Virtual Winter School on Computational Chemistry
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Computational Chemistry and Nanomaterials Sciences Group, Oak Ridge National Laboratory, USA
The density-functional tight-binding (DFTB) method  is an approximation to density functional theory (DFT) and allows a speedup of first principles electronic structure calculations by two to three orders of magnitude. In this talk, I will discuss DFTB-based simulations of nanoscale materials self-assembly in nonequilibrium on large length scales . Fullerene, carbon nanotube, and graphene formation were simulated on the nanosecond time scale, considering experimental conditions as closely as possible. An approximate density functional method was employed to compute energies and gradients on-the-fly in direct MD simulations, while the simulated systems were continually pushed away from equilibrium via carbon concentration or temperature gradients. We find that carbon nanostructure formation from feedstock particles involves a phase transition of sp to sp2 carbon phases, which begins with the formation of Y-junctions, followed by a nucleus consisting of pentagons, hexagons, and heptagons. The dominance of hexagons in the synthesized products is explained via annealing processes that occur during the cooling of the grown carbon structure, accelerated by transition metal catalysts when present. The dimensional structures of the final synthesis products (0D spheres – fullerenes, 1D tubes – nanotubes, 2D sheets – graphenes) are induced by the shapes of the substrates/catalysts, and their interaction strength with carbon. Our work prompts a paradigm shift away from traditional anthropomorphic formation mechanisms solely based on thermodynamic stability. Instead, we conclude that nascent carbon nanostructures at high temperatures are dissipative structures described by nonequilibrium dynamics in the manner proposed by Prigogine, Whitesides, and others. As such, the fledgling carbon nanostructures consume energy while increasing the entropy of the environment, and only gradually anneal to achieve their familiar, final structure, maximizing hexagon formation wherever possible [2,3].
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 a) Christensen, A. S.; Kubar, T.; Cui, Q.; Elstner, M. Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications,Chem. Rev. 2016,116, 5301-5337; b)http://www.dftbplus.org
 Irle, S; Page, A. J.; Saha, B.; Wang, Y.; Chandrakumar, K. R. S.; Nishimoto, Y.; Qian, H.-J.; Morokuma, K. Atomistic mechanism of carbon nanostructure self-assembly as predicted by nonequilibrium QM/MD simulations, in: J. Leszczynski, M. K. Shukla, Eds. “Practical Aspects of Computational Chemistry II: An Overview of the Last Two Decades and Current Trends”, Springer-European Academy of Sciences, Chapter 5, pp. 105-172 (April 2, 2012). ISBN 978-94-007-0922-5. DOI: 10.1007/978-94-007-0923-2_5 Preprint:https://www.dropbox.com/s/n2o3sjnb0t1z6mr/5_Online%20PDF.pdf?dl=0
 Page, A. J.; Ding, F.; Irle, S.; Morokuma, K. Insights into carbon nanotube and graphene formation mechanisms from molecular simulations: a review,Rep. Prog. Phys. 2015,78,036501/1-38.
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