Thermodynamic equilibrium between locally excited and charge-transfer states through thermally activated charge transfer in 1-(pyren-2′-yl)-o-carborane

Reversible conversion between excited-states plays an important role in many photophysical phenomena. Using 1-(pyren-2′-yl)-o-carborane as a model, we studied the photoinduced reversible charge-transfer (CT) process and the thermodynamic equilibrium between the locally-excited (LE) state and CT state, by combining steady state, time-resolved, and temperature-dependent fluorescence spectroscopy, fs- and ns-transient absorption, and DFT and LR-TDDFT calculations. Our results show that the energy gaps and energy barriers between the LE, CT, and a non-emissive ‘mixed’ state of 1-(pyren-2′-yl)-o-carborane are very small, and all three excited states are accessible at room temperature. The internal-conversion and reverse internal-conversion between LE and CT states are significantly faster than the radiative decay, and the two states have the same lifetimes and are in thermodynamic equilibrium.


Photophysics in a glass and in solution
temperatures lower than 218 K, the LE band became so weak and the viscosity of hexane became so large, that scattered light affects the measurements of the LE band, and a fast decay ( < 1 ns), which is shorter than the instrument response function (1.34 ns full-width-at-half-maximum), was found. However, the lifetime of the longer decay is still the same as that of the CT band.

Radiative decay and internal conversion rates in hexane solution
In hexane solution, where our steady state (temperature-dependent LE:CT band ratios) and time-resolved fluorescence experiments (monoexponential decays with identical lifetimes at any temperature) suggest that the LE and CT states of 1 are in thermodynamic equilibrium, and equations 1 and 2 apply at time t during a time-resolved measurement, the ratio of the two states is a constant, that is: (Eq S1) which indicates that the exponential term equals 1 and CT = LE as K is a time-independent constant. This is a prerequisite for a thermodynamically equilibrated dual-excited states system.
The total radiative decay rate (kr) in a thermodynamically equilibrated system can be calculated from the absolute fluorescence quantum yields of both emission bands ( = 0.11) and lifetimes measured in hexane at room temperature:  (1) x 10 6 s -1 , being ca. one order of magnitude faster than that of the CT band (kr,CT = 1.9 (1) x 10 5 s -1 ).
However, both rate constants are overall relatively small because they refer to (almost) forbidden transitions, from the pyrene LE state because it is symmetry forbidden and the CT state because of the small Franck-Condon factors caused by strong structural distortion.

Thermodynamic equilibrium in solvents with different polarities
The band ratio changes in hexane with dioxane additive, according to equation 5, where apostrophes represent dioxane added, and due to the fact that the radiative decay of pyrene is not much affected by solvent polarity, that is, kr,LE ≈ kr,LE´, equation S4 can be written as, The LE:CT band ratio changes from 1:2.6 to 1:16 by adding 10% of dioxane into the hexane solution of 1, indicating that kr,CT dramatically decreases by factor 0.019 with 10% dioxane added, according to equation 11. This is probably because a more polar solvent further stabilizes the CT state and distorts the molecular geometry from the ground state geometry and decreases the Franck-Condon factors, i.e., the degree of overlap of the nuclear wave functions for the ground state and excited state of 1.
Single-crystal X-ray diffraction and solid-state emission    This led to the conclusion that something was wrong either with the structural model, which looked reasonable with respect to the molecular packing, or with the data. It could be that the intensities obtained were incorrect due to the choice of inappropriate data collection parameters. The diffraction data from all three crystals showed diffuse reflection streaks along the reciprocal ⃗ * direction in every row with odd l indices ( Figure S13). Figure S13. Reciprocal layers of the single-crystal X-ray diffraction data reconstructed from the synchrotron data collection using CrysAlis Pro software. Diffuse scattering is observed in b * direction in every row with odd l indices as can be seen in the (0kl), (1kl), and (hk1) layers.