling matrix element measured for a glassy matrix. The solid line drawn through the data points corresponds to a best fit to eqn (5) with the parameters given in the text.

In summary, this research has established how the rate of electron exchange depends on the conformation of the biphenyl-based bridge. Triplet energy transfer occurs across an orthogonal geometry by way of nuclear tunnelling and/or coupling through the connecting σ bond but is accentuated by more favourable orientations of the bridge. The systems under investigation do not allow adoption of a coplanar arrangement but extrapolation of the data given in Fig. 4 implies that there is an 80-fold variation in rate between phenylene rings held at 0° and 90°. The methodology adapted here provides for the first detailed examination of how the torsion angle affects the extent of long-range electronic coupling.

Acknowledgements

We thank EPSRC (GR/R23305/01) and the University of Newcastle for financial support.

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Footnotes

† The starting materials 4,4′-diiodobiphenyl-2,2′-diol¹⁹ and [M(terpy)(4′-ethynyl-2,2′:6′,2″-terpyridine)](PF₆)₂ (M = Ru²⁺ or Os²⁺)²⁰ were prepared by literature methods. The synthetic procedure used to isolate the required target compounds will be reported elsewhere. In brief, the two oxygen atoms of the bridge were linked via alkyl or alkoxy chains to create the desired tethered molecules. These compounds were coupled in sequential reactions, using the Sonogashira method,¹¹ to the relevant synthons so as to afford the mixed-metal complexes.

‡ Time-resolved luminescence measurements were made after excitation of the sample with a 4-ns laser pulse delivered at 480 nm and with a repetition rate of 1 kHz. Data analysis was made after deconvolution of the instrument response function. Temperature-dependent studies were made with an Oxford Instruments Optistat DN cryostat. Transient absorption studies were made by conventional methods after excitation with a 5 ns laser pulse delivered at either 532 or 480 nm from a Q-switched Nd:YAG laser. In the latter case the laser beam was focussed through a 1 m cell filled with deuterium and the required excitation line was isolated with a prism coupled to a narrow bandpass filter. The sample was deoxygenated by purging with N₂. Other studies used a frequency-doubled, mode-locked Nd:YAG laser as excitation source. Some 200 individual laser shots were averaged at each delay time.

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