Stabilization of the Low‐Spin State in a Mononuclear Iron(II) Complex and High‐Temperature Cooperative Spin Crossover Mediated by Hydrogen Bonding

The tetrapyridyl ligand bbpya (bbpya=N,N‐bis(2,2′‐bipyrid‐6‐yl)amine) and its mononuclear coordination compound [Fe(bbpya)(NCS)₂] ( 1 ) were prepared. According to magnetic susceptibility, differential scanning calorimetry fitted to Sorai’s domain model, and powder X‐ray diffraction measurements, 1 is low‐spin at room temperature, and it exhibits spin crossover (SCO) at an exceptionally high transition temperature of T_1/2=418 K. Although the SCO of compound 1 spans a temperature range of more than 150 K, it is characterized by a wide (21 K) and dissymmetric hysteresis cycle, which suggests cooperativity. The crystal structure of the LS phase of compound 1 shows strong N?H???S intermolecular H‐bonding interactions that explain, at least in part, the cooperative SCO behavior observed for complex 1 . DFT and CASPT2 calculations under vacuum demonstrate that the bbpya ligand generates a stronger ligand field around the iron(II) core than its analogue bapbpy (N,N′‐di(pyrid‐2‐yl)‐2,2′‐bipyridine‐6,6′‐diamine); this stabilizes the LS state and destabilizes the HS state in 1 compared with [Fe(bapbpy)(NCS)₂] ( 2 ). Periodic DFT calculations suggest that crystal‐packing effects are significant for compound 2 , in which they destabilize the HS state by about 1500 cm^?1. The much lower transition temperature found for the SCO of 2 compared to 1 appears to be due to the combined effects of the different ligand field strengths and crystal packing.     

On the role of longitudinal momenta in high energy hadron-hadron scattering

We demonstrate a new method to calculate inelastic scattering cross-sections, which in contrary to the Regge-based methods takes into account the energy momentum conservation law. It is shown that the main contribution to integral expressing inelastic scattering cross-sections does not come from the multi-Regge domain. In particular, accounting for the longitudinal momenta contribution to virtualities is sufficient and results in the new mechanism of cross-section growth. The reasons for taking into account the sufficiently high number of interference contributions are shown and the approximate method for this purpose is developed. By fitting single free parameter of the model achieved a qualitative agreement of the total and inelastic cross sections with experimental data.     

Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending

This paper implements the approach introduced by MacKinnon (J Bus Econ Stat 12:167–176, 1994, J Appl Econom 11:601–618, 1996) to estimate the response surface of the test statistics of seasonal unit root tests with OLS and GLS detrending for quarterly and monthly time series. The Gauss code that is available in the supplementary material of the paper produces p values for five test statistics depending on the sample size, deterministic terms and frequency of the data. A comparison with previous studies is undertaken, and an empirical example using airport passenger arrivals to a tourist destination is carried out. Quantile function coefficients are reported for simple computation of critical values for tests at 1, 5 and 10 % significance levels.     

Arylidene Pyruvic Acids Motif in the Synthesis of New 2H,5H-Chromeno[4′,3′:4,5]thiopyrano[2,3-d]thiazoles via Tandem Hetero-Diels–Alder-Hemiacetal Reaction

We have developed a tandem hetero-Diels–Alder-hemiacetal reaction using arylidene pyruvic acids with 5-(ortho-hydroxybenzylidene)-substituted 4-thioxo-2-thiazolidinones, leading to 6-hydroxy-2-oxo-5-phenyl-3,5a,6,11b-tetrahydro-2H,5H-chromeno[4′,3′:4,5]thiopyrano[2,3-d][1,3]thiazole-6-carboxylic acids. The stereochemistry of cycloaddition was confirmed by NMR spectra and a single-crystal x-ray diffraction analysis.     

Multidimensional thermoelasticity for nonsimple materials – well-posedness and long-time behavior

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without a (second-order in space) Kelvin–Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case are proved. Further, a frictional damping for the elastic component is shown to lead to exponential stability. A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. Additionally, a connection between exponential stability and exact observability of unitary strongly continuous groups is established.