# PyProcar documentation¶

PyProcar is a robust, open-source Python library used for pre- and post-processing of the electronic structure data coming from DFT calculations. PyProcar provides a set of functions that manage data from the PROCAR format obtained from various DFT codes. Basically, the PROCAR file is a projection of the Kohn-Sham states over atomic orbitals. That projection is performed to every $$k$$-point in the considered mesh, every energy band and every atom. PyProcar is capable of performing a multitude of tasks including plotting plain and spin/atom/orbital projected band structures and Fermi surfaces- both in 2D and 3D, Fermi velocity plots, unfolding bands of a super cell, comparing band structures from multiple DFT calculations, plotting partial density of states and generating a $$k$$-path for a given crystal structure.

Currently supports:

1. VASP

2. Elk

3. Quantum Espresso

4. Abinit

5. Lobster

Instructions on performing DFT calculations to obtain the necessary files to run PyProcar are given in the DFT Preparation section.

The format of the PROCAR is as follows:

1.   PROCAR lm decomposed
2.    of k-points:    4         # of bands: 224         # of ions:  4
3.
4.    k-point    1 :    0.12500000 0.12500000 0.12500000     weight = 0.12500000
5.
6.   band   1 # energy  -52.65660295 # occ.  1.00000000
7.
8.   ion      s     py     pz     px    dxy    dyz    dz2    dxz    dx2    tot
9.     1  0.052  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.052
10.    2  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
11.    3  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
12.    4  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
13.    4  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
14.   tot 0.052  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.052

• Line 1 is a comment

• Line 2 gives the number of K points calculated (kpoint), number of bands (nband) and number of ions (nion)

• Line 4 gives the k-point and the weight

• Line 6 gives the energy for kpoints

• Line 8 Labels of calculated projections, column 11 is the total projection

• Line 9 Calculated projections for atom 1

• Line 10 Calculated projections for atom 2 and so on

• Line 14 after projections over all atoms, the total over every atomic projection is reported

This block is repeated for the other spin channel if the calculation was polarized. For spin polarized or non-collinear spin calculations there are additional blocks for each spin component.

The site projected wave function in the PROCAR is calculated by projecting the Kohn-Sham wave functions onto spherical harmonics that are non-zero within spheres of a Wigner-Seitz radius around each ion by:

$|<Y^{\alpha}_{lm}|\phi_{nk}>|^2$

where, $$Y^{\alpha}_{lm}$$ are the spherical harmonics centered at ion index $$\alpha$$ with angular moment $$l$$ and magnetic quantum number $$m$$, and $$\phi_{nk}$$ are the Kohn-Sham wave functions. In general, for a non-collinear electronic structure calculation the same equation is generalized to:

$\frac{1}{2} \sum_{\mu, \nu=1}^{2} \sigma_{\mu, \nu}^{i}<\psi_{n, k}^{\mu}\left|Y_{l m}^{\alpha}><Y_{l m}^{\alpha}\right| \psi_{n, k}^{\nu}>$

where $$\sigma^i$$ are the Pauli matrices with $$i = x, y , z$$ and the spinor wavefunction $$\phi_{nk}$$ is now defined as

$\begin{split}\phi_{nk} & = \begin{bmatrix} \psi_{nk}^{\uparrow} \\ \psi_{nk}^{\downarrow} \end{bmatrix}\end{split}$