Generalization of a result of Matsuo and Cherednik to the Calogero-Sutherland-Moser integrable models with exchange terms

A few years ago, Matsuo and Cherednik proved that from some solutions of the Knizhnik-Zamolodchikov (KZ) equations, which first appeared in conformal field theory, one can obtain wave functions for the Calogero integrable system. In the present communication, it is shown that from some solutions of generalized KZ equations, one can construct wave functions, characterized by any given permutational symmetry, for some Calogero-Sutherland-Moser integrable models with exchange terms. Such models include the spin generalizations of the original Calogero and Sutherland ones, as well as that with -function interaction.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995     

Dramatic Influence of an Anionic Donor on the Oxygen‐Atom Transfer Reactivity of a MnV–Oxo Complex

Addition of an anionic donor to an Mn^V(O) porphyrinoid complex causes a dramatic increase in 2‐electron oxygen‐atom‐transfer (OAT) chemistry. The 6‐coordinate [Mn^V(O)(TBP₈Cz)(CN)]^? was generated from addition of Bu₄N⁺CN^? to the 5‐coordinate Mn^V(O) precursor. The cyanide‐ligated complex was characterized for the first time by Mn K‐edge X‐ray absorption spectroscopy (XAS) and gives Mn?O=1.53 Å, Mn?CN=2.21 Å. In combination with computational studies these distances were shown to correlate with a singlet ground state. Reaction of the CN^? complex with thioethers results in OAT to give the corresponding sulfoxide and a 2e^?‐reduced Mn^III(CN)^? complex. Kinetic measurements reveal a dramatic rate enhancement for OAT of approximately 24 000‐fold versus the same reaction for the parent 5‐coordinate complex. An Eyring analysis gives ΔH^≠=14 kcal mol^?1, ΔS^≠=?10 cal mol^?1 K^?1. Computational studies fully support the structures, spin states, and relative reactivity of the 5‐ and 6‐coordinate Mn^V(O) complexes.     

Nonstandard GLh(n) quantum groups and contraction of covariant q-bosonic algebras

GL_h(n) × GL_h(m)-covariant h-bosonic algebras are built by contracting the GL_q(n) × GL_q(m)-covariant q-bosonic algebras considered by the present author some years ago. Their defining relations are written in terms of the corresponding R _h-matrices. Whenever n = 2, and m = 1 or 2, it is proved by using U_h(sl(2)) Clebsch-Gordan coefficients that they can also be expressed in terms of coupled commutators in a way entirely similar to the classical case. Some U_h(sl(2)) rank-(1/2) irreducible tensor operators, recently constructed by Aizawa in terms of standard bosonic operators, are shown to provide a realization of the h-bosonic algebra corresponding to n = 2 and m = 1.     

Partial widths of fixed generalized seniority spectral distributions

Analytic expressions are derived for the partial widths of the fixed generalized seniority spectral distributions, using an expansion of the hamiltonian in terms of irreducible tensors with respect to both symplectic and quasi-spin groups.     

FixedJ spectral distributions in large shell model spaces

A method is developed to exactly calculate the fixedJ quasiparticle centroid energies and partial widths. Some results obtained in the even-mass lead isotopes with various interactions are analysed. FixedJ quasiparticle distributions are used to predict an upper limit for the deviations between the quasiparticle approximation and the shell model results for the low-energy levels. The influence of the states with a high quasiparticle number in the low-energy region is seen to strongly depend upon the interaction. The importance of the dimensionalities and the internal widths in explaining the admixtures is stressed.     

\mathcal{P}\mathcal{T}-symmetric quartic anharmonic oscillator and position-dependent mass in a perturbative approach

To lowest order of perturbation theory we show that an equivalence can be established between a -symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian h. An important feature of h is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also determine the associated physical quantities.     

Representation theory of generalized deformed oscillator algebras

The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators {1, a, a , N}. Their commutators and Hermiticity properties are those of the boson oscillator algebra, except for [a, a ] _q = G(N), where [a, b] _q = ab – q ba and G(N) is a Hermitian, analytic function. The unitary irreductible representations are obtained by means of a Casimir operator C and the semi-positive operator a a. They may belong to one out of four classes: bounded from below (BFB), bounded from above (BFA), finite-dimentional (FD), unbounded (UB). Some examples of these different types of unirreps are given.     

Axial and equatorial ligand effects on biomimetic cysteine dioxygenase model complexes

Density functional theory (DFT) calculations are presented on biomimetic model complexes of cysteine dioxygenase and focus on the effect of axial and equatorial ligand placement. Recent studies by one of us [Y. M. Badiei, M. A. Siegler and D. P. Goldberg, J. Am. Chem. Soc. 2011, 133, 1274] gave evidence of a nonheme iron biomimetic model of cysteine dioxygenase using an i-propyl-bis(imino)pyridine, equatorial tridentate ligand. Addition of thiophenol, an anion - either chloride or triflate - and molecular oxygen, led to several possible stereoisomers of this cysteine dioxygenase biomimetic complex. Moreover, large differences in reactivity using chloride as compared to triflate as the binding anion were observed. Here we present a series of DFT calculations on the origin of these reactivity differences and show that it is caused by the preference of coordination site of anion versus thiophenol binding to the chemical system. Thus, stereochemical interactions of triflate and the bulky iso-propyl substituents of the ligand prevent binding of thiophenol in the trans position using triflate. By contrast, smaller anions, such as chloride, can bind in either cis or trans ligand positions and give isomers with similar stability. Our calculations help to explain the observance of thiophenol dioxygenation by this biomimetic system and gives details of the reactivity differences of ligated chloride versus triflate.     

Covariant (hh′)-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones

GL_h(n) ×GL_h(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras are built in terms of thecorresponding R_h and -matrices by contracting theGL_q(n) × -covariant q-bosonic (or q-fermionic) algebras , = 1, 2.When using a basis of wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra U_q(gl(n)) , a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingU_h(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some U_h(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of (2, 1).