@@ -26,13 +26,13 @@ In the case of magnetic systems, the quasiparticle energies for both spins are c

KPT

----

The k-points follow an internal ordering: first the irreducible parent k points, then the remaining equivalent k points. A list of the irreducible k-vectors is written to the output file. In the present example, there are eight irreducible k points and 64 k points in total. All 64 k-point indices can be used in the job definition. We have chosen the ones from the irreducible set. They correspond to the Γ (index 1), X (index 7), and L point (index 3). Clearly, for a different k-point set, e.g., 8x8x8, the k-point indices would change (except for the index 1, which always corresponds to the Γ point). Therefore, there is the possibility of defining k-point labels with

The k-points follow an internal ordering: first the irreducible parent k points, then the remaining equivalent k points. A list of the irreducible k-vectors is written to the output file. In the present example, there are eight irreducible k points and 64 k points in total. All 64 k-point indices can be used in the job definition. We have chosen the ones from the irreducible set. They correspond to the :math:`{\Gamma}` (index 1), X (index 7), and L point (index 3). Clearly, for a different k-point set, e.g., 8x8x8, the k-point indices would change (except for the index 1, which always corresponds to the :math:`{\Gamma}` point). Therefore, there is the possibility of defining k-point labels with

``KPT X=1/2*(0,1,1) L=1/2*(0,0,1)``

or

``KPT X=[1,0,0] L=1/2*[1,1,-1]``

The labels must be single (upper- or lower-case) characters. The two definitions are equivalent. The first gives the k vectors in internal coordinates, i.e., in the basis of the reciprocal basis vector, the second in cartesian coordinates in units of :math:`{2\pi/a}` with the lattice constant a . In the case of the fcc lattice of silicon, the lattice basis vectors are :math:`{a_1=a(011)/2}` , :math:`a_2=a(101)/2` , and :math:`a_3=a(110)/2` . The reciprocal basis vectors are thus :math:`{b_1=2\pi/a(−111)}` et cetera. For the X point, e.g., one then gets :math:`{(a_2+a_3)/2=2\pi/a(100)}` . In order for the cartesian coordinates (square brackets) to be interpreted correctly, Spex must obviously know the lattice constant a. (In Fleur, the lattice constant is taken to be the global scaling factor for the lattice vectors.) The so-defined k points must be elements of the k mesh defined by ``BZ``. We will later discuss how points outside the k mesh can be considered using the special label +. With the k labels, the above job definition can be written as ``JOB GW 1:(1,2,5) X:(1,3,5) L:(1-3,5)`` as in the input file described in :ref:`getting_started` There are two more special k-point labels: ``IBZ`` and ``BZ`` (e.g., ``JOB GW IBZ:(1,2,5)``) stand for all k points in the irreducible and the full k set, respectively. (The label ``BZ`` is included for completeness but is not needed in practice.) The ``IBZ`` label is helpful when a self-consistent GW calculation is to be performed, which requires the self-energy to be calculated for the whole irreducible Brillouin zone.

The labels must be single (upper- or lower-case) characters. The two definitions are equivalent. The first gives the k vectors in internal coordinates, i.e., in the basis of the reciprocal basis vector, the second in cartesian coordinates in units of :math:`{2\pi/a}` with the lattice constant a . In the case of the fcc lattice of silicon, the lattice basis vectors are :math:`{a_1=a(011)/2}` , :math:`a_2=a(101)/2` , and :math:`a_3=a(110)/2` . The reciprocal basis vectors are thus :math:`{b_1=2\pi/a(-111)}` et cetera. For the X point, e.g., one then gets :math:`{(a_2+a_3)/2=2\pi/a(100)}` . In order for the cartesian coordinates (square brackets) to be interpreted correctly, Spex must obviously know the lattice constant a. (In Fleur, the lattice constant is taken to be the global scaling factor for the lattice vectors.) The so-defined k points must be elements of the k mesh defined by ``BZ``. We will later discuss how points outside the k mesh can be considered using the special label +. With the k labels, the above job definition can be written as ``JOB GW 1:(1,2,5) X:(1,3,5) L:(1-3,5)`` as in the input file described in :ref:`getting_started` There are two more special k-point labels: ``IBZ`` and ``BZ`` (e.g., ``JOB GW IBZ:(1,2,5)``) stand for all k points in the irreducible and the full k set, respectively. (The label ``BZ`` is included for completeness but is not needed in practice.) The ``IBZ`` label is helpful when a self-consistent GW calculation is to be performed, which requires the self-energy to be calculated for the whole irreducible Brillouin zone.

The quasiparticle energies are written to standard output in tabular form::