Units and structure of the DOS, COOP, and COHP curves.

**NOTE: The support for full-spinor wavefunctions (non-collinear spin,
spin-orbit coupling) has necessitated a (backwards compatible)
cosmetic change in the output of the curves.

Non-spin-polarized curves show three columns: the first two are
identical (formally: "spin up = spin down"), and the third contains the total
(doubled, or sum) value.

Collinear spin-polarized curves show three columns: the first two are
for "spin up" and "spin down", and the third contains their sum.

Non-collinear curves (new feature) contain a single column with the
total value, as it is not possible to talk about "spin-channels" in
this case.

## DOS curves

They come out in (eV)^(-1). 

(**NOTE that in previous versions of the program the extra factor of
2 for non-spin cases was NOT really applied, despite statements to the
contrary in a previous version of these notes :-( ).

## COOP curves

They come out in (eV)^(-1).  If the last column is integrated up to
the Fermi level, (including all the interactions for all orbitals,
even those on-site (for this, specify a minimum distance of 0.0 in the
.mpr file and a big enough maximum distance)), the result is N (the
number of electrons in the unit cell). Spin-channel columns will
integrate to N/2.


## COHP curves

They come out in Ry * (eV)^(-1) (the Ry part comes from the
Hamiltonian factor -- THIS SHOULD BE CHANGED).  If the last column is
integrated up to the Fermi level, (including all the interactions for
all orbitals, even those on-site (for this, specify a minimum distance
of 0.0 in the .mpr file and a big enough maximum distance)), the
result is E_bs (the band-structure energy).  Spin-channel columns will
integrate to E_bs/2.

It is important to note that E_bs is *not* the Kohn-Sham energy, but
the sum of KS eigenvalues up to the Fermi level (with the appropriate
k-point weights). E_bs is now computed by Siesta as Tr(DM*H), where DM
is the density matrix (see the Siesta paper) and output as Ebs.

E_bs can also be computed integrating the DOS curves:

E_bs = Integral (DOS(E)*E*dE)

up to the Fermi level.

Mprop now includes a third column in the Filename.intdos file showing
the integrated E_bs(E). By reading the entry for a value of E close to
the Fermi level E_bs can estimated. This is useful to get Ebs for
legacy calculations performed with versions of Siesta that did not
compute E_bs.

In order for mprop to estimate the Fermi level accurately (to match
Siesta's own value), it is advisable to use a small smearing. By using
a relatively high number of sampling points ( -n option), and an
energy upper limit that matches E_fermi, the COOP and COHP curves can
be easily integrated by a simple sum (and a factor of the spacing).

For example:

mprop -s 0.1 -n 1000  -M E_fermi  Filename ( no .mpr extension)

