Hi,

If I may, I'll add a few more lines on Alessandro's comment that might be of use (or not...)

Let's say you want to change the charge state of one of the Li atoms in your cell. Assuming that it is atom number XY with atomic number 3, your input might look something like this:

Title [geometry] END [basis set] ... 3 3 -> Li example basis set 0 0 6 2. 1. 700.0 0.001421 220.0 0.003973 70.0 0.01639 20.0 0.089954 5.0 0.315646 1.5 0.494595 0 0 1 1. 1. 0.5 1.0 0 2 1 0. 1. 0.6 1.0 ... 99 0 CHEMOD 1 XY -> atom number whose charge you change for the initial guess 2.0 2.0 0.0 -> electronic charge of all shells in the basis set, here you alter the initial charge guess (note that the initial configuration is 2.0 1.0 0.0, so you will end up in the "-1" charge state) CHARGED END [SCF parameters] END

As usual, supercell size should be converged, localization of the defect confirmed, etc. Good luck with the defect formation energy corrections...one way to go is to use the multipole correction (aka Makov-Payne, see e.g., 2010 J. Phys.: Conf. Ser. 242 012004 or PRB 81, 205214 (2010))...or you can write your own piece of code to interface CRYSTAL's output to for example the scheme of Kumagai and Oba (Phys. Rev. B 89, 195205) !

Hope it helps.

Cheers,
Aleks

Hi,

Direct piezoelectric constants of a 3D lattice in CRYSTAL are defined and computed as:
$$
e_{ci}^{3D} = \left( \frac{\partial P_c}{\partial \eta_i}\right) = \frac{1}{V}\left( \frac{\partial^2 E}{\partial E_c\partial \eta_i}\right)
$$
that is as first derivatives of Cartesian components of the polarization (c=x,y,z) with respect to strain components, or, equivalently as second derivatives of the energy density (V is the volume of the 3D lattice cell) with respect to Cartesian components of an electric field \(E_c\) and strain components, where the strain \( \eta \) is dimensionless and thus the direct piezoelectric constants have units of \( \textup{charge/length}^2 \).

For 1D and 2D periodic lattices, as the volume (V) is not uniquely defined (or not defined at all in some cases), one may divide by the length \(l \) and area \( A\) of the lattice cell instead:
$$
e_{ci}^{1D} = \frac{1}{l}\left( \frac{\partial^2 E}{\partial E_c\partial \eta_i}\right) \quad \textup{and} \quad e_{ci}^{2D} = \frac{1}{A}\left( \frac{\partial^2 E}{\partial E_c\partial \eta_i}\right)
$$
that would thus be expressed in units of \( \textup{charge} \) or \( \textup{charge/length} \) for 1D and 2D lattices, respectively.

However, in CRYSTAL for 1D and 2D lattices we do not divide by \(l \) or \( A\) , and just define and compute the piezoelectric constants as:
$$
e_{ci}^\textup{1D and 2D} = \left( \frac{\partial^2 E}{\partial E_c\partial \eta_i}\right)
$$
with units of \( \textup{charge}\cdot\textup{length} \).

Yes, these constants are physically meaningful for 1D and 2D systems. For a 2D monolayer system, for instance, depending on what you need to compare with, you can do one of two things:

keep them as they are printed in the CRYSTAL output (units of \( \textup{charge}\cdot\textup{length} \))

divide the values you get in the CRYSTAL output by the area of the 2D cell (and thus express them in units of \( \textup{charge/length} \))

I would not divide by a volume because I would not know the physical meaning of the volume of a 2D monolayer system.

Hope this helps,

Thank you Giacomo Ambrogio.
I am greatful to the CRYSTAL code forum
This will help alot.

Best Wishes

Thank you Jacques for your kind help.
This will solve multiple problems of my current work

Regards
R.Zosiamliana

Thank you sir for your kind reply...