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Real space calculation of response functions using non-diagonal supercells

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We study the direct calculation of response functions using real space methods. By considering supercell matrices with non-zero off-diagonal elements, we show that it is possible to determine the response of a periodic system to a perturbation characterized by a wave vector with fractional coordinates k = ( m1/n1, m2/n2, m3/n3 ), where m1/n1, m2/n2, and m3/n3 are reduced fractions, using a supercell containing l_123 primitive cells, where l_123 is the lowest common multiple of n1, n2, and n3. Utilizing such supercells facilitates the performance of real space first principles vibrational calculations using Brillouin zone grids of unprecedented size. We calculate highly converged values of the zero-point renormalization to the thermal and optical band gaps of diamond arising from electron-phonon coupling. The use of non-diagonal supercell matrices enables real space methods to address problems that were previously only accessible to perturbative methods.

This talk is part of the Electronic Structure Discussion Group series.

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