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The intermittent emission or "blinking" of single violamine R (1) and 2′,7′-dichlorofluorescein (2) molecules incorporated into single crystals of potassium acid phthalate (KAP) is studied using confocal fluorescence microscopy. Blinking dynamics are quantified in terms of switching rates and on-and off-length probability distributions. Mixed crystals of KAP/1 and KAP/2 consist of photophysical subpopulations with ∼40% and ∼20% exhibiting persistent emission, respectively, and the remainder demonstrating a broad range of blinking behavior that is well described by a power-law distribution. The dependence of the power-law exponent on chromophore, experimental bin time, intensity threshold, and excitation power is examined. The blinking dynamics are also modeled using Monte Carlo simulations on the basis of a three-level electronic system with the rate constants for population and depopulation of the "dark" state being distributed. No correlation between molecular orientation and blinking dynamics is observed, suggesting that intermolecular electron transfer is not the origin of power-law behavior. Alternative origins for this behavior (e.g., conformational flexibility and spectral diffusion) are explored using a combination of experimental and computational techniques. Of these possibilities, the distributed kinetics exhibited by KAP/1 and KAP/2 are attributed to spectral diffusion.

The blinking dynamics of single violamine R (VR) molecules embedded in crystals of potassium acid phthalate (KAP) are analyzed using threshold and change-point detection (CPD) methods (Watkins, L. P.; Yang, H. J. Phys. Chem. B 2005, 109, 617). Analysis employing thresholding resulted in power-law distributions of on and off times corresponding to a power-law exponent of ∼2, consistent with a distributed kinetics model for population and depopulation of the nonemissive state. When the same emission time traces were analyzed using the CPD method, a power-law exponent of ∼1.5 is obtained. In addition, multiple emission states are observed using CPD, inconsistent with a simple two-state blinking model, and indicative of spectral diffusion. The role of spectral diffusion in the distributed blinking kinetics of KAP/VR is investigated by spectrally decomposing the emission using a dichroic mirror. Combining the CPD method with this experiment yielded the emission energy, intensity, and temporal duration of blinking events. A wide distribution of emission energies is observed, consistent with molecules experiencing a variety of dielectric environments within the crystal host. Time-dependent fluctuations in the spectral decomposition are observed, corresponding to spectral diffusion. Blinking events exhibited by single VR molecules in KAP are correlated, an effect referred to as memory. To our knowledge, this is the first reported observation of memory for a molecular system. Positive correlations are observed for consecutive on times and consecutive off times. In addition, adjacent on and off times demonstrate anticorrelation. These observations support the observation of spectral diffusion in this crystal environment, with this diffusion contributing to population and depopulation of the nonemissive state.

As a basis for electronic structure calculations, Gaussians are inconvenient because they show unsuitable behavior at larger distances, while Hankel functions are singular at the origin. This paper discusses a new set of special functions which combine many of the advantageous features of both families. At large distances from the origin, these “smoothed Hankel functions” resemble the standard Hankel functions and therefore show behavior similar to that of an electronic wave function. Near the origin, the functions are smooth and analytical. Analytical expressions are derived for two-center integrals for the overlap, the kinetic energy, and the electrostatic energy between two such functions. We also show how to expand such a function around some point in space and discuss how to evaluate the potential matrix elements efficiently by numerical integration. This supplies the elements needed for a practical application in an electronic structure calculation.

The excited-state decay kinetics of single 2',7'-dichlorofluorescein (DCF) molecules oriented and overgrown within crystals of potassium acid phthalate (KAP) are reported. Time-correlated single-photon counting measurements (TCSPC) of 56 DCF molecules in KAP reveal that single-exponential decay is exhibited by roughly half of the molecules. The remainder demonstrates complex excited-state decay kinetics that are well fit by a stretched exponential function consistent with dispersed kinetics. Histograms of single-molecule luminescence energies revealed environmental fluctuations and distinct chemical species. The TCSPC results are compared to Monte Carlo simulations employing a first-passage model for excited-state decay. Agreement between experiment and theory, on both bulk and single-molecule levels, suggests that a subset of the DCF molecules in KAP experience fluctuations in the surrounding environment that modify the energy barrier to proton transfer leading to dispersed kinetics.