WAVEDER: Difference between revisions
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<math> \langle \phi_{n'k} |{\bf S} | \frac{\partial \phi_{nk}}{\partial k_i}\rangle = \frac{1}{\epsilon_{nk} -\epsilon_{n'k}} \langle \phi_{n'k} | \frac{\partial (\mathbf{ H} - \epsilon_{nk} \mathbf{S})}{\partial k_i} | \phi_{nk} \rangle. </math> | <math> \langle \phi_{n'k} |{\bf S} | \frac{\partial \phi_{nk}}{\partial k_i}\rangle = \frac{1}{\epsilon_{nk} -\epsilon_{n'k}} \langle \phi_{n'k} | \frac{\partial (\mathbf{ H} - \epsilon_{nk} \mathbf{S})}{\partial k_i} | \phi_{nk} \rangle. </math> | ||
These matrix elements also correspond to the dipole moment between the states <math>\phi_{n'k}</math> and <math>\phi_{nk}</math>, which are used in both [[Practical guide to GW calculations|GW]] and [[Bethe-Salpeter-equations calculations|Bethe-Salpeter]] calculations. | |||
In the case of degenerate states, the matrix elements are set to zero, within numerical accuracy. | |||
== Related Tags and Sections == | == Related Tags and Sections == | ||
{{TAG|GW calculations}} | {{TAG|GW calculations}} | ||
{{TAG|BSE calculations}} | |||
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[[Category:Files]][[Category:Input files]][[Category:Output files]] | [[Category:Files]][[Category:Input files]][[Category:Output files]] | ||
Latest revision as of 16:40, 6 March 2025
The file WAVEDER contains the derivative of the orbitals with respect to k, more precisely the matrix
These matrix elements also correspond to the dipole moment between the states and , which are used in both GW and Bethe-Salpeter calculations.
In the case of degenerate states, the matrix elements are set to zero, within numerical accuracy.