To estimate the conduction band minimum (CBM) and valence band maximum (VBM) of a double perovskite, one commonly used approach is based on the Mulliken electronegativity method. This links the band edge positions to the compound’s average electronegativity.

Step 1: Calculate the Average Electronegativity (χ)

Use the geometric mean of the electronegativities of all constituent atoms (A, B, X, Y in A₂BB′X₆-type structure), weighted by their stoichiometry.

Example formula:

χ_avg = (χ_A^a * χ_B^b * χ_X^x * χ_Y^y) ^ [1 / (a + b + x + y)]

Where χ_A, χ_B, etc. are the electronegativity values of each element (from Mulliken or Pauling scale), and a, b, x, y are their respective atomic ratios.

Step 2: Estimate the Band Edge Positions

Conduction band position (E_CB):

E_CB = χ_avg - E_e - (E_g / 2)

Valence band position (E_VB):

E_VB = E_CB + E_g

Where:

• χ_avg is the average electronegativity of the compound,

• E_e is the energy of free electrons on the vacuum scale (typically ~4.5 eV),

• E_g is the band gap (from experiment or DFT).

Tools Needed:

• Electronegativity values (from tables),

• Experimental or calculated band gap (E_g),

• Optionally, DFT tools (like VASP) for higher accuracy.

Note:

This method gives a good approximation of CBM and VBM, especially for screening semiconductors for solar cells, photocatalysis, etc. For precision applications, use hybrid functionals or GW calculations.