Circular Dichroism and the G/beta tensors

[asalij]

I've been reviewing the documentation, associated paper , and the previous thread on this topic, but I still had some questions that seemed to be of public interest.

1. It is my understanding that the Yambo code assumes isotropy and is determining the CD from the trace of the G/beta tensors, but it is a bit unclear to be what the precise units are of the output (they are noted in eps in the output file). Have the prefactors in the first equation in the documentation been applied, or is this just the trace of a relevant tensor (if so, which one? the G or the beta?).

2. Can one explicitly get G tensor elements (or at least the trace) from yambo? If so, how?

3. It seems that yambo only supports CD calculations w/ BSE under the IP approximation as "dich" is a parameter of "BSEprop" and I get errors when not using IP. Is this accurate, or is there a way to use another level of theory (e.g., TD-DFT under ALDA?).

4. Yambo only includes electric dipole/magnetic dipole contributions, yes? Is there a method to extract electric quadrupole moments, or is this not a supported feature? If not, I may get around to implementing this an contributing upstream.

Edit: typography

[Davide Sangalli]

Premise. The CD in yambo is an ongoing development which is not yet finalized.
It works for computing the trace of the beta/G tensor at the IP level. Extensions to the implementation are still ongoing.

1. It is my understanding that the Yambo code assumes isotropy and is determining the CD from the trace of the G/beta tensors, but it is a bit unclear to be what the precise units are of the output (they are noted in eps in the output file). Have the prefactors in the first equation in the documentation been applied, or its this jsut the trace of a relevant tensor (if so, which one? the G or the beta?).

In output yambo prints (omega/c)*beta(omega)=-i/c*G

2. Can one explicitly get G tensor elements (or at least the trace) from yambo? If so, how?

Not at the moment. One should slightly change the implementation for the magnetic dipole term, and also add the terms due to the electric quadrupole contribution. In the trace the electric quadrupole term goes to zero.

3. It seems that yambo only supports CD calculations w/ BSE under the IP approximation as "dich" is a parameter of "BSEprop" and I get errors when not using IP. Is this accurate, or is there a way to use another level of theory (e.g., TD-DFT under ALDA?).

It depends on the system studied. Dichroism beyond IP is largely implemented but not yet finalized in the released version

4. Yambo only includes electric dipole/magnetic dipole contributions, yes? Is there a method to extract electric quadrupole moments, or is this not a supported feature?

Yambo only includes the magnetic dipole, while it neglects the electric quadrupole.

5. If not, I may get around to implementing this an contributing upstream.

We can discuss about this in case you are interested ...

Best,
D.

[asalij]

Davide, thanks for your response.

In output yambo prints (omega/c)*beta(omega)=-i/c*G

OK, good to know--the output being in units of (eps) made this a bit unclear. At present, I'm mostly interested in getting order of magnitude estimations for the trace of the G tensor, so it seems like Yambo is ideal for this use case.

In the trace the electric quadrupole term goes to zero.

I'm aware. It's my understanding that most general purpose codes such as Yambo make an assumption of isotropy in this sense.

[asalij]

Davide,

Upon finalizing some items, I figured its best to confirm this all in a public forum for future users.

1. As is noted on the yambo wiki (https://wiki.yambo-code.eu/wiki/index.p ... _molecules), there is a factor to relate the change in refractive index, and the beta tensor, namely $\frac{8\pi}{3}$ in what I presume to be cgs units. Is this the specific prefactor used in the yambo code?

2. I understand the relation

(omega/c)*beta(omega)=-i/c*G

as implicitly setting the mass and charge of the electron to 1 as well as the reduced Planck's constant to 1. If not, the full relation would be $\beta = \frac{-i \hbar m_e}{\omega q_e^2}G$, no?

I appreciate that these sorts of units concerns are part of why calculated signals are often provided in arbitrary units, but sometimes it is ideal to get a value in precise units so as to permit ready comparison to the literature as well as to be able to provide that comparison for others.

[asalij]

I don't mean to excessively push this issue, and greatly appreciate all of the work done by the Yambo team, but the more I look into the yambo outputs and codebase the more I am confused on this matter. For instance, it is extraordinarily hard for someone who is not a maintainer to determine what, exactly, are the units at any stage in https://github.com/yambo-code/yambo/blo ... bse/K_IP.F.

I see that Elena Molteni, Giancarlo Cappellini and you (Davide Sangalli) were working in part from Barron's Molecular Light Scattering and Optical Activity, a text I am quite familiar with. In it, the G tensor is provided in units of [\hbar]^2[c]^2[e]^2/[eV]^3, which become dimensionless when scaled by either (- \mu_0 * c * N) where \mu0 is the permeability of free space and N is the number electron density in order to obtain the change in the circularly-polarized refractive index (\delta n) or by (\omega l N \mu0) where l is pathlength and \omega is angular frequency to obtain the measured circular dichroism/birefringence signal. Davide, from your prior response, where does the number density fit in, the permeability/permittivity of free space? My sense is that, for a molecule, yambo is effectively determining the signal for whatever volume the initial Quantum Espresso calculation was performed in, which would make the results highly dependent on cell volume. For a crystal, this is pretty intrinsic, but for a isolated system in an arbitrary bounding box, I believe that this would make any results need to be scaled by an effective volume, yes?

The yambo output states that terms are given as Im(eps) and Re(eps), hinting at an equivalence with the (dimensionless) permittivity scaled by the permittivity of free space. However, from your prior response and from the documentation, it would appear that the output is actually in terms of the circularly-polarized refractive index. Which one is it? I'm aiming to get one thing that is 100% solid in order to derive all other quantities from. Namely, should I be certain that the printed quantity is either the complex refractive index for change is left-handed vs. right-handed or the dielectric change (dimensionless)?

Other items of convention:
CD appears to be defined as A_R-A_L instead of (A_L-A_R)/2 or another definition.
Here right-handed polarization (R) would be (x-1j*y) in the Cartesian basis, yes, and not the reverse?