[Pw_forum] Units of Raman Tensor

[S. Sanchez]

Dear QE users,

I have a question regarding the Raman Tensor units. I have seen in the QE
forum that units of the Raman Tensor resulting from the use of ph.x code are
given in: "A^2" (Angstroms^2).

Question: do these units results after a multiplication of the third-order
rank tensors (dchi/dr, where "r" indicates atomic displacement) by their
respective normal-mode displacements? Or do the units of "A^2" correspond
only to the dchi/dr tensor?

My question arises given the fact that the dchi/dr tensor can be obtained as
the third order derivative of the Energy (in units of Ry or Ha) with respect
to the atomic displacement (bohr) and two times the electric field (e/bohr).

dchi/dr=d^3E/(dr*de1*de2)
where E is the Energy; r the displacement, e1 and e2 the electric fields.
Replacing the above-mentioned units, I can only get units of Ha*bohr
((Ry/2)*bohr); where e^2=1 for Hartree or e^2=2 for Rydberg.

Thanks for your help,
S. Sanchez
Researcher
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