Fresh PR for polariton-cq

[FoleyLab]

Incorporates changes suggested by @loriab and @dgasmith and omits extra files accidentally incorporated in the SCF/ folder.

Description This pull request provides reference implementations of hybrid ab initio / cavity quantum electrodynamics methods for computing mean-field ground- and excited-states of molecules strongly coupled to a single quantized photon. What are your new additions? Please provide a brief list.

• New Features
  • [x] Restricted Hartree-Fock energy and orbitals for a molecule coupled to a single quantized photon provided in helper_CQED_RHF.py
  • [x] Configuration Interaction Singles energies and wavefunctions for a molecule coupled to a single quantized photon in helper_CS_CQED_CIS.py
  • [x] Ability to provide complex energy for the photon to account for dissipation / energy uncertainty in the photonic degree of freedom is provided in helper_CS_CQED_CIS.py
  • [x] Example calculations with tests are provided in CQED_RHF.py and CS_CQED_CIS.py
  • [x] Key equations and references provided in README.md Any questions for the community?
• [ ] The CS_CQED_CIS has not been reported in the literature to my knowledge, so I don't know of peer-reviewed reference values, so the main independent test comes from the limit where the molecule is not coupled to a photon, where the method reduces to ordinary CIS which can be compared directly with Psi4 values - is that adequate? Status
• [ ] Click when ready for review-and-merge

[FoleyLab]

lgtm! but did the Polaritonic-Quantum-Chemistry dir not get a file like https://github.com/psi4/psi4numpy/blob/master/tests/test_RI_CC.py so that the scripts in this PR get tested?

@loriab thank you! I just added test_RI_CQEDQC.py to the tests directory that will run CQED_RHF.py and CS_CQED_CIS.py.

[dgasmith]

Thanks @FoleyLab , apologies the review was pretty slow here- this method is a bit outside of wheelhouse!