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## transition dipole moment

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glabcher
Posts: 4
Joined: Mon May 18, 2015 9:09 pm

### transition dipole moment

Dear all,

I need to calculate transition dipole moments for each k-vector k between valence n and conduction n' bands. I am thinking to use simple integral to find (for example x component of) t.d.m. :

m_x= - e * integral (PSI*_n,k (x) * x * PSI_n',k (x) dx )

where PSI_n,k (x) is a real-space wavefunction:

PSI_n,k (r) = sum_G (C_n,k (G) * exp i(k+G)r )

C_n,k plane-wave coefficients with the corresponding G values I am getting from WFK.

Does anyone know if I am doing this right or I should do it in different way?

Thanks!

raul_l
Posts: 74
Joined: Sun Jan 08, 2012 7:45 pm

### Re: transition dipole moment

This only accounts for the local part, no? With separable pseudopotentials or with PAW I think there are additional terms. It might be easier to let abinit calculate the matrix elements and extract pmat from optic.f90.
Raul Laasner
Netherlands Institute for Space Research

glabcher
Posts: 4
Joined: Mon May 18, 2015 9:09 pm

### Re: transition dipole moment

Raul,

Thanks for your reply. Does abinit calculate the matrix elements within the DFT method? I know it does for TDDFT. My goal is to obtain electric and magnetic dipole moments from DFT calculations.

And I have one more question about optic.f90. When I run this code, it asks me to provide the name of the data and output files. What is "the data file" in this case? is it WFK file?

Thanks

raul_l
Posts: 74
Joined: Sun Jan 08, 2012 7:45 pm

### Re: transition dipole moment

From what I understand the matrix elements are determined by the calculation of the ddk perturbations, which means TDDFT. optic requires the first-order changes in the wavefunction as input (smarter people can correct me). The relevant calculation should be done in abinit. I'm using optic only for the extraction of the matrix elements.
Raul Laasner
Netherlands Institute for Space Research

mverstra
Posts: 655
Joined: Wed Aug 19, 2009 12:01 pm

### Re: transition dipole moment

See http://www.abinit.org/doc/helpfiles/for ... optic.html

It's DFPT for the ddk, not TDDFT, which would involve finite frequencies for the perturbing E field.

The matrix elements of the d/dk operator give the commutator of H with x, which are related to p or the optical matrix elements you are looking for (pmat). Note that this is a solid by default, so polarization rather than electric dipole. The magnetic moment (again not a simple dipole unless you have a finite system in a big box) has a spin part which you get out of a ground state run. The orbital part is also used in abinit within the PAW formalism, e.g. for NMR calculations. I am not sure where/if this is output.
Matthieu Verstraete
University of Liege, Belgium