Dear friend Hridoy Saha

To calculate the band structure of a CuO nanoparticle using CASTEP with LDA+U potential, you can follow these steps:

• Specify the LDA+U potential for the calculation by adding the keyword "LDA+U" to the xc_functional section of the input file. You can also specify the U value for Cu and O separately using the keywords "U_value_Cu" and "U_value_O".
• Set the k-point sampling for the Brillouin zone. For a nanoparticle, a Monkhorst-Pack grid with a spacing of 0.2 Å^-1 is a good starting point.
• Set the energy cutoff for the plane-wave basis set. A value of 500 eV is a good starting point.

Note that the exact parameters may vary depending on the size and shape of the CuO nanoparticle, so it is important to perform convergence tests and adjust the parameters as needed. Also, keep in mind that LDA+U potential may have some limitations and may not accurately describe the band structure of some materials.

Unfortunately, it's not possible to find the band structure of CuO nanoparticles using CASTEP. CASTEP is a software package designed for performing electronic structure calculations on periodic systems. As nanoparticles are not periodic, CASTEP is not suitable for this type of calculation. You may want to look into other software packages, such as GPAW or VASP, which are designed for performing calculations on non-periodic systems.

Isolated nanoparticles don't have "band structures" they just have energy levels, because they aren't a periodic system. If you really want to compute the energy levels in CASTEP you need to make a large simulation cell and place your nanoparticle inside, making sure that the cell is large enough that the nanoparticle doesn't interact with its periodic neighbours.

CASTEP uses a periodic basis set, so in all honesty if you're only going to do non-periodic simulations, then CASTEP may not be the most appropriate simulation package for you. ( Wali Mohd Dar VASP also uses the same basis set, so that has exactly the same issues; GPAW might be OK though.)

If you want a molecular crystal of nanoparticles, or nanoparticles on a substrate, then CASTEP is a good choice. You need to construct a simulation cell with the appropriate shape and size, and arrange your nanoparticle(s) in the cell. To perform LDA+U, you set the main XC functional in the param file:

xc_functional : lda

and define the Hubbard U you want for Cu in the cell file; e.g. to use U = 4 eV for the Cu d-states you would put:

%block hubbard_u

Cu d: 4.0 eV

%endblock hubbard_u

Hope that helps,

Phil Hasnip

(CASTEP developer)

DOI: 10.1039/D2RA06303D

RSC Adv., 2022, 12, 32853-32884

You can see this paper