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EOM vs RPA vs RDM vs GW(?) strategies #68

Open PaulWAyers opened 2 years ago

PaulWAyers commented 2 years ago

What is the relationship between these different strategies for generating the correlation energy.

GW approximation is closely related to RPA. RPA is closely related to EOM/response. EOM response is closely related to adiabatic connection approach.

Exactly what are the relationships?

Three different ways of deriving pp-RPA are referenced in https://aip.scitation.org/doi/10.1063/1.4977928

Link between GW and RPA https://aip.scitation.org/doi/10.1063/1.5128415 https://journals.aps.org/prb/abstract/10.1103/PhysRevB.91.165110 https://journals.aps.org/pra/pdf/10.1103/PhysRevA.82.032502 https://www.tddft.org/TDDFT2010/workshop/dobson.pdf https://arxiv.org/pdf/1506.01737.pdf (maybe) https://www.nature.com/articles/s41524-019-0242-8.pdf?proof=t (maybe)

Trace vs. other formula: https://www.frontiersin.org/articles/10.3389/fchem.2021.751054/full https://pubs.acs.org/doi/10.1021/ct200501r

PaulWAyers commented 2 years ago

The following paper may explain this a little bit? ct200501r.pdf

PaulWAyers commented 2 years ago
  1. Lehman representation (Green's Function). Key link between RPA, EOM, and GF methods.
  2. Tamm-Damcoff approximation vs. truncating the right-hand-side.
  3. What are all the relationships (and equivalencies) between methods in general.
PaulWAyers commented 1 year ago

See also https://arxiv.org/abs/2212.08982