The coupled perturbed electron propagator in the two-particle-hole and extended two-particle-hole Tamm-Dancoff approximations

The equations satisfied by the first-order perturbed electron propagator in an applied external field are examined at a level equivalent to the two-particle-hole Tamm-Dancoff and extended two-particle-hole Tamm-Dancoff approximations (2ph-TDA). These schemes are derived with the intention of evaluating linear and quadratic response properties through second and third order in correlation. Their derivation is based on a combination of the diagrammatic and algebraic superoperator methods. Both schemes account for the polarization of the 2p-1h and 2h-1p responses and bielectron interactions under an external field. The 2ph-TDA scheme is correct up to second order in electronic correlation and includes infinite geometric series of mixed RPA-ladder-type character. Its extended version is derived consistently through third order and accounts for a first-order screening of the external field and bielectron interaction by the effects of electronic correlation. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 483–509, 1997