A note on calculating electronic DOS

The calculation of the total/local/projected DOS is performed using the method of tetrahedra. In this method the whole Brillouin zone (BZ) is split into tetrahedra, the energies $\varepsilon_{n\mathbf{k}}$ at the vertices of which are to be calculated by the DFT code. These energies are collected in a file band.out (Sections 4 - 6) and then (together with the information contained in the file brill.dat written by tetr) are used by lev00 to calculate the DOS.

Calculation of the volume integrals in the reciprocal space in Eqs. (3.4), (3.5) is done analytically in the method of tetrahedra. It is also possible to do a smearing (convolution) of your original (raw) DOS curves for every band, $N_{n}(\epsilon)$, by calculating instead the integral

$$\bar{N}_{n}(\epsilon)=\int_{E_{bot}-\gamma\sigma}^{E_{top}+\... ...a\sigma}g(\epsilon-\varepsilon)N_{n}(\varepsilon)d\varepsilon,$$ (3.9)

Here $g(\epsilon-\varepsilon)$ is a Gaussian function with some dispersion $\sigma$; $E_{bot}$ and $E_{top}$ define the ``raw'' boundaries for each physical band and the factor $\gamma$ allows you to broaden them. The energy integral in Eq. (3.9) can be calculated in two ways leading to slow and fast methods:

• slow - since in the method of tetrahedra the raw DOS is always a set of continuous functions of energy in finite intervals (within each tetrahedron), the integration can also be worked out analytically and the result be expressed via exponentials and error functions; this method is slow, but yet exact on many occasions.
• fast - alternatively, the integral in Eq. (3.9) can aslo be calculated numerically.