NiO has inversion symmetry.
Thus the wavefunction can be written purely as real function (no
imaginary terms) and this is what wien2k utilizes (for performance reasons).
Obviously, from a pure real wave function you get a pure real density
matrix.
Apparently, VASP does not use this, has an
Dear Peter, developers and users:
Are there any additional phase factors associated with the complex
spherical harmonics (besides the commonly used Condon-Shortley Phase) when
wien2k calculates the local one-body density matrix in SRC_lapwdm, which is
needed, for instance, for LDA+U?
I
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