Classification of graded Hecke algebras for complex reflection groups

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well as complex reflection groups. Received: July 25, 2001     

Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

Generalized Exponents and Forms

We consider generalized exponents of a finite reflection group acting on a real or complex vector space V. These integers are the degrees in which an irreducible representation of the group occurs in the coinvariant algebra. A basis for each isotypic component arises in a natural way from a basis of invariant generalized forms. We investigate twisted reflection representations (V tensor a linear character) using the theory of semi-invariant differential forms. Springer’s theory of regular numbers gives a formula when the group is generated by dim V reflections. Although our arguments are case-free, we also include explicit data and give a method (using differential operators) for computing semi-invariants and basic derivations. The data give bases for certain isotypic components of the coinvariant algebra.     

Quasiclassical trajectory calculations of the OH+NO2 association reaction on a global potential energy surface

We report a full-dimensional potential energy surface (PES) for the OH+NO(2) reaction based on fitting more than 55,000 energies obtained with density functional theory-B3LYP6-311G(d,p) calculations. The PES is invariant with respect to permutation of like nuclei and describes all isomers of HOONO, HONO(2), and the fragments OH+NO(2) and HO(2)+NO. Detailed comparison of the structures, energies, and harmonic frequencies of various stationary points on the PES are made with previous and present high-level ab initio calculations. Two hydrogen-bond complexes are found on the PES and confirmed by new ab initio CASPT2 calculations. Quasiclassical trajectory calculations of the cross sections for ground rovibrational OH+NO(2) association reactions to form HOONO and HONO(2) are done using this PES. The cross section to form HOONO is larger than the one to form HONO(2) at low collision energies but the reverse is found at higher energies. The enhancement of the HOONO complex at low collision energies is shown to be due, in large part, to the transient formation of a H-bond complex, which decays preferentially to HOONO. The association cross sections are used to obtain rate constants for formation of HOONO and HONO(2) for the ground rovibrational states in the high-pressure limit.     

Hg+Br-->HgBr recombination and collision-induced dissociation dynamics

A global potential energy surface has been constructed for the system HgBr+Ar-->Hg+Br+Ar to determine temperature dependent rate constants for the collision-induced dissociation (CID) and recombination of Hg and Br atoms. The surface was decomposed using a many-body expansion. Accurate two-body potentials for HgBr, HgAr, and ArBr were calculated using coupled cluster theory with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)], as well as the multireference averaged coupled pair functional method. Correlation consistent basis sets were used to extrapolate to the complete basis set limit and corrections were included to account for scalar and spin-orbit relativistic effects, core-valence correlation, and the Lamb shift. The three-body potential was computed with the CCSD(T) method and triple-zeta quality basis sets. Quasiclassical trajectories using the final analytical potential surface were directly carried out on the CID of HgBr by Ar for a large sampling of initial rotational, vibrational, and collision energies. The recombination rate of Hg and Br atoms is a likely first step in mercury depletion events that have been observed in the Arctic troposphere during polar sunrise. The effective second order rate constant for this process was determined in this work from the calculated CID rate as a function of temperature using the principle of detailed balance, which resulted in k(T) = 1.2 x 10(-12) cm(3) molecule(-1) s(-1) at 260 K and 1 bar pressure.     

Ab initio thermochemistry involving heavy atoms: an investigation of the reactions Hg + IX (X = I, Br, Cl, O)

Accurate 0 K enthalpies have been calculated for reactions of mercury with a series of small iodine-containing molecules (I2, IBr, ICl, and IO). The calculations have been carried out with the coupled cluster singles and doubles method with a perturbative correction for connected triple excitations [CCSD(T)] using sequences of correlation consistent basis sets and accurate relativistic pseudopotentials. Corrections have been included to account for core-valence correlation, spin-orbit coupling, scalar relativity, and the Lamb shift. In a few cases coupled cluster calculations with iterative triple (CCSDT) and quadruple (CCSDTQ) excitations have been carried out to estimate the effects of higher order electron correlation. The pseudopotential calculations have also been compared to all electron calculations using second- and third-order Douglas-Kroll-Hess Hamiltonians. In addition to the reaction enthalpies, heats of formation, bond lengths, and harmonic vibrational frequencies have been calculated for the stable triatomic products HgI2, HgIBr, HgICl, and HgIO. Accurate dissociation energies, equilibrium bond lengths, and harmonic vibrational frequencies have also been calculated for each of the diatomic molecules involved in this study (HgI, HgBr, HgCl, HgO, I2, IBr, ICl, and IO). The reported enthalpies are expected to have accuracies of 1 kcal/mol or better.     

Synthesis of and structure–property relationships in zinc complexes of bis‐metaphenylene semiquinone biradical species

The design of novel, functionalized bis‐metaphenylene semiquinone (SQ) ligands and their corresponding metal complexes which combine conformational flexibility and electron‐withdrawing, electron‐donating, and conjugating substituents enable investigation of multiple structure–property relationships. Along these lines, we report the synthesis of three new bis(Zn^II(SQ)Tp^Cum,Me) complexes containing the bis‐metaphenylene coupling fragment. Using electron paramagnetic resonance spectroscopy, ab initio computations and superconducting quantum interference device magnetometry, we show how spin‐density is affected by the bis‐metaphenylene system substituents. Copyright © 2011 John Wiley & Sons, Ltd.     

The sign representation for Shephard groups

Shephard groups are unitary reflection groups arising as the symmetries of regular complex polytopes. For a Shephard group, we identify the representation carried by the principal ideal in the coinvariant algebra generated by the image of the product of all linear forms defining reflecting hyperplanes. This representation turns out to have many equivalent guises making it analogous to the sign representation of a finite Coxeter group. One of these guises is (up to a twist) the cohomology of the Milnor fiber for the isolated singularity at in the hypersurface defined by any homogeneous invariant of minimal degree. Received: 28 September 2000 / Published online: 18 January 2002     

On the Spectroscopic and Thermochemical Properties of ClO,BrO, IO,and Their Anions

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.     

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.