The pentad rotation-vibrational states of 12CD4: Wavenumber analysis of infrared and Raman spectra of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands

The so-called pentad of ¹²CD₄ consists of the vibrational states v₁ = 1(symmetry A₁), v₃ = 1(F₂), v₂ = 2(A₁ + E), v₂ = v₄ = 1(F₁ + F₂), and v₄ = 2(A₁ + E + F₂). All states are located in the 1950 to 2250-cm^?1 region and all are strongly interacting. In the present work we have assigned more than 5000 infrared rotation-vibrational transitions and 163 isotropic Raman transitions from the vibrational ground state to the pentad. We have used infrared and Raman spectra of a resolution better than 0.01 cm^?1. From the experimental wavenumbers 2567 pentad rotation-vibrational energy levels with J ≦ 20 have been determined. These levels are reported in the paper. The levels have been used for refinements of the spectroscopic constants of two physically different effective Hamiltonians for the pentad states. For all levels with J ≦ 12 an unweighted standard deviation of 0.004 cm^?1 is obtained for both Hamiltonians, whereas the standard deviation increases more or less rapidly with J above 12 due to the imperfections of the Hamiltonians. The values of the spectroscopic constants of both Hamiltonians (85 and 106, respectively) are reported and the effects of the approximations are discussed.     

Extensions of set partitions

A τ-partition of a subset of a given p-set X can be extended in many different ways to a τ-partition of X. The Stirling number of the second kind S(p, τ) can be defined as the number of all τ-partitions of X, and can be regarded as the number of all possible extensions of the τ-partitions of all the τ-subsets of X. In this paper we study the number of extensions for a particular choice of τ-partitions of the m-subsets of X, with 1 ? m ? p.     

Simplicity of crossed products by endomorphisms

Conditions are given for simplicity of the crossed product of a unital C^*-algebra by an endomorphism.     

Double-resonance circuit for nuclear magnetic resonance spectroscopy

A new double-resonance probe circuit design is described. The circuit contains no quarter-wavelength elements or equivalents, yet nonetheless achieves adequate isolation between the two input channels. It contains relatively few components, and so is both compact and efficient. It has been incorporated in two solid-state nuclear magnetic resonance (NMR) probes, with excellent results.     

The structure of substituted biphenyls as studied by proton NMR in nematic solvents. Single conformation model versus maximum entropy analysis

Published [11,12] proton nuclear magnetic resonance data for two substituted biphenyl molecules dissolved in nematic solvents are analysed in terms of the single conformation model and compared with the results of the maximum entropy analysis of [11]. It is shown that (i) this model, in which the number of adjustable parameters is less than the number of data, can describe very well the data for both molecules and (ii) the results of the maximum entropy analysis provide global support for this model. It is argued that the ultimate support of the single conformation model would be that introduction of a sufficiently large number of additional data in the maximum entropy analysis leads to a distribution for the dihedral angle between the two phenyl rings with two symmetrical very sharp peaks.     

Study by Mössbauer spectroscopy of arsenides Fe2−xMnxAs

The study by Mössbauer spectroscopy of the Fe_2?xMn_xAs series confirms that the iron atom completely occupies site I of the structure and leads to Néel temperatures in aggeement with those deduced from magnetic susceptibility measurements. In the range x = 0.8 to x = 1.4, the hyperfine structure is unresolved. On passing from Fe₂As to Mn₂As, three types of magnetic structures are encountered; contrary to the conclusion drawn from neutron diffraction measurements, the spins in Mn₂As are not perpendicular to the c-axis, and FeMnAs does not have the magnetic structure of Mn₂As.The internal magnetic field curves as a function of temperature are in this series either over-Brillouin with first-order antiferromagnetic (AF) to paramagnetic (P) transition or under-Brillouin. In order to explain the set of the observed magnetic anomalies, the existence of itinerant magnetism is postulated.     

Notes on probabilistic radiative transfer

Some further applications are made of Frischs' theorem on the surface values of functions satisfying linear integral equations of transfer. The meaning of the surface values is discussed in terms of random walks.     

An ab initio description of the excited states of the reaction O(3P, 1D) + H2 → OH(2Π, 2Σ+) + H. An attempt to describe several potential energy surfaces with constant accuracy

A new aspects of the role of the solvent mode in the photoinduced electron-transfer process of electron donor and acceptor system in polar solvents has been exploited. Taking into account the important fact that the vibrational frequency of the solvent mode in the initial neutral state of the reactants is considerably smaller than that in the final ionic state, we have derived a new formula for the energy-gap dependence of the electron-transfer rate. In this formulation, the activation energy is greatly reduced and the electron-transfer rate is almost independent of the energy gap over a wide down-hill energy region. This qualitative feature explains the experimental results for the relation between the bimolecular quenching rate constant k_w and the standard free-energy change ΔG° associated with electron transfer in the “anomalous region”.     

Thermal averaging of the spin-rotation coupling in small molecules leads to an isotropic NMR shielding

It has been known for over 70 years that nuclear spins couple to molecular rotation via a Zeeman interaction. This spin–rotation coupling can be observed as a discrete splitting in molecular beam magnetic resonance experiments, but is quenched by molecular collisions at higher pressures. We show that because of differential thermal population of M_J levels at high magnetic fields, the spin rotation coupling retains a small isotropic component at high field. For all but the smallest molecules at very low temperature, the residual coupling is temperature independent and linear in the magnetic field; it therefore closely mimics the chemical shift. The ‘super spin rotation’ shift may in the future be a necessary correction to ultra – high precision computations of the NMR chemical shielding of small molecules in gases and liquids.     

A polynomial time algorithm for computing the nucleolus for a class of disjunctive games with a permission structure

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems there is some hierarchical ordering of the players. In this paper we consider a class of games with a permission structure describing situations in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. The corresponding restricted game takes account of the limited cooperation possibilities by assigning to every coalition the worth of its largest feasible subset. In this paper we provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with a permission structure which economic applications include auction games, dual airport games, dual polluted river games and information market games.