circular dichroism

[Davide Sangalli]

Dichroism was implemented and it is being tested for isolated systems, i.e. gamma point only.
We are presently working on a draft to present the approach.

However, the implementation is general and the code would run also at finite k.
In presence of k-points, and thus of a periodic system, the issue is the calculation of the "dipoles" needed for dichroism, i.e. the expectation value of the orbital angular momentum.
This is ill-defined in periodic boundary conditions (same as the position operator).
Yambo writes it a the vector product of position and velocity operator expectation values, introducing a sum over states which is truncated.
This may introduce errors and it has never been tested.

Best,
D.

[elena.mol]

Hi,

1) Yes, we have implemented it for gamma only, in view to applications to isolated systems (such as molecules).

2) Yes. You can also look, e.g., at equations 1-5 in E. Molteni et al., J. Phys. Chem. B 2015, 119, 4803−4811, DOI: 10.1021/jp5118568

Best
Elena


Elena Molteni
ISM-CNR, Area della Ricerca di Roma 1,
and Università degli Studi di Milano

Dear Gosia,

1) Yes, I think that it is implemented for gamma only, actually I do not know what the code does in presence of a k point sampling. Someone else could answer on that
2) If I'm not wrong it is the trace of the equation 2.13 you can find in the paper D. Varsano et al Phys. Chem. Chem. Phys., 2009, 11, 4481–4489
3) What is I here, the absorption? so it is a frequency dependent quantity? If so, the numerator is the CD itself, but you do not have access to I_R and I_L separately.

About the shift, take into account the you are in independent particle framework, so excitonic effect are not present. Such effects should shift your CD spectra to lower energies.

@Davide, can you confirm that?

Best,

Daniele

[Davide Sangalli]

1) Yes, I think that it is implemented for gamma only, actually I do not know what the code does in presence of a k point sampling. Someone else could answer on that
2) If I'm not wrong it is the trace of the equation 2.13 you can find in the paper D. Varsano et al Phys. Chem. Chem. Phys., 2009, 11, 4481–4489
(preprint here)
3) What is I here, the absorption? so it is a frequency dependent quantity? If so, the numerator is the CD itself, but you do not have access to I_R and I_L separately.

About the shift, take into account the you are in independent particle framework, so excitonic effect are not present. Such effects should shift your CD spectra to lower energies.

@Davide, can you confirm that?

Best,

Daniele

Please have a look at these for equations:
https://arxiv.org/abs/2202.02079
https://arxiv.org/abs/2202.12702 (The code for the second manuscript is not yet released)

1) In the first manuscript there is a comment on the possibility of using it for extended systems.
2) Yeah, it is the beta of eq. 2.13 in the manuscript pointed out by Daniele
3) Please notice that this is a bit different from absorption. Dichroism, as defined for molecules in gas phase comes from the trace of the beta tensor.
If you are interested in dichroism from an oriented sample, you may want to compute the kerr parameters, from which you can extract eps_R and eps_L
See here: https://journals.aps.org/prb/abstract/1 ... .86.125139

Best,
D.