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Starting from the general expression for the ground state correlation energyin the adiabatic connection fluctuation dissipation theorem (ACFDT) framework,it is shown that the dielectric matrix formulation, which is usually applied tocalculate the direct random phase approximation (dRPA) correlation energy, canbe used for alternative RPA expressions including exchange effects. Within thisfamework, the ACFDT analog of the second order screened exchange (SOSEX)approximation leads to a logarithmic formula for the correlation energy similarto the direct RPA expression. Alternatively, the contribution of the exchangecan be included in the kernel used to evaluate the response functions. In thiscase the use of an approximate kernel is crucial to simplify the formalism andto obtain a correlation energy in logarithmic form. Technical details of theimplementation of these methods are discussed and it is shown that one can takeadvantage of density fitting or Cholesky decomposition techniques to improvethe computational efficiency; a discussion on the numerical quadrature made onthe frequency variable is also provided. A series of test calculations onatomic correlation energies and molecular reaction energies shows that exchangeeffects are instrumental to improve over direct RPA results.

Dielectric matrix formulation of correlation energies in the Random Phase Approximation (RPA): inclusion of exchange effects