Solving wave equations on fullerene surfaces

Activity: Talk or presentation typesLecture and oral contribution

Documents

James Emil Avery - Other

  • Xray and Neutron Science
Can we solve the electronic wave equations when there is no coordinate system? The question arises from the wish to treat certain polyhedral carbon molecules, fullerenes and fulleroids[1,2], as two-dimensional closed surfaces. This would allow us to solve for their electronic structure on their intrinsic surface manifolds, which can be derived directly from the bond structure. The wave equation restricted to the (non-Euclidean) surface could then be solved without reference to any three-dimensional geometry of the molecule, and hence without the need for quantum chemical geometry optimization.

The resulting 2D system can potentially be solved several orders of magnitude faster than the full wave equation. But because it is a non-trivial task to find global coordinate systems for such curved surfaces, we must devise methods that can do without.

In this talk, I describe the mathematical challenges this poses, and my work in progress on solutions to overcome them.

[1] P. SCHWERDTFEGER, WIRZ, LUKAS AND J.E. AVERY, The Topology of Fullerenes, Wiley Interdisciplinary Reviews: Computational Molecular Science, 5, 1, 96-145, Wiley 2015. DOI: 10.1002/wcms.1207

[2] P. SCHWERDTFEGER, WIRZ, LUKAS AND J.E. AVERY, Program Fullerene: A software package for constructing and analyzing structures of regular fullerenes, J. Comp. Chem, 34, 17, 1508-1526, Wiley, 2013. DOI: 10.1002/jcc.23278
7 Jul 2017

Event (Conference)

Title17th Intl. Conf. on Computational and Mathematical Methods in Science and Engineering
Abbreviated titleCMMSE
Date03/07/201708/07/2017
Website
LocationCosta Ballena
CityRota, Cadiz
CountrySpain
ContextInternational event

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