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Isogeometric analysis in electronic structure calculations

Properties and behavior of various, even hypothetical, materials can be predicted via ab-initio electronic structure calculations that can provide all the necessary information : the total energy of the system and its derivatives with respect to appropriate parameters. In case of non-periodic structures, the existing well-established methods for electronic structure calculations either use special bases, predetermining and limiting the shapes of wave functions, or require artificial computationally expensive arrangements, like large supercells. We developed a new method for non-periodic electronic structures based on the density functional theory, environment-reflecting pseudopotentials and the isogeometric analysis with Bezier extraction, ensuring continuity for all quantities up to the second derivative. The approach is especially suitable for calculating the total energy derivatives like Hellman-Feynman forces and for molecular-dynamics simulations. Its main assets are the universal basis with the excellent convergence control and the capability to calculate precisely the non-periodic structures even lacking in charge neutrality.

Charge density of the Fullerene molecule C60: equidensity surfaces with time-varying levels
Isogeometric analysis in electronic structure calculations, R. Cimrman, M. Novák, R. Kolman, M. Tůma, J. Vackář, Mathematics and Computers in Simulation (2016, in press)