Laterally 4-nitrobenzyloxycarbonyl substituted phenyl benzoates: The first two-ring mesogens with a lateral branch containing a phenyl ring

The synthesis and properties of laterally 4-nitrobenzyloxycarbonyl substituted phenyl benzoates are described; these compounds represent the first two-ring mesogens having a phenyl ring in the lateral branch. The lengths of the terminal chains of the core carrying the branch have a great influence, as shown by the phase behaviour of two homologous series. Compounds having long alkyloxy groups exhibit enantiotropic smectic A phases. It should be emphasized that the mesophase thermal stability of these strongly branched derivatives can be higher than that of the laterally unsubstituted parent compound. Connecting two of the new mesogens by means of an aliphatic spacer results in a novel type of twin molecule.     

THE SIZE OF FARSIGHTED STABLE COALITIONS IN A GAME OF POLLUTION ABATEMENT

Abstract The game theoretical analysis of international environmental problems has received increasing attention in recent years. Major issues are as follows. Under which conditions will an international environmental agreement (IEA) be signed? Will the agreement be stable? Game theory has given different answers to these questions; in particular, it is possible to show that if countries are myopic then only small stable coalitions occur, but if they are farsighted then both large and small stable coalitions exist. This paper studies the size of a farsighted stable IEA by considering a quadratic cost function in a pollution abatement model. Following Rubio and Ulph [2006] , we consider both the case of non‐negative emissions as well as the case of unrestricted ones.     

Theoretical determination of the magnetic properties of 2-pyrone and 4-pyrone,and o-benzoquinone and p-benzoquinone

A series of theoretical procedures, relying on the conventional common-origin and distributed-origin approaches, and adopting extended gaugeless as well as London basis sets, have been applied at the Hartree-Fock level of accuracy to predict magnetic susceptibilities and nuclear magnetic shieldings of four molecular systems that aroused particular interest and discussion concerning their aromatic character. The theoretical results are of near Hartree-Fock quality. Comparison with experimental values for magnetic susceptibilities seems to indicate that the latter need to be revised. Analysis of calculated properties and of plots of current density induced by the magnetic field in the π-electrons provides simple and effective tools for the classification of 2- and 4-pyrones, and o- and p-benzoquinone as non-aromatic.     

High resolution FTIR spectra and analysis of the ν11 fundamental and of the ν2 + ν11, ν5 + ν12 and ν7 + ν16 combination bands of 12C6D6

We report results from measurements of the high resolution FTIR spectrum for the fully deuterated benzene molecule C₆D₆ in the range 450–3500 cm^?1. Accurate spectroscopic constants have been obtained for the fundamental vibration ν₁₁ at 496.208 cm^?1 and improved ground state constants have been deduced from a fit of ground state combination differences. The J structure of the combination parallel bands ν₂ + ν₁₁ (at 2798.1 cm^?1), ν₅ + ν₁₂ (1802.5 cm_?1) and ν₇, + ν₁₆ (2619.3 cm^?1) of C₆D₆ has been analysed as well, from which improved values of the band origin and of the B and D _j constants of the excited states have been obtained. The strongest hot bands accompanying these parallel transitions have been assigned by means of the anharmonic force field calculated by Maslen et al. [1992, J. chem. Phys., 97, 4233]. In particular (ν₁₁ + ν₁₆) ? ν₁₆ is assigned to the band at 492.4 cm^?1 even though its shape is typical of a perpendicular transition (PAPE). New values for the ν₅, ν₁₂ and ν₁₆ band origins are determined from the band origins of combination bands and from calculated anharmonic constants. Numerous anharmonic constants are derived from the assignment of hot band and combination transitions.     

Collective hyperspherical coordinates for polyatomic molecules and clusters

For n-body dynamics an analysis is made of the properties of configuration space within a symmetric hyperspherical framework. Coordinates are conveniently broken up into spatial (or external) rotations, kinematic invariants (related to the inertia moments) and kinematic (or internal) rotations. Their usefulness is demonstrated for the study of constrained intramolecular motions and of concerted reactions and for collective modes of polyatomic molecules and clusters. For a fixed hyperradius, which is a measure of total inertia, the space of kinematic invariants is the surface of a right spherical triangle that leads to the tetrahedral (for n = 4) or octahedral (for n ≥ 5) tessellation of the sphere. Alternative parametrizations are discussed, including the proper one to deal with the umbrella inversion motion of ammonia.     

State selective predissociation spectroscopy of hydrogen chloride ions (HCl+) via the A2Σ+ ← X2Π3/2 transition

The photodissociation of hydrogen chloride ions (HCl⁺) has been investigated through the A²Σ⁺ (ν′ = 6, 7 and 8) ← X ²Π_3/2 (ν″ = 0) transition. The spectra reveal that state selective photodissociation with complete resolution of the spin, orbital, and rotational angular momentum is possible in the A ²Σ⁺ (ν′ = 6) state. The analysis of these spectra yields the rotational and the spin-rotation coupling constant of the A ²Σ⁺ (ν′ = 6) state. The lifetime of HCl⁺ decreases significantly with increasing vibrational excitation in the ²Σ⁺ state. Within the experimental error limits no J dependence of the lifetime is observerd. The state selective photodissociation of the HCl⁺ ions is also shown to be a very sensitive probe for unexpected parity transitions in the 2 + 1 REMPI formation of the HCl⁺ ions in the X 2Π_3/2 (ν″ = 0) state.     

Anharmonic force field for methanol

An ab initio quartic anharmonic force field for methanol has been calculated at the equilibrium position using the CCSD(T) method for the structure and the harmonic potential energy surface, and the MP4(SDQ) method for the anharmonic part of the surface. A triple zeta basis set was employed with symmetrized curvilinear internal valence coordinates in all calculations. The internal coordinate force field constants have been transformed into force constants in the dimensionless normal coordinate representation for various isotopomers. Vibrational term values for CH₃OH, CH₃OD, CD₃OH, and CD₃OD have been obtained using second order perturbation theory. Particular care has been devoted to the inclusion of Fermi resonance interactions between different vibrational states. A good accuracy has been achieved in the calculation of the fundamentals for all the isotopomers, the mean absolute error being 5.8 cm^?1.     

The Local Stabilizability Problem for Nonlinear Systems

This paper deals with the local smooth stabilizability problemfor nonlinear control systems defined by ordinary differentialequations. Several approaches to this problem are reviewed anddiscussed: in particular, it is shown that certain results canbe improved (at least from a practical point of view) by combiningdifferent approaches.     

PLÜCKER RELATIONS AND SPHERICAL VARIETIES: APPLICATION TO MODEL VARIETIES

A general framework for the reduction of the equations defining classes of spherical varieties to (possibly infinite-dimensional) grassmannians is proposed. This is applied to model varieties of types A, B and C; in particular, a standard monomial theory for these varieties is presented.     

Algorithms for Brownian dynamics

We derive a class of efficient and stable algorithms of Brownian dynamics using a formula, derived by Suzuki, to express time-ordered operators. These algorithms are simpler than those derived by Helfand from Runge-Kutta algorithms and, like Helfand algorithms, can be combined with SHAKE to describe the Brownian dynamics of constrained systems.