Molecular structure of ThBr4(DME)2 (DME = 1,2-dimethoxyethane)

The molecular structure of ThBr₄(DME)₂ (DME = 1,2-dimethoxyethane), the first structurally characterized thorium complex containing a simple bidentate ether ligand, is described. The eight-coordinate complex presents a distorted dodecahedral geometry, with Th—Br and Th—O bond lengths in the ranges 2.8516(13)–2.8712(13) Å and 2.564(8)–2.620(8) Å, respectively. ThBr₄(DME)₂ is monoclinic, space group P2₁/n, a = 7.672(1), b = 14.581(1), c = 15.847(2) Å, = 102.24(1)°, V = 1732.4(3) ų, and Z = 4.     

A spectral approach to polyhedral dimension

Thespectrum spec( ) of a convex polytope is defined as the ordered (non-increasing) list of squared singular values of [A|1], where the rows ofA are the extreme points of . The number of non-zeros in spec( ) exceeds the dimension of by one. Hence, the dimension of a polytope can be established by determining its spectrum. Indeed, this provides a new method for establishing the dimension of a polytope, as the spectrum of a polytope can be established without appealing to a direct proof of its dimension. The spectrum is determined for the four families of polytopes defined as the convex hulls of:

1. The edge-incidence vectors of cutsets induced by balanced bipartitions of the vertices in the complete undirected graph on 2_q vertices (see Section 6).
2. The edge-incidence vectors of Hamiltonian tours in the complete undirected graph onn vertices (see Section 6).
3. The arc-incidence vectors of directed Hamiltonian tours in the complete directed graph ofn nodes (see Section 7).
4. The edge-incidence vectors of perfect matchings in the complete 3-uniform hypergraph on 3_q vertices (see Section 8).

In the cases of (ii) and (iii), the associated dimension results are well-known. The dimension results for (i) and (iv) do not seem to be well-known. General principles are discussed for ‘balanced polytopes’ arising from complete structures.     

Recognition and classification of nonlinear chaotic signals

We propose a method of identifying and classifying signals generated by nonlinear, chaotic processes even when there are other signals and noise present. The method compares probability densities constructed from signals with a library of known densities. We note that there are many different invariant densities that can be constructed and that the characteristic functional of these densities factorizes into a product of characteristic functionals. Each member of the product is the characteristic functional of one of the signals present. This factorization provides a means of identifying the presence of a particular signal. Simple examples are given to demonstrate the method.     

Methods for controlling the regioselection in the reaction of 3-amino-5-benzylthio-1,2,4-triazole with acetylacetaldehyde dimethyl acetal

The reaction of 3-amino-5-benzylthio-1,2,4-triazole with acetylacetaldehyde dimethyl acetal affords 2-benzylthio-5-methyl-1,2,4-triazolo[1,5a]pyrimidine or 2-benzylthio-7-methyl-1,2,4-triazolo[1,5a]pyrimidine regioselectively depending on the reaction conditions.     

Molecular rectification and conductance switching in carbon-based molecular junctions by structural rearrangement accompanying electron injection

Molecular junctions were fabricated consisting of a 3.7 nm thick layer of nitroazobenzene (NAB) molecules between a pyrolyzed photoresist substrate (PPF) and a titanium top contact which was protected from oxidation by a layer of gold. Raman spectroscopy, XPS, and AFM revealed that the NAB layer was 2-3 molecules thick and was bonded to the two conducting contacts by C-C and N-Ti covalent bonds. The current/voltage behavior of the PPF/NAB(3.7)/Ti junctions showed strong and reproducible rectification, with the current at +2 V exceeding that at -2 V by a factor of 600. The observed current density at +3 V was 0.71 A/cm(2), or about 10(5) e(-)/s/molecule. The i/V response was strongly dependent on temperature and scan rate, with the rectification ratio decreasing for lower temperature and faster scans. Junction conductivity increased with time over several seconds at room temperature in response to positive voltage pulses, with the rate of increase larger for more positive potentials. Voltage pulses to positive potentials and back to zero volts revealed that electrons are injected from the Ti to the NAB, to the extent of about 0.1-1 e(-)/molecule for a +3 V pulse. These electrons cause an activated transition of the NAB into a more conductive quinoid state, which in turn causes an increase in conductivity. The transition to the quinoid state involves nuclear rearrangement which occurs on a submillisecond to several second time scale, depending on the voltage applied. The quinoid state is stable as long as the applied electric field is present, but reverts back to NAB within several minutes after the field is relaxed. The results are interpreted in terms of a thermally activated, potential dependent electron transfer into the 3.7 nm NAB layer, which brings about a conductivity increase of several orders of magnitude.     

Engineering redox functions in a nucleic acid binding protein

A nucleic acid binding protein, rop, has conserved topology with a number of redox proteins; this is exploited to engineer haem binding, expanding its function as a redox protein.     

A new arithmetic for linear free radical copolymerization

As a consequence of their method of production, polymer chains are polydisperse in size, composition and sequence distribution. In this work we present a new method of uniquely identifying these “polymer isomers” termed “Digital Encoding of Polymeric Chains”. The method involves replacing distinguishable features of the chain such as monomer units, branches, etc. with a number. This unique sequence of numbers provides a digital code, which, depending on the base of the arithmetic used (binary, ternary) can be translated into a unique decimal equivalent number. We have applied this technique to the case of binary copolymerization in a CSTR at steady state and show how the sequence spectra of the chain populations are conveniently obtained. Furthermore, the technique shows that rich information about the copolymerization kinetics, reactivity ratios and termination mode can be obtained from analysis of the short chains of the distribution. The implications for this in parameter estimation and controlled polymerization are discussed in this paper.     

Syn and anti aryl nitrenium ions

Calculations at several levels of ab initio molecular orbital theory have been carried out on 20 polycyclic aryl nitrenium ions of general structure ArNH⁺ and containing from two to four condensed rings. Electronic interactions between the aryl ring and the NH⁺ group stabilize all ions relative to PhNH⁺ by amounts varying from 14 to 40 kcal mol⁻¹ depending on the ring system and on the site of substitution. Apart from a few symmetrical cases, the ions exist in distinct syn and anti configurations, separated by substantial inversion barriers. At the HF/6‐31G(d) level, the latter are predicted to lie in the rather narrow range of 27.8±2.0 kcal mol⁻¹. Simple PMO analyses are presented based on the analogy with odd alternant hydrocarbon cations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 231–243, 1999