Density functional study of ternary FexCoy Niz (x + y + z = 7) clusters

Abstract

Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s-waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D ? 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2, 1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ?2(? +). We study the characterization of these extensions in the harmonic oscillator through their spectra which - except for the Friedrichs extension - are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous-D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of 'heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s-waves in D > 0 dimensions. " 2006 Wiley-VCH Verlag GmbH & Co. KGaA.",,,,,,"10.1002/prop.200610328",,,"http://hdl.handle.net/20.500.12104/40530","http://www.scopus.com/inward/record.url?eid=2-s2.0-33845650822&partnerID=40&md5=0d758f853d3fa36c49094adeaf0ddc66",,,,,,"12",,"Fortschritte der Physik",,"1083

1108",,"54",,"Scopus

WOS",,,,,,"Centrifugal barrier; Centripetal well; Free particle; Harmonic oscillator; Lie algebra sp(2, ?); s-waves",,,,,,"Dependence of s-waves on continuous dimension: The quantum oscillator and free systems",,"Article" "42304","123456789/35008",,"Guzmán-Ramírez, G., Departamento de Química, Centro Universitario de Ciencias, Exactas e Ingenierías, Universidad de Guadalajara, Guadalajara 44430, Mexico; Salvador, P., Institut de Química Computacional i Departament de Química, Universitat de Girona, 17071 Girona, Spain; Robles, J., Departamento de Farmacia, Universidad de Guanajuato, Guanajuato 36050, Mexico; Vega, A., Departamento de Física Teórica, Atómica y óptica, Universidad de Valladolid, 47011, Valladolid, Spain; Aguilera-Granja, F., Instituto de Física Manuel Sandoval Vallarta, Universidad Autónoma de San Luis Potosí, San Luis Potosi 78000, Mexico",,"Guzman-Ramirez, G.

Salvador, P.

Robles, J.

Vega, A.

Aguilera-Granja, F.",,"2013",,"We report a study of magnetic, electronic and structural properties of free standing FexCoyNiz clusters with x + y + z = 7 using density functional theory. We analyze the dependence of the structural phase diagram, the local magnetic moments and the geometrical properties of these ternary clusters as a function of the concentration in the whole concentration range. We also introduce and test an alternative definition of the chemical order based on bond order descriptors. A reactivity and stability study is performed by computing electronic properties such as the (vertical) ionization potential, electron affinity, electro negativity and band gap. Calculation of condensed Fukui indexes using 3D-space analysis atomic definitions is carried out in order to predict the most favorable adsorption sites toward electron donor species. " Springer-Verlag Berlin Heidelberg 2012.