Kernel
code overview
This code constructs the direct and exchange Kernel matrix on the coarse grid. This is done essentially by computing Eqs 34, 35 and 4246 of Rohlfing and Louie, PRB 62, 4927 (2000).
Summary of input and output files
Required input files

kernel.inp
: Input parameters. 
WFN_co
: Wavefunctions on coarse grid. Recommended: use an unshifted grid of the same size as the qgrid inepsmat
. Shift will increase number of qvectors needed inepsmat
. 
epsmat[.h5]
: Inverse dielectric matrix (q\ne 0), created usingepsilon
. Must contain the all q=kk' generated fromWFN_co
, including with symmetry ifuse_symmetries_coarse_grid
is set. The file has a.h5
extension if the code was built with HDF5 support. 
eps0mat[.h5]
: Inverse dielectric matrix (q\rightarrow 0), created usingepsilon
The file has a.h5
extension if the code was built with HDF5 support. Note Kernel does not require quasiparticle eigenvalues. It may be run in parallel withsigma
Additional input
WFNq_co
: Coarsegrid wavefunctions for finiteQ calculations. Currently not supported
Output files

bsedmat
: Direct kernel matrix elements on unshifted coarse grid. 
bsexmat
: Exchange kernel matrix elements on unshifted coarse grid. 
bsemat.h5
: Includes data from both of above if compiled with HDF5 support. For specification, seebsemat.h5.spec
.
Details: wings of epsilon
For semiconductors, the wings of \chi have terms of the following form:
The matrix element on the right is \langle u_{ck+q}  u_{vk} \rangle where u is the periodic part of the Bloch function. From k.p perturbation theory, this matrix element is proportional to q. The matrix element on the left with a nonzero G is typically roughly a constant as a function of q for small q (q being a small addition to G).
Thus for a general Gvector, \chi_\mathrm{wing}(G,q) \propto q. This directly leads to the wings of the screened untruncated Coulomb interaction being proportional to 1/q. Note that this function changes sign as q \rightarrow q. Thus, when treating the q=0 point, we set the value of the wing to zero (the average of its value in the miniBrillouin zone (mBZ).
For Gvectors on highsymmetry lines, some of the matrix elements on the left of the equation above will be zero for q=0, and therefore proportional to q. For such cases, \chi_\mathrm{wing}(G,q) \propto q^2, and the wings of the screened Coulomb interaction are constant as a function of q. However, setting the q\rightarrow 0 wings to zero still gives us, at worst, linear convergence to the final answer with increased kpoint sampling, because the q\rightarrow 0 point represents an increasingly smaller area in the BZ. Thus, we still zero out the q\rightarrow 0 wings, as discussed in A Baldereschi and E Tosatti, Phys. Rev. B 17, 4710 (1978).
In the future, it may be worthwhile to have the user calculate \chi / \epsilon at two qpoints (a third qpoint at q=0 is known) in order to compute the linear and quadratic coefficients of each \chi_\mathrm{wing}(G,q) so that all the correct analytic limits can be taken. This requires a lot of messy code and more work for the user for only marginally better convergence with respect to kpoints (the wings tend to make a small difference, and this procedure would matter for only a small set of the Gvectors).
It is important, as always, for the user to converge their calculation with respect to both the coarse kpoint grid used in sigma and kernel as well as with the fine kpoint grid in absorption.
Tricks and hints

To optimize distribution of work among MPI processors, choose the number of processors to divide:
 n_k^2, if n_\mathrm{pes} \le n_k^2; or
 n_k^2 n_c^2, if n_\mathrm{pes} \le n_k^2 n_c^2; or
 n_k^2 n_c^2 n_v^2, if n_\mathrm{pes} \le n_k^2 n_c^2 n_v^2,
where n_\mathrm{pes} is the number of MPI ranks, n_k is the number of symmetryunfolded kpoints, and n_v (n_c) is the number of valence (conduction) bands included in the
kernel
calculation. 
Converters from old versions of file formats to current version are available in version 2.4.