Electron impact ionization of He above the threshold

Near-threshold ionization of He has been studied by using a uniform semiclassical wavefunction for the two outgoing electrons in the final channel. The quantum mechanical transition amplitude for the direct and exchange scattering derived earlier by using the Kohn variational principle has been used to calculate the triple differential cross sections. Contributions from singlets and triplets are critically examined near the threshold for coplanar asymmetric geometry with equal energy sharing by the two outgoing electrons. It is found that in general the tripler contribution is much smaller compared to its singlet counterpart. However, at unequal scattering angles such as theta (1) = 60 degrees, theta (2) = 120 degrees the smaller peaks in the triplet contribution enhance both primary and secondary TDCS peaks. Significant improvements of the primary peak in the TDCS are obtained for the singlet results both in symmetric and asymmetric geometry indicating the need to treat the classical action variables without any approximation. Convergence of these cross sections are also achieved against the higher partial waves. Present results are compared with absolute and relative measurements of Rosel et al (1992 Phys. Rev. A 46 2539) and Selles et al (1987 J. Phys. B. At. Mel. Phys. 20 5195) respectively.

Optimal basis set for electronic structure calculations in periodic systems

An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a single (i.e., common to all points in the Brillouin zone) basis set for the expansion of the electronic orbitals. Considerations from k.p-approximation theory help to understand the efficiency of the method. The accuracy and the convergence properties of the method as a function of the optimal basis set size are analyzed for a test calculation on a 16-atom Na supercell.

Correlation Effects in the Compton Profile of Silicon

Ab initio nonlocal pseudopotential variational quantum Monte Carlo techniques are used to compute the correlation effects on the valence momentum density and Compton profile of silicon. Our results for this case are in excellent agreement with the Lam-Platzman correction computed within the local density approximation. Within the approximations used, we rule out valence electron correlations as the dominant source of discrepancies between calculated and measured Compton profiles of silicon.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

The solution of the time-dependent Schrodinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600397]

Quantum chemistry and in situ FTir spectroscopy studies on potential-dependent properties of CO adsorbed on Pt electrodes

The electronic and vibrational properties of CO adsorbed on Pt electrodes at different potentials have been studied, by using methods of self-consistent-charge discrete variational Xa (SCC-DV-Xa) cluster calculations and in situ FTir spectroscopy. Two new models have been developed and verified to be successful: (1) using a "metallic state cluster" to imitate a metal (electrode) surface; and (2) charging the cluster and shifting its Fermi level (e{lunate}) to simulate, according to the relation of -d e{lunate}e dE, quantitatively the variation of the electrode potential (E). It is shown that the binding of PtCO is dominated by the electric charge transfer of dp ? 2p, while that of s ? Pt is less important in this binding. The electron occupancy of the 2p orbital of CO weakens the CO bond and decreases the v. Variation of E mainly influences the charge transfer process of dp ? 2p, but hardly influences that of s ? Pt. A linear potential-dependence of v has been shown and the calculated dv/dE = 35.0 cm V. All results of calculations coincide with the ir experimental data. © 1993.

Quantum chemistry studies on electronic properties of CN adsorbed on silver electrodes

The electronic properties of CN adsorbed on Ag electrodes at different potentials have been studied by using the method of self-consistent-charge discrete variational Xa (SCC-DV-Xa) cluster calculations. It is shown that the binding of NCAg is dominated by both electrostatic and polarization effects derived from the charge of CN, and that the transfer of s charge from CN to silver is the largest donation contribution. The electrode potential influences this charge transfer process and the interaction between CN adsorbate and silver electrode. The results of quantum chemistry calculations fit well with the experimental data of in situ spectroscopic studies on the CN/Ag electrode systems. © 1991.

Positron scattering and annihilation in hydrogenlike ions

Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates Zeff, and annihilation ? spectra for positron collisions with the hydrogenlike ions He+, Li2+, B4+, and F8+. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using B-spline basis sets. To elucidate the role of the positron-ion repulsion, the annihilation rate is also estimated analytically in the Coulomb-Born approximation. It is found that the energy dependence and magnitude of Zeff are governed by the Gamow factor that characterizes the suppression of the positron wave function near the ion. For all of the H-like ions, the correlation enhancement of the annihilation rate is found to be predominantly due to corrections to the annihilation vertex, while the corrections to the positron wave function play only a minor role. Results of the calculations for s-, p-, and d-wave incident positrons of energies up to the positronium-formation threshold are presented. Where comparison is possible, our values are in excellent agreement with the results obtained using other, e.g., variational, methods. The annihilation-vertex enhancement factors obtained in the present calculations are found to scale approximately as 1+(1.6+0.46l)/Zi, where Zi is the net charge of the ion and l is the positron orbital angular momentum. Our results for positron annihilation in H-like ions provide insights into the problem of positron annihilation with core electrons in atoms and condensed matter systems, which have similar binding energies.

