Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H_2, CH) and triatomic (H_3, CH_2) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently

Force attractor in confined comminution of granular materials.

We reveal a novel attractor in the space of contact forces that bounds the behavior of granular materials during confined comminution. The attractor is reached asymptotically as the porosity reduces and the grain size distribution attains an ultimate power law scaling. The ultimate distribution of the contact forces follows a clear log-normal distribution, distinctively different from previous observations in uncrushable systems. Supporting evidence comes both from comprehensive discrete element simulations and a theoretical Apollonian model

DEM of triaxial tests on crushable sand

This paper presents simulations of high-pressure triaxial shear tests on a crushable sand. The discrete element method is used, featuring a large number of particles and avoiding the use of agglomerates. The triaxial model features a flexible membrane, therefore allowing realistic deformation, and a simple breakage mechanism is implemented using the octahedral shear stress induced in the particles. The simulations show that particle crushing is essential to replicate the realistic behaviour of sand (in particular the volumetric contraction) in high-pressure shear tests. The general effects of crushing during shear are explored, including its effects on critical states, and the influence of particle strength and confining pressure on the degree of crushing are discussed

‘Multi-Epitope-Targeted’ Immune-Specific Therapy for a Multiple Sclerosis-Like Disease via Engineered Multi-Epitope Protein Is Superior to Peptides

Antigen-induced peripheral tolerance is potentially one of the most efficient and specific therapeutic approaches for autoimmune diseases. Although highly effective in animal models, antigen-based strategies have not yet been translated into practicable human therapy, and several clinical trials using a single antigen or peptidic-epitope in multiple sclerosis (MS) yielded disappointing results. In these clinical trials, however, the apparent complexity and dynamics of the pathogenic autoimmunity associated with MS, which result from the multiplicity of potential target antigens and “epitope spread”, have not been sufficiently considered. Thus, targeting pathogenic T-cells reactive against a single antigen/epitope is unlikely to be sufficient; to be effective, immunospecific therapy to MS should logically neutralize concomitantly T-cells reactive against as many major target antigens/epitopes as possible. We investigated such “multi-epitope-targeting” approach in murine experimental autoimmune encephalomyelitis (EAE) associated with a single (“classical”) or multiple (“complex”) anti-myelin autoreactivities, using cocktail of different encephalitogenic peptides vis-a-vis artificial multi-epitope-protein (designated Y-MSPc) encompassing rationally selected MS-relevant epitopes of five major myelin antigens, as “multi-epitope-targeting” agents. Y-MSPc was superior to peptide(s) in concomitantly downregulating pathogenic T-cells reactive against multiple myelin antigens/epitopes, via inducing more effective, longer lasting peripheral regulatory mechanisms (cytokine shift, anergy, and Foxp3+ CTLA4+ regulatory T-cells). Y-MSPc was also consistently more effective than the disease-inducing single peptide or peptide cocktail, not only in suppressing the development of “classical” or “complex EAE” or ameliorating ongoing disease, but most importantly, in reversing chronic EAE. Overall, our data emphasize that a “multi-epitope-targeting” strategy is required for effective immune-specific therapy of organ-specific autoimmune diseases associated with complex and dynamic pathogenic autoimmunity, such as MS; our data further demonstrate that the “multi-epitope-targeting” approach to therapy is optimized through specifically designed multi-epitope-proteins, rather than myelin peptide cocktails, as “multi-epitope-targeting” agents. Such artificial multi-epitope proteins can be tailored to other organ-specific autoimmune diseases

Benchmark calculation for tunnelling through a multidimensional asymmetric double well potential

A benchmark calculation is presented for the quantum dynamics of tunnelling through a multidimensional asymmetric double well potential. A model Hamiltonian is used with a 1-dimensional tunnelling mode coupled to an (M − 1)-dimensional harmonic bath, a system-bath problem. The benchmark calculation uses a basis set expansion of the wavefunction, with separate basis functions for the system and bath. Indistinguishability of configurations is exploited to greatly reduce the expense of the calculation, and a fully converged result is achieved. Comparison is offered to existing quantum dynamical methods that have tested this model problem, and further benchmark results not previously studied are presented

Hexamethylcyclopentadiene: time-resolved photoelectron spectroscopy and ab initio multiple spawning simulations

Progress in our understanding of ultrafast light-induced processes in molecules is best achieved through a close combination of experimental and theoretical approaches. Direct comparison is obtained if theory is able to directly reproduce experimental observables. Here, we present a joint approach comparing time-resolved photoelectron spectroscopy (TRPES) with ab initio multiple spawning (AIMS) simulations on the MS-MR-CASPT2 level of theory. We disentangle the relationship between two phenomena that dominate the immediate molecular response upon light absorption: a spectrally dependent delay of the photoelectron signal and an induction time prior to excited state depopulation in dynamics simulations. As a benchmark molecule, we have chosen hexamethylcyclopentadiene, which shows an unprecedentedly large spectral delay of (310 \ub1 20) fs in TRPES experiments. For the dynamics simulations, methyl groups were replaced by "hydrogen atoms" having mass 15 and TRPES spectra were calculated. These showed an induction time of (108 \ub1 10) fs which could directly be assigned to progress along a torsional mode leading to the intersection seam with the molecular ground state. In a stepladder-type approach, the close connection between the two phenomena could be elucidated, allowing for a comparison with other polyenes and supporting the general validity of this finding for their excited state dynamics. Thus, the combination of TRPES and AIMS proves to be a powerful tool for a thorough understanding of ultrafast excited state dynamics in polyenes.Peer reviewed: YesNRC publication: Ye

Review: ‘Gimme five’: future challenges in multiple sclerosis. ECTRIMS Lecture 2009

This article is based on the ECTRIMS lecture given at the 25th ECTRIMS meeting which was held in Düsseldorf, Germany, from 9 to 12 September 2009. Five challenges have been identified: (1) safeguarding the principles of medical ethics; (2) optimizing the risk/benefit ratio; (3) bridging the gap between multiple sclerosis and experimental autoimmune encephalitis; (4) promoting neuroprotection and repair; and (5) tailoring multiple sclerosis therapy to the individual patient. Each of these challenges will be discussed and placed in the context of current research into the pathogenesis and treatment of multiple sclerosis

Basis set generation for quantum dynamics simulations using simple trajectory-based methods

Methods for solving the time-dependent Schrödinger equation generally employ either a global static basis set, which is fixed at the outset, or a dynamic basis set, which evolves according to classical-like or variational equations of motion; the former approach results in the well-known exponential scaling with system size, while the latter can suffer from challenging numerical problems, such as singular matrices, as well as violation of energy conservation. Here, we suggest a middle road: building a basis set using trajectories to place time-independent basis functions in the regions of phase space relevant to wave function propagation. This simple approach, which potentially circumvents many of the problems traditionally associated with global or dynamic basis sets, is successfully demonstrated for two challenging benchmark problems in quantum dynamics, namely, relaxation dynamics following photoexcitation in pyrazine, and the spin Boson model