Bond lengths and valences in tungsten oxides

Equations relating bond strength (valence) to bond length have been developed for tungsten-oxygen and phosphorus-oxygen bonds. Bond-valence sums have been carried out for the different tungsten atoms in phosphate tungsten bronzes and other mixed-valence tungsten oxides and for the Mo atoms in TeMo₅O₁₆. Valences intermediate between 5 and 6 are generally found, in agreement with physical measurements that indicate delocalization of d electrons in these materials. Evidence is presented that shows that the degree of distortion of WO₆ octahedra increases with apparent oxidation state of tungsten.     

A local functional calculus

This paper introduces a local functional calculus for a class of bounded operators on a Hilbert space. Properties of the local functional calculus are investigated and an application is given to subnormal operators. Also, the concept of a locally rationally multicyclic operator is introduced and the Berger-Shaw Theorem is discussed.During the preparation of this paper the author was partially supported by National Science Foundation grant MCS 83-20426.     

Construction of a (64, 2 37, 12) Code via Galois Rings

Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4^m 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 2₃₇, 12) code as the binary image, under the Gray map, of an extended cyclic code defined over the integers modulo 4 using Galois rings. The Nordstrom-Robinson code is defined in this same way, and like the Nordstrom-Robinson code, the new code is better than any linear code that is presently known.     

Balancing dynamic and nondynamic correlation for diradical and aromatic transition states: a renormalized coupled-cluster study of the cope rearrangement of 1,5-hexadiene

Single-reference coupled-cluster calculations employing the completely renormalized CCSD(T) (CR-CCSD(T)) approach have been used to examine the mechanism of the Cope rearrangement of 1,5-hexadiene. In agreement with multireference perturbation theory, the CR-CCSD(T) method favors the concerted mechanism of the Cope rearrangement involving an aromatic transition state. The CCSD(T) approach, which is often regarded as the "gold standard" of electronic structure theory, seems to fail in this case, favoring pathways through diradical structures.     

Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states

The method of moments of coupled-cluster equations (MMCC), which provides a systematic way of improving the results of the standard coupled-cluster (CC) and equation-of-motion CC (EOMCC) calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The MMCC theory and its generalized MMCC (GMMCC) extension that enables one to use the cluster operators resulting from the standard as well as nonstandard CC calculations, including those obtained with the extended CC (ECC) approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction (CI) and CC or EOMCC energies. These relationships can be used to design the noniterative corrections to the CC/EOMCC energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference CC/EOMCC methods fail. Several MMCC and GMMCC approximations are discussed, including the renormalized and completely renormalized CC/EOMCC methods for closed- and open-shell states, the quadratic MMCC approaches, the CI-corrected MMCC methods, and the GMMCC approaches for multiple bond breaking based on the ECC cluster amplitudes.     

THE QUENCHING OF TYROSINE AND TRYPTOPHAN FLUORESCENCE BY H2O AND D2O*

Abstract— The quantum yields and lifetimes of the fluorescence of tyrosine and tryptophan were determined in D₂O-H₂O and glycerol-H₂O solvent mixtures of varying composition from 10 vol.% to 100% H₂O at 15°C. Forboth amino acids the ratio of the quantum yields in D₂O and H₂O (i.e., q_D/q_H) was smaller than the ratio of the corresponding lifetimes (_D/_H). For tyrosine the ratio of the quantum yields in glycerol and H₂O (q_G/q_H) was also smaller than the corresponding _G/_H ratio, but for tryptophan q_G/g_HG/_H. The proximity of the q vs. plots for tyrosine in the two solvent mixtures indicates that at 15°C neither D₂O nor glycerol, in the pure state or when diluted with H₂O, quench tyrosine significantly. However, H₂O quenches tyrosine by a dynamic process, which increases both the radiative and the nonradiative rate constant. The quenching action is attributed to a tyrosine-H₂O exciplex, whose formation is independent of bulk viscosity and dielectric constant. Unlike tyrosine, tryptophan is quenched weakly by D₂O by a static process at 15°C (i.e., involving no change in), but H₂O quenches tryptophan much more efficiently by a dynamic process, which involves the nonradiative rate constant, but not the radiative constant. These results are explained on the basis of electrostatic complexation of the ammonium group to the carbon atom adjacent to the ring nitrogen with a lifetime which is longer thanin D₂O but shorter thanin H₂O, with solvent reorientation possibly also being an important factor in the quenching. This explanation is consistent with the fact that concentrated (8 M) urea increases q andof aqueous tryptophan ? 15–20%, while guanidine hydrochloride (6.4 M) has the opposite effect, i.e., it decreases q and t of tryptophan ? 15–20%, and with the fact that neither 8 M urea nor 6.4 M guanidine hydrochloride affects any fluorescence parameter of tyrosine at all.     

Asymptotic properties of sequences of iterates of nonlinear transformations

By considering functions defined on the unit interval with a single zero minimum and a single unit maximum we are led to a version of the doubling or universal transformation. The fixed point functions of this doubling transformation have certain invariance properties under conjugacy. These invariance properties lead to a widening of the concept of universality to power law conjugacy classes in which the Feigenbaum divergence parameter is a function only of the product of the powers with which iterating functions approach unity at the maximum and zero at the minimum. We also construct an effective method for computing the divergence parameter from iterates, and derivatives of iterates, generated by the appropriate fixed point function.On leave from Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia.