Large Deviation Techniques Applied to Systems with Long-Range Interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.     

Induced Chiroptical Changes of a Water‐Soluble Cryptophane by Encapsulation of Guest Molecules and Counterion Effects

We report the synthesis of the water‐soluble cryptophanol derivative 1 and the study of the chiroptical properties of its two enantiomers (>99 % ee) by polarimetry, electronic circular dichroism (ECD), and vibrational circular dichroism (VCD). We show that cryptophanol 1 exhibits unusual chiroptical properties in water under basic conditions (pH>12). For instance, the shapes of the ECD and VCD spectra of 1 in water were strongly dependent on the nature of the alkali metal ions (Li⁺, Na⁺, K⁺, Cs⁺) surrounding the cryptophane and whether or not a guest molecule is present inside the cavity of the host. To the best of our knowledge, this is the first example in which the nature of these counterions governs the chiroptical properties of a host molecule. Moreover, specific ECD spectra were obtained depending on the size of the guest molecules. This makes 1 a good sensor for small neutral molecules in aqueous solvent. Finally, VCD experiments associated with DFT calculations show that the chiroptical changes can be directly correlated to the presence of charges close to the aromatic rings and with a conformational change of the alkyl chains upon encapsulation.     

Vicinal interproton couplings through two heteroatoms. II—Coupling 3J(H?N?O?H) occurring in m-Nitrophenylhydroxylamines

The proton NMR spectra of certain arylhydroxylamines in DMSO-d₆ show a vicinal coupling through nitrogen and oxygen. The assignment of OH and NH signals was made using a ¹⁵N labelled derivative.     

Constructing a covering triangulation by means of a nowhere-zero dual flow

Tutte conjectured that every graph with no isthmus can be provided with an integral nowhere-zero flow with no absolute value greater than k=5. As yet the result is established for k=6, and it is used for proving that the existence of a triangular imbedding of a graph G in a surface S implies the existence of a triangular imbedding of G_(m) in a surface $\text{S}\text{?}$ with the same orientability characteristic as S. G_(m) stands for the composition of G by an independent set of m vertices.     

Langevin Dynamics,Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.     

High affinity of water-soluble cryptophanes for cesium cations

Exceptionally high affinity for cesium cations was achieved in aqueous solution using two enantiopure cryptophanes. Complexation of cesium was evidenced by (133)Cs NMR spectroscopy and by electronic circular dichroism (ECD). Binding constants as high as 6 × 10(9) M(-1) have been measured by isothermal titration calorimetry (ITC). Very strong complexation of rubidium cations (K ~10(6) M(-1)) has also been measured. Chiral hosts allowed the detection of the two cations at low concentrations (μM) using ECD.     

Conformational analysis of quinine and its pseudo enantiomer quinidine: a combined jet-cooled spectroscopy and vibrational circular dichroism study

Laser-desorbed quinine and quinidine have been studied in the gas phase by combining supersonic expansion with laser spectroscopy, namely, laser-induced fluorescence (LIF), resonance-enhanced multiphoton ionization (REMPI), and IR-UV double resonance experiments. Density funtional theory (DFT) calculations have been done in conjunction with the experimental work. The first electronic transition of quinine and quinidine is of π-π* nature, and the studied molecules weakly fluoresce in the gas phase, in contrast to what was observed in solution (Qin, W. W.; et al. J. Phys. Chem. C2009, 113, 11790). The two pseudo enantiomers quinine and quinidine show limited differences in the gas phase; their main conformation is of open type as it is in solution. However, vibrational circular dichroism (VCD) experiments in solution show that additional conformers exist in condensed phase for quinidine, which are not observed for quinine. This difference in behavior between the two pseudo enantiomers is discussed.