Mathematics background of engineering students in Northern Ireland and Finland

The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The number of compulsory courses in maths is proportionally large; this means that all upper secondary pupils in Finland (about 55% of the population) follow a curriculum which has a formal maths content of 8%, at the very minimum. In contrast, recent data have indicated that only about 13% of Northern Ireland school leavers studied mathematics in upper secondary school. The compulsory courses of the advanced maths syllabus in Finland are largely composed of pure maths with a small amount of statistics but no mechanics. They lack some topics (for example, in advanced calculus and numerical methods for integration) which are core in Northern Ireland. This is not surprising given the much broader curriculum within upper secondary education in Finland. In both countries, there is a wide variation in the mathematical skills of school leavers. However, given the prevalence of maths within upper secondary education in Finland, it is to be expected that young adults in that country demonstrate high numeracy proficiency.

Quantum annealing of an ising spin-glass by Green's function Monte Carlo

We present an implementation of quantum annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

Dynamic identification of building structures: new strategies:Meccanica dei materiali e delle strutture

In this paper the evolution of a time domain dynamic identification technique based on a statistical moment approach is presented. This technique can be used in the case of structures under base random excitations in the linear state and in the non linear one. By applying Itoˆ stochastic calculus, special algebraic equations can be obtained depending on the statistical moments of the response of the system to be identified. Such equations can be used for the dynamic identification of the mechanical parameters and of the input. The above equations, differently from many techniques in the literature, show the possibility of obtaining the identification of the dissipation characteristics independently from the input. Through the paper the first formulation of this technique, applicable to non linear systems, based on the use of a restricted class of the potential models, is presented. Further a second formulation of the technique in object, applicable to each kind of linear systems and based on the use of a class of linear models, characterized by a mass proportional damping matrix, is described.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Positron scattering and annihilation on noble-gas atoms

Positron scattering and annihilation on noble-gas atoms is studied ab initio using many-body theory methods for positron energies below the positronium formation threshold. We show that in this energy range, the many-body theory yields accurate numerical results and provides a near-complete understanding of the positron–noble-gas atom system. It accounts for positron-atom and electron-positron correlations, including the polarization of the atom by the positron and the nonperturbative effect of virtual positronium formation. These correlations have a large influence on the scattering dynamics and result in a strong enhancement of the annihilation rates compared to the independent-particle mean-field description. Computed elastic scattering cross sections are found to be in good agreement with recent experimental results and Kohn variational and convergent close-coupling calculations. The calculated values of the annihilation rate parameter Zeff (effective number of electrons participating in annihilation) rise steeply along the sequence of noble-gas atoms due to the increasing strength of the correlation effects, and agree well with experimental data.

Kinetics of levoglucosan and formaldehyde formation during cellulose pyrolysis process

The mechanisms and kinetics studies of the formation of levoglucosan and formaldehyde from anhydroglucose radical have been carried out theoretically in this paper. The geometries and frequencies of all the stationary points are calculated at the B3LYP/6-31+G(D,P) level based on quantum mechanics, Six elementary reactions are found, and three global reactions are involved. The variational transition-state rate constants for the elementary reactions are calculated within 450-1500 K. The global rate constants for every pathway are evaluated from the sum of the individual elementary reaction rate constants. The first-order Arrhenius expressions for these six elementary reactions and the three pathways are suggested. By comparing with the experimental data, computational methods without tunneling correction give good description for Path1 (the formation of levoglucosan); while methods with tunneling correction (zero-curvature tunneling and small-curvature tunneling correction) give good results for Path2 (the first possibility for the formation of formaldehyde), all the test methods give similar results for Path3 (the second possibility for the formation of formaldehyde), all the modeling results for Path3 are in good agreement with the experimental data, verifying that it is the most possible way for the formation of formaldehyde during cellulose pyrolysis. © 2012 Elsevier Ltd. All rights reserved.

Kinetics study on thermal dissociation of levoglucosan during cellulose pyrolysis

(Chemical Equation Presented) The mechanisms and kinetics studies of the levoglucosan (LG) primary decomposition during cellulose pyrolysis have been carried out theoretically in this paper. Three decomposition mechanisms (C-O bond scission, C-C bond scission, and LG dehydration) including nine pathways and 16 elementary reactions were studied at the B3LYP/6-31 + G(D,P) level based on quantum mechanics. The variational transi-tion- state rate constants for every elementary reaction and every pathway were calculated within 298-1550 K. The first-order Arrhenius expressions for these 16 elementary reactions and nine pathways were suggested. It was concluded that computational method using transition state theory (TST) without tunneling correction gives good description for LG decomposition by comparing with the experimental result. With the temperature range of 667-1327 K, one dehydration pathway, with one water molecule composed of a hydrogen atom from C3 and a hydroxyl group from C2, is a preferred LG decomposition pathway by fitting well with the experimental results. The calculated Arrhenius plot of C-O bond scission mechanism is better agreed with the experimental Arrhenius plot than that of C-C bond scission. This C-O bond scission mechanism starts with breaking of C1-O5 and C6-O1 bonds with formation of CO molecule (C1-O1) simultaneously. C-C bond scission mechanism is the highest energetic barrier pathway for LG decomposition. © 2013 Elsevier Ltd. All rights reserved.