# Projected density of states calculation {#sec:gr_tuto_pdosL}

More information can be extracted by projecting the wavefunctions onto
atomic orbitals and then computing the density of states using only
certain components. Such a function is called a projected density of
states (PDOS). It is possible to compute the fraction of the density of
states originating from a specific atom, atoms certain species, orbitals
with a specific angular momentum for example. In the case of graphene, I
expect the PDOS to be equivalent for both atoms by symmetry. I thus look
at its angular momentum components. Copy the following input file and
save it to a text file named `c2_pdos.txt`.

``` shell
info.calculationType = 'dos'
info.savepath = 'results/c2_pdos'
atom.element = [1 1]
la = 4.648725932
atom.xyz = [1 1/sqrt(3) 0;1 -1/sqrt(3) 0]/2*la
domain.latvec = [1/2 sqrt(3)/2 0; 1/2 -sqrt(3)/2 0; 0 0 4]*la
domain.lowres = 0.3
dos.range = [-0.70,0.20]
dos.projL = [0,1]
dos.projM = [-1,0,1]
element.species = 'C'
element.path = './C_TM_LDA.mat'
kpoint.gridn = [45,45,1]
kpoint.shift = [0,0,0]
LCAO.status = 1
rho.in = 'results/c2_scf'
```

Then pass it to RESCU and execute the program as follows

``` shell
rescu -i c2_pdos.txt;
```

New keywords are highlighted in blue. I will briefly explain each of
them.

-   `info.savepath` was changed not to overwrite the dos results;
-   `dos.projL` tells RESCU to decompose the DOS in its $L=0$ and $L=1$
    components (otherwise known as $s$ and $p$);
-   `dos.projM` tells RESCU to decompose the DOS in its $M=-1$, $M=0$
    and $M=1$ components. RESCU will compute the PDOS for every
    combinations of `dos.projL` and `dos.projM`.

The $L$ and $M$ values refer to the real spherical harmonics entering
the atomic orbital definitions. Ill-defined $L$ and $M$ combinations are
ignored. In the current example, $(L,M)=(0,0)$ give the $s$-PDOS,
$(L,M)=(0,-1)$ give the $p_y$-PDOS, $(L,M)=(0,1)$ give the $p_z$-PDOS,
$(L,M)=(0,0)$ give the $p_x$-PDOS. The position of the graphene lattice
with respect to the $x$-axis and $y$-axis is arbitrary as the problem is
periodic along these dimensions. I thus sum up the $p_x$ and $p_y$ PDOS
in `fig:c2_pdos`{.interpreted-text role="numref"}. The $p_{z}$ states
makes up for most of the DOS around the Fermi energy.

<figure>
<img src="figs/c2_pdos.png" id="fig:c2_pdos" alt="figs/c2_pdos.png" />
<figcaption>Projected density of states of graphene.</figcaption>
</figure>
