Double ionization of a three-electron atom: Spin correlation effects

We study the effects of spin degrees of freedom and wave function symmetries on double ionization in three-electron systems. Each electron is assigned one spatial degree of freedom. The resulting three-dimensional Schr\"odinger equation is integrated numerically using grid-based Fourier transforms. We reveal three-electron effects on the double ionization yield by comparing signals for different ionization channels. We explain our findings by the existence of fundamental differences between three-electronic and truly two-electronic spin-resolved ionization schemes. We find, for instance, that double ionization from a three-electron system is dominated by electrons that have the opposite spin

Rôle of the Jahn-Teller Coupling in the Luminescence Spectra of Fe²⁺ in Zinc-Blende Compounds

The luminescence spectra of Fe2+ in zinc-blende-type II—VI and III—V compounds do not show an equally spaced set of emission lines as predicted by spin orbit interaction in a plain crystalline field. The unequal separation between these lines is a signature of the Jahn-Teller effect in these systems. Attention is focused here on the general trend of the 5 E-derived energy levels providing the end states for the emission transitions. The intervall between the second and third energy levels (γ4 and γ3) is employed as a sensitive test based on the two following characteristics: First, this is the spacing that varies the most; second, the emissions to these levels are usually quite sharp as they involve energies not overlapping with phonon-assisted transitions. This property is studied in the plane [hω,EJT] (energy of the coupling phonon and the Jahn-Teller energy which is directly related to the coupling strength). The general behaviour is then studied under different theoretical conditions, in particular those that maximize the effect. Application of this theory to each real compound is thus possible by choosing the right combination of the two variables. To this end, the examples of luminescent substitutional Fe2+ ions in ZnS, ZnTe, and CdTe are discussed based on published spectra. The main emphasis is placed on new precise measurements of the ZnSe : Fe2+ emission. With crystals containing different iron concentrations, changing line shapes, including self-inversion of several emission lines, have been obtained in the 2600 to 2800 cm-1 spectral range. The properties of the four host/impurity systems are satisfactorily explained while an overall description emerges for the whole family of these compounds from a compilation of the derived coupling parameters

Restricted space ab initio models for double ionization by strong laser pulses

Double electron ionisation process occurs when an intense laser pulse interacts with atoms or molecules. Exact {\it ab initio} numerical simulation of such a situation is extremely computer resources demanding, thus often one is forced to apply reduced dimensionality models to get insight into the physics of the process. The performance of several algorithms for simulating double electron ionization by strong femtosecond laser pulses are studied. The obtained ionization yields and the momentum distributions of the released electrons are compared, and the effects of the model dimensionality on the ionization dynamics discussed

Understanding the Sources of Error in MBAR through Asymptotic Analysis

Multiple sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple thermodynamic states. Commonly, the data are then recombined to construct estimates of free energies and ensemble averages using the Multistate Bennett Acceptance Ratio (MBAR) formalism. However, the error of the MBAR estimator is not well-understood: previous error analysis of MBAR assumed independent samples and did not permit attributing contributions to the total error to individual thermodynamic states. In this work, we derive a novel central limit theorem for MBAR estimates. This central limit theorem yields an error estimator which can be decomposed into contributions from the individual Markov chains used to sample the states. We demonstrate the error estimator for an umbrella sampling calculation of the alanine dipeptide in two dimensions and an alchemical calculation of the hydration free energy of methane. In both cases, the states' individual contributions to the error provide insight into the sources of error of the simulations. Our numerical results demonstrate that the time required for the Markov chain to decorrelate in individual thermodynamic states contributes considerably to the total MBAR error. Moreover, they indicate that it may be possible to use the contributions to tune the sampling and improve the accuracy of MBAR calculations.Comment: 13 pages, 4 figur

Error bounds for dynamical spectral estimation

Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular simulations, its error properties remain poorly understood. Here we analyze the error of a dynamical spectral estimation method called "the variational approach to conformational dynamics" (VAC). We bound the approximation error and estimation error for VAC estimates. Our analysis establishes VAC's convergence properties and suggests new strategies for tuning VAC to improve accuracy.Comment: 34 pages, 7 figure

Fucose Binding Cancels out Mechanical Differences between Distinct Human Noroviruses

The majority of nonbacterial gastroenteritis in humans and livestock is caused by noroviruses.Like most RNA viruses, frequent mutations result in various norovirus variants. The strain-dependentbinding profiles of noroviruses to fucose are supposed to facilitate norovirus infection. It remains unclear, however, what the molecular mechanism behind strain-dependent functioning is. In this study,by applying atomic force microscopy (AFM) nanoindentation technology, we studied norovirus-likeparticles (noroVLPs) of three distinct human norovirus variants. We found differences in viral mechanical properties even between the norovirus variants from the same genogroup. The noroVLPswere then subjected to fucose treatment. Surprisingly, after fucose treatment, the previously foundconsiderable differences in viral mechanical properties among these variants were diminished. Weattribute a dynamic switch of the norovirus P domain upon fucose binding to the reduced differencesin viral mechanical properties across the tested norovirus variants. These findings shed light on themechanisms used by norovirus capsids to adapt to environmental changes and, possibly, increasecell infection. Hereby, a new step towards connecting viral mechanical properties to viral prevalenceis taken.<br/

Developing a Multi-Dimensional Early Elementary Mathematics Screener and Diagnostic Tool: The Primary Mathematics Assessment

There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention efforts. We propose a mathematics assessment that screens and provides diagnostic information in six domains that are important to building a strong foundation in mathematics. This article describes the conceptual framework and psychometric qualities of a web-based assessment tool, the Primary Math Assessment (PMA). The PMA includes a screener to identify students at risk for poor math outcomes and a diagnostic tool to provide a more in-depth profile of children’s specific strengths and weaknesses in mathematics. The PMA allows teachers and school personnel to make better instructional decisions by providing more targeted analyses