The results of a simple local-density energy band model (Xα) are used to carry through a calculation of the phonon dispersion relations in fcc Ne and Ar. Adiabatic phonons, calculated from the computed Xα total energy surface, are perturbed by the Fröhlich Hamiltonian with electron-phonon matrix elements calculated from the Xα energy bands. The use of low-order perturbation theory gives results in fair comparison with observed values, but shows the general scheme to be feasible. Except for questions of the exact physical content of the Xα model itself, the calculation is entirely ab initio, and is believed to be the first such achieved in insulators.
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Work supported by Research Corporation and National Science Foundation, and based in part on the Ph.D. thesis of J. P. Worth.
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Worth, J.P., Trickey, S.B. Energy band theory and the lattice dynamics of rare gas crystals. J Low Temp Phys 38, 393–411 (1980). https://doi.org/10.1007/BF00114334
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DOI: https://doi.org/10.1007/BF00114334