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Chapter 1

Algorithms for Predicting the Physical Properties of Nanocrystals and Large Clusters

The electronic structure problem for nanoscale systems is a computationally challenging problem. The large number of degrees of freedom, both electronic and nuclear, and requiring a highly precise solution, make the problem impossible to solve without some effective approximations. Here I illustrate some advances in algorithm developments by solving the electronic structure problem within density functional theory in real space using pseudopotentials and density functional theory. The algorithms presented are based on a Chebyshev-filtered subspace iteration, which results in a significant speedup over methods based on standard sparse iterative diagonalization. I illustrate this method for a variety of nanostructures by calculating the electronic and vibrational states for silicon nanocrystals, the electronic properties of doped semiconductor nanocrystals, and the magnetic properties of metallic iron clusters.

Print publication date: 21 Jun 2011
Copyright year: 2011
Print ISBN: 978-1-84973-133-1
PDF eISBN: 978-1-84973-268-0