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Topological models of magnetic field induced current density field in small molecules

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Abstract

Three-dimensional models of the quantum mechanical current density induced in the electrons of LiH, BeH2, and CO2 molecules by a magnetic field applied perpendicularly to the bond axis have been constructed at the Hartree-Fock level of accuracy. The topological features of the current density vector field are described via a stagnation graph that contains the isolated points and the lines at which the current vanishes, and by planar and spatial streamline plots.

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Notes

  1. Bohm and Peat [18] emphasize the importance of the intrinsic wave-particle dichotomy characterizing the Hamilton-Jacobi theory as a classical root of quantum mechanics. According to these authors, Hamilton had already developed the optico-mechanical similarity to such an extent that he might have put forward a wave mechanics analogous to wave optics. Therefore they speculate that, allowing for the Hamilton-Jacobi formulation in the regime of short wavelength, a wave mechanics might be derived from the classical mechanics of the nineteeth century, just as a wave optics is derived from geometric optics.

  2. The topological index \(\iota\) counts the number of times that the current density vector J B rotates completely while one walks counterclockwise around a circle of radius ε, so small that J B has no zeroes inside except the SP at its center. The topological index \(\iota\) of a saddle (vortex) line is −1 (+1). Both SPs have (r, s) = (2, 0).

  3. The LINUX and WINDOWS versions of the graphic code used to obtain three-dimensional representations of the stagnation graph and current density vector field of a series of molecules can be downloaded at https://theochem.chimfar.unimo.it/VEDO3/.

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Acknowledgments

Financial support to the present research from the Italian MURST (Ministero dell’Università e della Ricerca Scientifica e Tecnologica), via FAR and PRIN funds, is gratefully acknowledged.

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Authors and Affiliations

  1. Dipartimento di Chimica dell’Università degli Studi di Modena, Via Campi 183, 41100, Modena, Italy

    Stefano Pelloni & Paolo Lazzeretti

  2. Dipartimento di Chimica dell’Università degli Studi di Salerno, Via Ponte don Melillo, 84084, Fisciano (SA), Italy

    Riccardo Zanasi

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  1. Stefano Pelloni
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  2. Paolo Lazzeretti
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Correspondence to Paolo Lazzeretti.

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Dedicated to the memory of Professor Oriano Salvetti and published as part of the Salvetti Memorial Issue.

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Pelloni, S., Lazzeretti, P. & Zanasi, R. Topological models of magnetic field induced current density field in small molecules. Theor Chem Acc 123, 353–364 (2009). https://doi.org/10.1007/s00214-009-0530-3

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