Percolation features of cooperative Jahn-Teller systems: Ising EFT framework

Elastic exchange between two nearest Jahn-Teller (JT) centers in two or three dimensional dense crystals, can give an ordered macroscopic distortion known as cooperative JT effect (CJTE). A very diluted JT crystal does not show this effect. In the dynamic JT effect (DJTE), tunneling between different equivalent distorted wells has a pronounced influence on the CJTE. We investigate this phenomenon using a progressive increase in the concentration of these centers in the JT crystals, based on a bond percolation vector spin analogy technique within the framework of effective field theory (EFT). Mean field theory (MFT) was extensively used in previous studies of CJTE; however it neither includes correlation between JT centers in the lattice due to the complexity of the distortion field in the crystal nor the effect of tunneling between wells. We resort to an alternative procedure, by describing a JT center as a pseudo-spin vector \(\vec S\), induced to represent the degenerate JT-distorted states, where two nearest JT centers interact via an elastic exchange described by an Ising type spin interaction. The DJTE is considered to be similar to an elastic transverse field term in the Hamiltonian portraying the effect of tunneling between equivalent wells in the adiabatic potential energy surface (APES). We will be particularly discussing S = 1, S = 3/2 and S = 5/2 spin cases, where 2S + 1 wells in the APES are present and what JT systems they actually represent, with a percolative mechanism applied to the interactions between different JT centers. The different lattices are distinguished by their coordination numbers. Strong tunneling effects can suppress the CJTE and lead to a new state of criticality. Generalizations to higher spin systems will be obtained using a scaling technique. For the relevant distortions, we determine single site correlations, the macroscopic average distortion describing a structural phase transition and the elastic isothermal susceptibility as a function of temperature. The critical bond percolation threshold and the critical tunneling parameter are also obtained.     

Preparation of 3-Bromo-1,2,4,5-tetrazine

In this synthetic procedure, a seven-step protocol for the preparation of monosubstituted 3-bromo-1,2,4,5-tetrazine is presented. The procedure features efficient transformations and purification methods starting from commercially readily available starting materials and affords the title compound on a gram scale with 13 % overall yield in reliable purity (>97 %). Detailed experimental procedures, supported by images and additional notes, allow the preparation of a valuable advanced building block, enabling further applications in bioconjugation, protein labelling, bio-orthogonal chemistry, heterocycle syntheses, high energy materials, and drug release, among others.     

Discrete-time approximation of decoupled Forward–Backward SDE with jumps

We study a discrete-time approximation for solutions of systems of decoupled Forward–Backward Stochastic Differential Equations (FBSDEs) with jumps. Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the number of time steps n$n$ goes to infinity. The rate of convergence is at least n^−1/2+ε$n^{-1/2+\epsilon }$, for any ε>0$\epsilon >0$. When the jump coefficient of the first variation process of the forward component satisfies a non-degeneracy condition which ensures its inversibility, we achieve the optimal convergence rate n^−1/2$n^{-1/2}$. The proof is based on a generalization of a remarkable result on the path-regularity of the solution of the backward equation derived by Zhang [J. Zhang, A numerical scheme for BSDEs, Annals of Applied Probability 14 (1) (2004) 459–488] in the no-jump case.     

Synthesis of the 11β-hydroxymethyl-androst-4-en-3,17-dione

The 11β-hydroxymethyl-androst-4-en-3,17-dione 5 was prepared within five synthetic steps starting from the commercially available adrenosterone with an overall yield of 24%. The 11-ketosteroid 1 was subjected to a Peterson methylenation. The subsequent hydroboration/oxidation sequence in position 11 was regio- and stereoselectively conducted using the borane-methyl sulfide complex at 0 °C. The target molecule was then obtained by deprotection using in situ generated TMSI.     

A note on utility based pricing and asymptotic risk diversification

In principle, liabilities combining both insurancial risks (e.g. mortality/longevity, crop yield,...) and pure financial risks cannot be priced neither by applying the usual actuarial principles of diversification, nor by arbitrage-free replication arguments. Still, it has been often proposed in the literature to combine these two approaches by suggesting to hedge a pure financial payoff computed by taking the mean under the historical/objective probability measure on the part of the risk that can be diversified. Not surprisingly, simple examples show that this approach is typically inconsistent for risk adverse agents. We show that it can nevertheless be recovered asymptotically if we consider a sequence of agents whose absolute risk aversions go to zero and if the number of sold claims goes to infinity simultaneously. This follows from a general convergence result on utility indifference prices which is valid for both complete and incomplete financial markets. In particular, if the underlying financial market is complete, the limit price corresponds to the hedging cost of the mean payoff. If the financial market is incomplete but the agents behave asymptotically as exponential utility maximizers with vanishing risk aversion, we show that the utility indifference price converges to the expectation of the discounted payoff under the minimal entropy martingale measure.     

Dissociation of N2 on a Si(111)-7x7 Surface at Room Temperature

We demonstrate that the strong N₂ bond can be efficiently dissociated at low pressure and ambient temperature on a Si(111)-7x7 surface. The reaction was experimentally investigated by scanning tunnelling microscopy and X-ray photoemission spectroscopy. Experimental and density functional theory results suggest that relatively low thermal energy collision of N₂ with the surface can facilitate electron transfer from the Si(111)-7x7 surface to the π*-antibonding orbitals of N₂ that significantly weaken the N₂ bond. This activated N₂ triple bond dissociation on the surface leads to the formation of a Si₃N interface.     

1, 1-dichloroalkylphosphonates: Convenient starting materials for low-coordinated trivalent phosphorus compounds

Diisopropyl 1,1-dichloroalkylphosphonates bearing various groups (alkyl, aryl, allyl, benzyl, phenylthiolate, trimethylsilyl) in the α-position were reduced to the corresponding primary 1,1-dichlorophosphines by the LiAlH₄-AlCl₃ system in diethyl ether. Subsequent dehydrochlorination with tertiary amines in the presence of trapping dipolar compounds (ethyl diazoacetate or n-hexylazide) led to the expected 1,2,4-diazaphospholes or 3H-1,2,3,4-triazaphospholes.