Angular momentum integral

[JangidBhavnesh]

Is it possible to calculate the angular momentum integral with libcint?

For example, I have highly paramagnetic TM-Complex, where the unpair electrons are localized on metal center, then using that as origin, can I calculate the 1e integrals in presence of magnetic field?

[sunqm]

No, integrals with magnetic field is not supported. You can instead compute the angular momentum integrals, such as int1e_cg_irxp https://github.com/sunqm/libcint/blob/master/scripts/auto_intor.cl#L12 . Then adjust the phase and multiply to the magnetic fields.

[JangidBhavnesh]

Okay.

Thanks

[JangidBhavnesh]

I have follow-up question here:

To include the picture change corrections in 1e property integrals, like dipole moment or angular momentum integral, I am looking for the 'pOp' type integrals (O is the corresponding property operator).

For the dipole moment, based on PySCF documentation and examples, I think those integrals are 'int1e_sprsp'. However, for the
angular momentum integrals, I have not found the 'int1e_cg_spirxpsp' type integrals. Do you know if I can compute these integrals via Libcint?

Thanks

[JangidBhavnesh]

I have written the expression of the above integral as described here, and was able to compute these integrals using Libcint.

"int1e_cg_spirxpsp" (#C(0 1) sigma dot p \| rc cross p \| sigma dot p))

Is there a test that I can do to make sure these integrals are correct?

I tried to compute the $$\langle L^2_{PC} \rangle$$ for a CAS wave function, and they were different from the $$\langle L^2_{NR}\rangle$$ but that doesn't prove or disprove it.

Test-system
Al atom, ground-state $${}^2\mathrm{P}$$ state: Hence L-value will be 1. For the NR case, I got the 1, but the picture change corrected $$\langle L^2_{PC}\rangle$$, I got 0.999, I don't know whether that is right!.