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]] | ||
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
[math]\displaystyle{ \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]\displaystyle{ \phi_{n'k} }[/math] and [math]\displaystyle{ \phi_{nk} }[/math], 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.