# 2.4. Projected density of states calculation

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.

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

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. 2.4.2. The $$p_{z}$$ states makes up for most of the DOS around the Fermi energy.