In this work, we develop a new flexible formalism to calculate anharmonic interatomic interactions from first principles at arbitrary order. Using the recently-developed slave-mode basis, we Taylor-expand the potential with a minimal number of independent coefficients. The anharmonic dynamical tensor, a higher-order generalization of the dynamical matrix in strain+reciprocal space, is calculated via a generalized frozen phonon methodology. We perform high-throughput calculations, emphasizing efficiency with multidimensional finite differences and Hellman-Feynman forces. Applying the methodology to graphene, we show convergence through fifth order terms. Our calculated force constants produce stress-strain curves, bond-length relaxations, and phonon spectra that agree well with those expected within DFT. We show that to fully capture anharmonic effects, long-range interactions must be included.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D8708CRN |
| Date | January 2017 |
| Creators | Kornbluth, Mordechai C. |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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