A theoretical analysis of the excited states in 2-benzoylthiophene

The lower excited states of 2-benzoylthiophene have been studied using ab initio quantum chemical methods based on multiconfigurational wave functions. Six singlet and six triplet excited states have been characterized. The geometry has been optimized for the two lowest triplet states, which are responsible for the photoreactivity of the chromophore in the photosensitizing drug tiaprofenic acid. The T¹(π → π?) and T₂(n → π?) states have been found to be close in energy with the π → π? state slightly lower. The excited states have been characterized using density difference and spin density plots. The different photochemical behaviour of the two triplet states can be rationalized from the theoretical data.     

II: PROPERTIES OF DIATOMIC AND TRIATOMIC MOLECULES

Results are presented from a theoretical study of the × ⁶Σ⁺, A ⁶Σ⁺ and ⁶Δ electronic states of CrH using multiconfiguration second-order perturbation theory in the multi-state formalism (MS-CASPT2). It is shown that the results for the spectroscopic constants and radiative lifetimes for the A state are in agreement with experiment and an earlier multireference configuration interaction study only if the two close lying × and A states are allowed to interact at a level of approximation that includes dynamic correlation.     

2‐Chloro­phenyl 3‐nitro­benzene­sulfonate and 2,4‐di­chloro­phenyl 3‐nitro­benzene­sulfonate: supramole­cular aggregation through C–H⋯O, π–π and van der Waals interactions

In 2‐chloro­phenyl 3‐nitro­benzene­sulfonate, C₁₂H₈ClNO₅S, and 2,4‐di­chloro­phenyl 3‐nitro­benzene­sulfonate, C₁₂H₇Cl₂NO₅S, weak C—H⋯O interactions generate S(5), S(6) and (7) rings. The supramolecular aggregation is completed by the presence of π–π interactions and intermolecular van der Waals short contacts.     

The size of the sync basin

We suggest a new line of research that we hope will appeal to the nonlinear dynamics community, especially the readers of this Focus Issue. Consider a network of identical oscillators. Suppose the synchronous state is locally stable but not globally stable; it competes with other attractors for the available phase space. How likely is the system to synchronize, starting from a random initial condition? And how does the probability of synchronization depend on the way the network is connected? On the one hand, such questions are inherently difficult because they require calculation of a global geometric quantity, the size of the "sync basin" (or, more formally, the measure of the basin of attraction for the synchronous state). On the other hand, these questions are wide open, important in many real-world settings, and approachable by numerical experiments on various combinations of dynamical systems and network topologies. To give a case study in this direction, we report results on the sync basin for a ring of n > 1 identical phase oscillators with sinusoidal coupling. Each oscillator interacts equally with its k nearest neighbors on either side. For k/n greater than a critical value (approximately 0.34, obtained analytically), we show that the sync basin is the whole phase space, except for a set of measure zero. As k/n passes below this critical value, coexisting attractors are born in a well-defined sequence. These take the form of uniformly twisted waves, each characterized by an integer winding number q, the number of complete phase twists in one circuit around the ring. The maximum stable twist is proportional to n/k; the constant of proportionality is also obtained analytically. For large values of n/k, corresponding to large rings or short-range coupling, many different twisted states compete for their share of phase space. Our simulations reveal that their basin sizes obey a tantalizingly simple statistical law: the probability that the final state has q twists follows a Gaussian distribution with respect to q. Furthermore, as n/k increases, the standard deviation of this distribution grows linearly with square root of n/k. We have been unable to explain either of these last two results by anything beyond a hand-waving argument.     

On the physical basis for Urbach's rule

The low-energy tail of the E 6 a exciton in GeS obeys Urbach's rule, with Urbach parameters σ₀ = 1.45 ± 0.05, and $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{= 8.7 ± 0.6 meV}$. The energy ?ω_p corresponds to a previously measured rigid-layer vibrational mode which has no associated electric field. This finding is inconsistent with Dow and Redfield's unified theory of Urbach and exponential absorption edges. Our results are consistent with Sumi and Toyazawa's theory of Urbach edges, and with Fivaz and Mooser's model for electron-phonon interactions in layered compounds.