Phonons from density-functional-perturbation theory: Difference between revisions

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== References ==
== References ==
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[[Category:Phonons]]

Revision as of 13:13, 20 July 2022

In density functional theory we solve the Hamiltonian

Taking derivatives with respect to a perturbation we obtain the Sternheimer equation

Once the derivative of the orbitals is computed from the Sternheimer equation we can write

The force constants are then computed using

where yields the forces for a given set of orbitals.

At the end of the calculation if LEPSILON=.TRUE., the Born effective charges are computed using Eq. (42) of Ref. [1].

where is the atom index, the direction of the displacement of atom and the polarization direction. The results should be equivalent to the ones obtained using LCALCEPS and LEPSILON.

When IBRION=7 or 8 VASP solves the Sternheimer equation above with an ionic displacement perturbation. If IBRION=7 no symmetry is used and the displacement of all the ions is computed. When IBRION=8 only the irreducible displacements are computed with the physical quantities being reconstructed by symmetry.

References