Spin Dependent d-band Center

A simple Python/Tkinter GUI to compute spin-resolved and effective d-band centers directly from a VASP DOSCAR (ISPIN=2, LORBIT=11).

Features

• Load a DOSCAR (ISPIN=2, LORBIT=11).
• Select atom range (Group of atoms using comma, such as 2-5,7-8,.. etc)
• Compute:
  • Spin-up d-band center ($\varepsilon_{d\uparrow}$)
  • Spin-down d-band center ($\varepsilon_{d\downarrow}$)
  • Effective d-band center ($\varepsilon_{\mathrm{eff}}$)
  • Hammer–Nørskov d-band center, $\varepsilon_{\mathrm{HN}}$
  • Fractional occupations $f_\uparrow$, $f_\downarrow$

Equations

Let energies be aligned such that (E_F = 0), i.e., we use (E - E_F) internally.

• Spin-resolved d-band centers (integrated over the full energy grid):

$$ \varepsilon_{d\sigma} = \frac{\int_{-\infty}^{+\infty} E D_{d\sigma}(E - E_F) dE} {\int_{-\infty}^{+\infty} D_{d\sigma}(E - E_F) dE} $$

• Fractional occupations (integrated up to the Fermi level):

$$ f_\sigma = \frac{1}{N_{\text{atoms}}\times 5} \int_{-\infty}^{E_F} D_{d\sigma}(E) dE $$

• Effective d-band center (Bhattacharjee, S., Waghmare, U. & Lee, SC. An improved d-band model of the catalytic activity of magnetic transition metal surfaces. Sci Rep 6, 35916 (2016). https://doi.org/10.1038/srep35916):

$$ \varepsilon_{\mathrm{eff}} = \frac{f_\uparrow\varepsilon_{d\uparrow} + f_\downarrow \varepsilon_{d\downarrow}} {f_\uparrow + f_\downarrow}-(\varepsilon_{d\downarrow} - \varepsilon_{d\uparrow}) \frac{f_\uparrow - f_\downarrow}{f_\uparrow + f_\downarrow} $$

• Hammer–Nørskov d-band center (spin-summed, full energy range):

$$ \varepsilon_{\mathrm{HN}} = \frac{\int E \big(D_{d\uparrow}(E)+D_{d\downarrow}(E)\big) dE} {\int \big(D_{d\uparrow}(E)+D_{d\downarrow}(E)\big) dE} $$

Optionally, the reduced fractional occupation is

$$ \mu = \frac{f_\uparrow - f_\downarrow}{f_\uparrow + f_\downarrow}. $$

Installation

• Python 3.8+ (standard library only).
• Tkinter must be available (usually bundled with Python). On Debian/Ubuntu:
  • sudo apt-get install python3-tk

For ubuntu

• Just type in your terminal:

  sudo apt update

  pip install --upgrade Spin-dependent-d-band-center

• Then in bash type:

  d-band-satadeep

--> This will launch the application (see the pic below)

Usage: If you don't want to use pip install

python3 d-band.py

• Click “Browse…” and select your DOSCAR (generated with ISPIN=2, LORBIT=11).
• Enter the atom ranges (e.g., 3-5,8-7,22-25 etc).
• Click “Compute”.
• Once executed the window will look like the following:

Notes

• The app shifts energies so that (E_F=0). Integrals for (f_\sigma) run from the grid minimum to 0; centers use the full grid range.
• The code aggregates the five d-orbitals (dxy, dyz, dz2, dxz, dx2) for each spin channel.
• Results shown in eV.

Credits

Created by Satadeep Bhattacharjee, IKST, Bangalore