Computation and analysis of molecular Hartree—Fock momentum intracules

An efficient general algorithm for the computation of molecular momentum intracule densities from Hartree-Fock wavefunctions using Gaussian basis functions is described. The momentum intracules for a number of systems are examined, and comparison with their position space counterparts discussed.     

Intramolecular vibrational relaxation in aromatic molecules. 2: An experimental and computational study of pyrrole and triazine near the IVR threshold

The threshold region of vibrational energy redistribution (IVR) presents a great experimental and computational challenge for organic molecules with more than 10 degrees of freedom. The density of states ρ_tot is high and requires high resolution measurements over a wide range to cover all relevant timescales experimentally. Yet ρ_tot is sufficiently low that IVR quantities like the initial relaxation time τIVR or the number of participating states N_eff are very sensitive to the coupling structure. To highlight the competing effects of molecular symmetry and mode localization on the accessible density of states, this work complements a study of benzene (Callegari, A., Merker, U., Engels, P., Srivastava, H. K., Lehmann, K. K., and Scoles, G., 2000, J. chem. Phys., 113, 10583) by measuring the CH overtone spectra of pyrrole (C₄H₄NH) and 1,2,3-triazine (C₃N₃H₃) using eigenstate-resolved double-resonance spectroscopy. Large scale computations of IVR dynamics were undertaken, applying filter diagonalization to analytically fitted fourth-order ab initio force fields. With an overall adjustment to the anharmonicity of the potential, the modelled N_eff and τ_IVR agree with the experimental quantities within a factor of 2 to 3, which is reasonable for a rate theory in the threshold regime. The models also correctly predict the experimentally observed trends of τ_IVR and N_eff for the two molecules, and provide insight into the highly off-resonant coupling mechanism, which yields very sharp linewidths.     

Effects of linking chain length and magnetic field on the kinetics of photoprocesses in covalently bonded porphyrin—viologen dyads

The formation and decay kinetics of chain linked triplet radical pairs derived from photo-induced electron transfer reactions in a series of 21 zinc porphyrin-flexible spacer-viologen (ZnP-Sp _n -Vi²⁺) dyads containing 2–138 atoms (n) in the spacer, have been examined by nanosecond laser flash photolysis techniques in an external magnetic field. In non-viscous polar solvents (acetone and CHCl₃ plus CH₃OH = 1:1 v/v), the effect of the spacer length on the rate constant of forward electron transfer can be described by the equation: k _et = k ⁰ _et(n + 6)^?1.5, with k ⁰ _et = 3 × 10¹⁰ s^?1 and 1.2 × 10¹⁰ s^?1 for electron transfer from the singlet and triplet states of ZnP, respectively. In zero magnetic field, the value of the triplet radical pair recombination rate constant, k _r(0) = 0.7 × 10⁶-8 × 10⁶ s^?1, is significantly smaller than k _et. The dependence of k _r(0) on n has an extremum with the maximum near n = 20. In a strong magnetic field (B = 0.21 T), significant retardation of triplet radical pair recombination is observed. In strong magnetic fields the effect of the chain length on triplet radical pair recombination rates is rather small and k _r(B) may vary in the range 0.3 × 10⁶-1 × 10⁷ s^?1. The phenomena observed are discussed in terms of the interplay of molecular and spin dynamics in the limits of slow and fast encounters, taking into account the exchange-interaction.     

Optical components from a new vitrifying liquid crystal

New low molar mass liquid crystalline vitrifying materials have been synthesized and tested for application in optical films. The molecules were based on spiro compounds derived from pentaerythritol and mesogenic groups derived from cyanobiphenylyl moieties. The resulting materials showed glass transition temperatures as high as 85 degrees C and nematic to isotropic phase transition temperatures up to 222 degrees C. Crystallization from the melt was strongly suppressed. Well-aligned, solid, birefringent layers were obtained from the materials by spincoating. Uniaxially oriented layers with an optic axis tilted with respect to the substrate were obtained by spincoating the liquid crystals on pretilt amplification layers. When an anisotropic dye was incorporated in the liquid crystals, polarizers with a tilted absorption axis were obtained. In addition, the compounds were found to be suitable as hosts for photo-induced reorientation of photo-isomerizable dyes.     

A uniqueness theorem in inverse scattering of elastic waves

The scattering of plane elastic waves in an isotropic inhomogeneousmedium is considered. The existence and uniqueness of the directproblem is stated, and a reciprocity principle for the far fieldsof the scattered waves formulated. Finally, it is proved thatthe knowledge of the far-field patterns for a bounded sequenceof different frequencies and certain sets of incoming planewaves uniquely determines the density of the medium.     

THE PHOTOCHEMISTRY OF 14 C-5-BROMO-2''-DEOXYURIDYLYL-(3''→5'')-THYMIDINE DETERMINATION OF QUANTUM YIELDS AS A FUNCTION OF pH

Abstract— Quantum yields for the formation of the major photoproduct of 2-¹⁴C-5-bromo-2'-deoxyuridylyl-(3'→5')-thymidine (BrdUpT) have been determined by irradiation of the 2-¹⁴C-BrU-labeled dinucleotide at pH 2.3, 5.9, 7.05, 8.0 and 10.25 with U.V. light at 280nm. At acidic and neutral pH the quantum yield was 0.0063; the value decreased markedly above pH 8.0 to 0.0025 at pH 10.25. Some evidence of the formation of additional photoproducts at high and low pH was found. Some aspects of the mechanism of the reaction are discussed.
Consideration of p K_a values calculated for singlet and triplet excited states indicates that the decrease in the quantum yield of main photoproduct at high pH is due to dissociation of the excited bromodeoxyuridine moiety. It is suggested that the formation of BrdUpT photoproduct and the debromination of bromouracil-labeled DN A occur via different excited states.     

Nonlocal reaction--diffusion equations and nucleation

A nonlocal reaction-diffusion equation is presented and analysedusing matched asymptotic expansions and multiple timescales.The problem models a binary mixture undergoing phase separation.The particular form of the equation is motivated by argumentsfrom the calculus of variations, with the nonlocality arisingfrom an enforcement of conservation of mass. It is shown thatthe evolution of the solution can be characterized by trackingthe motion of fronts separating phases. The propagation of theinterfaces is found to be a coarsening process which dependsin a nonlocal fashion on mean curvature. Several special featuresof the equations of motion for the fronts are studied, and therelation of this evolution to Cahn-Hilliard theory and nucleationis discussed     

INVITED PAPER: Some mathematical aspects of security in the automated business environment

In the automated business world, personal contact and paper-basedtransactions are being replaced by digital electronic communications.This transition raises many new security issues, and has seenthe emphasis of cryptography broaden from secrecy to includemessage integrity, user verification, digital signature, andaccess control. In this paper, we consider some of the waysin which mathematics is playing a crucial role in securing theautomated business environment. We begin with a brief introduction to cryptography and the principlesupon which the design of cipher systems is based. We then considerstream ciphers and block ciphers in turn, discussing their respectiveuses, design requirements, and crypt-analysis. Here statisticalmethods are of prime importance, as well as algebraic methodsfor generating and combining bit strings and blocks. The section on public key systems includes a discussion of severalmathematical techniques that provide one way functions. Theseare functions that are easy to perform but difficult to invert,often based on some difficult mathematical problem, and areat the heart of public key systems. Two public key systems (RSAand El Gamal) are described, and the status of algorithms forsolving the difficult problems upon which they are based factoringand discrete logarithms is reviewed. Finally we discuss applications of digital-signature and user-verificationtechniques. These are becoming of increasing importance in today'sautomated business world.