An Isserlis’ Theorem for Mixed Gaussian Variables: Application to the Auto-Bispectral Density

This work derives a version of Isserlis’ theorem for the specific case of four mixed-Gaussian random variables. The theorem is then used to derive an expression for the auto-bispectral density for quadratically nonlinear systems driven with mixed-Gaussian iid noise. C.C. Olson is a NRC Postdoctoral Research Associate.     

Thermochemistry of Binding of Lead(II) and Cadmium(II) by Saccharides in Aqueous Solution

Solution calorimetry was used to determine enthalpies and stability constants for binding of lead(II) or cadmium(II) by galacturonic acid and several monosaccharides in aqueous solution. New values for enthalpies of solution in water are reported for galacturonic acid and maltose monohydrate. The interaction of water solvent with the reactants is the largest factor in the binding process.     

Halophilic reactions of a stable silylene with chloro and bromocarbons

A number of disilanes have been synthesized from a stable silylene, 1 (N,N'-di-tert-butyl-1,3-diaza-2-silacyclopent-4-en-2-ylidene), and a variety of halocarbons. It is proposed that disilane formation is a result of an initial halophilic interaction between the silylene and halocarbon. Formation of disilanes from 1 and CCl4, 2a, CHCl3, 2b, CH2Cl2, 2c, benzyl chloride, 2d, and bromobenzene, 5, are described here. An X-ray crystal structure of 2b was determined.     

Bending of DNA by asymmetric charge neutralization: all-atom energy simulations

DNA dodecamers of the alternating d(CG).d(CG) sequence with six phosphate groups either charge-neutralized or substituted by neutral methylphosphonates across the major or minor groove have been subjected to energy minimization to determine the conformational effect of the asymmetric elimination of phosphate charge. We report bending angles, directions of bending, and detailed structural characteristics such as groove widths and local base-pair parameters. Our principal results are that charge neutralization on one face of the DNA induces significant bending toward the neutralized face, in agreement with theoretical predictions on a simplified model and experimental data on a similar base-pair sequence, and that the DNA conformation averaged over all stereospecific methylphosphonate substitutions is nearly the same as the conformation produced by charge neutralization of the phosphates. Individual isomers, however, cover a wide range of structures, with the magnitude and direction of overall bending sensitive to the precise stereochemical pattern of neutralization. Our simulation does not explicitly contain counterions, and the results therefore suggest that counterions can influence DNA structure by neutralizing the phosphate charge. These data provide new hints into the molecular mechanisms which underlie the deformations of DNA structure induced by the binding of positively charged proteins and other tightly associated cationic species.     

Conformation-dependent state selectivity in O-O cleavage of ONOONO: an "inorganic cope rearrangement" helps explain the observed negative activation energy in the oxidation of nitric oxide by dioxygen

ONOONO has been proposed as an intermediate in the oxidation of nitric oxide by dioxygen to yield nitrogen dioxide. The O-O bond breaking reactions of this unusual peroxide, and subsequent rearrangements, were evaluated using CBS-QB3 and B3LYP/6-311G hybrid density functional theory. The three stable conformers (cis,cis-, cis,trans-, and trans,trans-ONOONO, based on the O-N-O-O dihedral angles of either approximately 0 degrees or approximately 180 degrees ) are predicted to have very different O-O cleavage barriers: 2.4, 13.0, and 29.8 kcal/mol, respectively. These large differences arise because bond breaking leads to correlation of the nascent NO(2) fragments with either the ground (2)A(1) state or the excited (2)B(2) state of NO(2), depending on the starting ONOONO conformation. A cis-oriented NO(2) fragment correlates with the (2)A(1) state, whereas a trans-oriented NO(2) fragment correlates with the (2)B(2) state. Each NO(2) fragment that correlates with (2)A(1) lowers the O-O homolysis energy by approximately 15 kcal/mol, similar to the approximately 17-25 kcal/mol (2)A(1) --> (2)B(2) energy difference in NO(2). Hence, this provides an unusual example of conformation-dependent electronic state selectivity. The O-O bond homolysis of cis,cis-ONOONO is particularly interesting because it has a very low barrier and arises from the most stable ONOONO conformer, and also due to obvious similarities to the well-known [3,3]-sigmatropic shift of 1,5-hexadiene, i.e., the Cope rearrangement. As an additional proof of our state selectivity postulate, a comparison is also made to breakage of the O-O bond of cis,cis-formyl peroxide, where no significant stabilization of the transition state is available because the (2)A(1) and (2)B(2) states of formyloxy radical are near-degenerate in energy. In the case of trans,trans-ONOONO, the O-O bond breaking transition state is a concerted rearrangement yielding O(2)NNO(2), whereas for cis,cis- and cis,trans-ONOONO, the initially formed NO(2) radical pairs can undergo further rearrangement to yield ONONO(2). It is proposed that previous spectroscopic observations of certain N=O stretching frequencies in argon-matrix-isolated products from the reaction of NO with O(2) (or (18)O(2)) are likely from ONONO(2), not the OONO radical as reported.     

Colloidal dynamics on disordered substrates

Using Langevin simulations, we examine driven colloids interacting with quenched disorder. For weak substrates the colloids form an ordered state and depin elastically. For increasing substrate strength, we find a sharp crossover to inhomogeneous depinning and a substantial increase in the depinning force, analogous to the peak effect in superconductors. The velocity versus driving force curve shows criticality at depinning, with a change in scaling exponent occurring at the order to disorder crossover. Upon application of a sudden pulse of driving force, pronounced transients appear in the disordered regime which are due to the formation of long-lived colloidal flow channels.     

Observation of unusual surface ordering in a uniaxial Sm-A phase formed by a highly biaxial compound

We have studied one banana-shaped compound using null-transmission ellipsometry. By studying free-standing films of various thicknesses we confirm that this compound exhibits the Sm-A phase. This is the first banana-shaped compound with a relatively small bend angle (approximately 140 degrees) in which a uniaxial phase has been observed. At the lower temperature end of the Sm-A phase we observe unusual ordering at the surface of the film.     

Balancing families of sets

Given k finite sets S₁,…,S_k, to what extent is it possible to partition their union into two parts A and B in such a way that, for each j, S_j ∩ A and S_j ∩ B contain approximately the same number of elements? Bounds are found for this and similar questions.     

Step structures on III-V phosphide (001) surfaces: how do steps and Sb affect CuPt ordering of GaInP2?

The observation of III-V phosphide (001)-(2 x 2) surfaces makes it possible to solve a long standing mystery of step structures. First-principles calculations show that a bulklike type-B step on a hydrogenated 2 x 2 surface is more stable than a rebonded one by 1.1 eV/unit step. In contrast, this energy difference for a H-free beta(2 x 4) surface is only 0.5 eV/unit step. The large difference explains why the CuPt ordering of GaInP is stronger in metal-organic chemical vapor deposition than in molecular beam epitaxy. However, a minute amount of Sb will preferentially attach to the 2 x 2 surface steps and induce additional step structures that cause ordering disruption.