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We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps, we quantify the growth of spatial structures in the chaotic dynamics as the strength of diffusion is increased. When the diffusion strength is increased from zero, we find that the leading Lyapunov exponent decreases rapidly from a positive value to zero to yield a small window of periodic dynamics which is then followed by chaotic dynamics. For values of the diffusion strength beyond the window of periodic dynamics, the leading Lyapunov exponent does not vary significantly with the strength of diffusion with the exception of a small variation for the largest diffusion strengths we explore. The Lyapunov spectrum and fractal dimension are described analytically as a function of the diffusion strength using the eigenvalues of the coupling operator. The spatial features of the CLVs are quantified and compared with the eigenvectors of the coupling operator. The chaotic dynamics are composed entirely of physical modes for all of the conditions we explore. The leading CLV is highly localized and localization decreases with increasing strength of the spatial coupling. The violation of the dominance of Oseledets splitting indicates that the entanglement of pairs of CLVs becomes more significant between neighboring CLVs as the strength of diffusion is increased. 

Fluorescence quenching of an excited guest encapsulated within a cationic host by a cationic molecule was examined on an anionic inorganic surface. Repulsion between the host and the quencher was overcome by adsorbing both an anionic surface. Dimethyl stilbene (DMS), octa amine (OAm216+), viologen derivatives (VD2+) and saponite are used as guest, cationic capsule, cationic electron acceptor and anionic inorganic surface, respectively. The fluorescence behavior of DMS within OAm216+ (denoted as DMS@OAm216+) was observed by steady-state and time-resolved fluorescence measurements. As a result of electron transfer the fluorescence of DMS@OAm216+ was quenched by VD2+ under the presence of saponite, while no quenching was observed in theabsence of saponite. Those results indicate that the dynamic electron transfer between DMS@OAm216+ and VD2+ which are electrostatically repulsive, can be observed in the (DMS@OAm216+)-VD2+-saponite triad supramolecular system where the two cationic systems are brought closer by the anionic clay sheet. 

Excited state chemistry and physics of molecules, in addition to their inherent electronic and steric features, depend on their immediate microenvironments. This study explores the influence of an organic capsule, slightly larger than the reactant molecule itself, on the excited state chemistry of the encapsulated molecule. Results presented here show that the confined molecule, in fact, is not isolated and can be manipulated from outside even without direct physical interaction. Examples where communication between a confined molecule and a free molecule present outside is brought about through electronic and energy transfer processes are presented. Geometric isomerization of octa acid encapsulated stilbenes induced by energy and electron transfer by cationic sensitizers that attach themselves to the anionic capsule is examined. The fact that isomerization occurs when the sensitizer present outside is excited illustrates that the reactant and sensitizer are communicating across the molecular wall of the capsule. Ability to remotely activate a confined molecule opens up new opportunities to bring about reactions of confined radical ions and triplet excited molecules generated via long distance energy and electron transfer processes. 

Ultrafast transient absorption spectroscopy reveals new excited-state dynamics following excitation of trans -azobenzene ( t -Az) and several alkyl-substituted t -Az derivatives encapsulated in a water-soluble supramolecular host–guest complex. Encapsulation increases the excited-state lifetimes and alters the yields of the trans → cis photoisomerization reaction compared with solution. Kinetic modeling of the transient spectra for unsubstituted t -Az following nπ* and ππ* excitation reveals steric trapping of excited-state species, as well as an adiabatic excited-state trans → cis isomerization pathway for confined molecules that is not observed in solution. Analysis of the transient spectra following ππ* excitation for a series of 4-alkyl and 4,4′-dialkyl substituted t -Az molecules suggests that additional crowding due to lengthening of the alkyl tails results in deeper trapping of the excited-state species, including distorted trans and cis structures. The variation of the dynamics due to crowding in the confined environment provides new evidence to explain the violation of Kasha's rule for nπ* and ππ* excitation of azobenzenes based on competition between in-plane inversion and out-of-plane rotation channels.