Search results for " mechanics"

High-resolution spectroscopy and analysis of the ν4 band of 80SeF6

2001

Abstract The Fourier-transform spectrum of the ν4 bending region of 80 SeF 6 around 435 cm −1 has been recorded at a temperature of 217 K with a resolution of 2.3×10 −3 cm −1 . This fundamental has been analyzed using the set of programs called highly spherical top data system (HTDS). Altogether 958 transitions were assigned and fitted with an rms of 0.0003 cm −1 . The effective Hamiltonian was developed up to the fourth order. Parameters and simulations are presented. The ν4 band center is located at 435.099 cm −1 .

Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta.

2011

In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demons…

Theoretical investigation of the electronic structure of fullerenes

1994

Summary form only given. Research in the growing family of fullerene compounds are in continuous expansion. Much theoretical and experimental effort has been devoted to the study of the electronic properties these carbon cages present. However, although significant work has been done, the purpose of this paper is to provide a detailed theoretical analysis of the electronic properties of several fullerenes. We have calculated the electronic structure of these carbon cages within the valence effective Hamiltonian (VEH) approach. The calculated one-electron energy levels are correlated with experimental UPS spectra. The good correlation between calculated and experimental values shows VEH appr…

On the fractional integral of Weyl inL p

1994

Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

2016

In this chapter we deal with abelian integrals. They play a key role in the infinitesimal version of the 16th Hilbert problem. Recall that 16th Hilbert problem and its ramifications is one of the principal research subject of Christiane Rousseau and of the first author. We recall briefly the definition and explain the role of abelian integrals in 16th Hilbert problem. We also give a simple well-known proof of a property of abelian integrals. The reason for presenting it here is that it serves as a model for more complicated and more original treatment of abelian integrals in the study of Hamiltonian monodromy of fully integrable systems, which is the main subject of this chapter. We treat i…

Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians

2015

Computing the Trace

2001

So far we have been interested in the general expression for the WKB-propagation function. Now we turn our attention to the trace of that propagator, since we want to exhibit the energy eigenvalues of a given potential. From earlier discussions we know that the energy levels of a given Hamiltonian are provided by the poles of the Green’s function:

ChemInform Abstract: Magnetic Exchange Between Metal Ions with Unquenched Orbital Angular Momenta: Basic Concepts and Relevance to Molecular Magnetism

2010

This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…

A Unified AMBER-Compatible Molecular Mechanics Force Field for Thiolate-Protected Gold Nanoclusters.

2016

We present transferable AMBER-compatible force field parameters for thiolate-protected gold nanoclusters. Five different sized clusters containing both organo-soluble and water-soluble thiolate ligands served as test systems in MD simulations, and parameters were validated against DFT and experimental results. The cluster geometries remain intact during the MD simulations in various solvents, and structural fluctuations and energetics showed agreement with DFT calculations. Experimental diffusion coefficients and crystal structures were also reproduced with sufficient accuracy. The presented parameter set contains the minimum number of cluster-specific parameters enabling the use of these p…

Fractal dynamics in chaotic quantum transport

2013

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis -- a widely used method in time series analysis -- and show its usefulness in the interpretation of the conductance curves. Comparison with a s…