On homogenization of time-dependent random flows

We study a diffusion with a random, time dependent drift. We prove the invariance principle when the spectral measure of the drift satisfies a certain integrability condition. This result generalizes the results of [13, 7]. Received: 25 February 2000 / Revised version: 11 December 2000 /?Published online: 14 June 2001     

Strong Connections and Chern–Connes Pairing¶in the Hopf–Galois Theory

We reformulate the concept of connection on a Hopf–Galois extension B⊆P in order to apply it in computing the Chern–Connes pairing between the cyclic cohomology HC ^{2 n} (B) and K ₀ (B). This reformulation allows us to show that a Hopf–Galois extension admitting a strong connection is projective and left faithfully flat. It also enables us to conclude that a strong connection is a Cuntz–Quillen-type bimodule connection. To exemplify the theory, we construct a strong connection (super Dirac monopole) to find out the Chern–Connes pairing for the super line bundles associated to a super Hopf fibration. Received: 8 March 2000 / Accepted: 5 January 2001     

Analytical gradients for Singer's multicenter n‐electron explicitly correlated Gaussians

Analytical gradients for Singer's basis of n‐electron multicenter explicitly correlated Gaussian functions are derived and implemented to variationally optimize the energy and wave function of molecular systems within the Born–Oppenheimer approximation. Wave functions are optimized with respect to (½n(n+1)+3n) nonlinear variational parameters and one linear coefficient per term in the basis set. Preliminary results for the ground states of H₃⁺ and H₃ suggest that the method can be more flexible and can achieve lower energies than previously reported calculations. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 151–159, 2001     

Suppression of mesoscopic order by complementary interactions in supramolecular polymers

We show here that complementary interactions can suppress mesoscopic order and thus lead to a counterintuitive change in material properties. We present results for telechelic supramolecular polymers based on poly(propylene oxide) (PPO), thymine (Thy), and diaminotriazine (DAT). The self-complementary systems based on Thy exhibit lamellar order and 2D crystallization of Thy in the bulk. We show that the microphase segregation is inhibited by addition of DAT: the strong complementary Thy-DAT interaction inhibits crystallization of thymine in microdomains and lamellar structuration. As a result, the supramolecular polymer with only weakly self-complementary stickers is a solid, whereas the supramolecular polymer with strongly complementary stickers is a liquid.     

Calibration-quality adiabatic potential energy surfaces for H3(+) and its isotopologues

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion H(3)(+). The underlying Born-Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born-Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41,655 ab initio points is presented which gives a standard deviation better than 0.1 cm(-1) when restricted to the points up to 6000 cm(-1) above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for H(3)(+), H(2)D(+), and HD(2)(+) are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the H(3)(+) isotopologues considered to better than 0.2 cm(-1). This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the H(3)(+) isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of H(3)(+) resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16,000 cm(-1), and (c) results suggest that we can predict accurately the lines of H(3)(+) towards dissociation and thus facilitate their experimental observation.     

Explicitly correlated Gaussian calculations of the (2)D Rydberg states of the boron atom

Accurate non-relativistic variational calculations are performed for the seven lowest members of the (2)D Rydberg series (1s(2)2s2p(2), and 1s(2)2s(2)nd, n = 3, [ellipsis (horizontal)], 8) of the boron atom. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations allowing for determining the isotopic shifts of the energy levels. The Gaussian basis is optimized independently for each state with the aid of the analytic energy gradient with respect to the Gaussian parameters. The calculations represent the highest accuracy level currently achievable for the considered states. The computed energies are compared with the available experimental data.     

Rifamycin antibiotics—new compounds and synthetic methods. Part 3: Study of the reaction of 3-formylrifamycin SV with primary amines and ketones

In the third stage of our study concerning the search for new antibacterial rifamycin antibiotics, the reactions of 3-formylrifamycin SV (1) with a range of primary alkylamines and ketones of general structure R₁–CH₂–CO–R₂ (R₁H or alkyl and R₂alkyl or aryl) has been investigated. A new synthetic method for the preparation of a new group of rifamycin derivatives with an α,β-unsaturated imine substituent at C-3 has been developed.These compounds showed a tendency to reversibly isomerise in organic solvents and, in the presence of water, to rapidly hydrolyse. The structures of four isolated microcrystalline compounds 2, 3, 4, 5 and a reaction's mechanism have been proposed on the basis of mass spectrometry results as well as (1D) and (2D) ¹H and ¹³C NMR analysis. The new synthetic route reported herein is a promising pathway to new reactive rifamycins displaying broader capabilities than the plain 3-formylrifamycin SV.     

Precision measurements and computations of transition energies in rotationally cold triatomic hydrogen ions up to the midvisible spectral range

First-principles computations and experimental measurements of transition energies are carried out for vibrational overtone lines of the triatomic hydrogen ion H(3)(+) corresponding to floppy vibrations high above the barrier to linearity. Action spectroscopy is improved to detect extremely weak visible-light spectral lines on cold trapped H(3)(+) ions. A highly accurate potential surface is obtained from variational calculations using explicitly correlated Gaussian wave function expansions. After nonadiabatic corrections, the floppy H(3)(+) vibrational spectrum is reproduced at the 0.1 cm(-1) level up to 16600 cm(-1).     

The Carter constant for inclined orbits about a massive Kerr black hole: near-circular,near-polar orbits

In an extreme mass-ratio binary black hole system, a non-equatorial orbit will list (i.e. increase its angle of inclination, i) as it evolves in Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits, for which the instantaneous Carter constant (Q) is at its maximum value (Q _X ) for given values of latus rectum (l̃) and eccentricity (e), has been introduced as a laboratory in which the consistency of dQ/dt with corresponding evolution equations for d l̃/dt and de/dt might be tested independently of a specific radiation back-reaction model. To demonstrate the use of the abutment as such a laboratory, a derivation of dQ/dt, based only on published formulae for d l̃/dt and de/dt, was performed for elliptical orbits on the abutment. The resulting expression for dQ/dt matched the published result to the second order in e. We believe the abutment is a potentially useful tool for improving the accuracy of evolution equations to higher orders of e and l̃⁻.     

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.