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We present a comparative study of particle-hole and particle-particlechannels of random-phase approximation (RPA) for molecular dissociations ofdifferent bonding types. We introduced a \textit{direct} particle-particle RPAscheme, in analogy to the \textit{direct} particle-hole RPA formalism, wherebythe exchange-type contributions are excluded. This allows us to compare thebehavior of the particle-hole and particle-particle RPA channels on the samefooting. Our study unravels the critical role of exchange contributions indetermining behaviors of the two RPA channels for describing stretchedmolecules. We also made an attempt to merge particle-hole RPA andparticle-particle RPA into a unified scheme, with the double-counting termsremoved. However, benchmark calculations indicate that a straightforwardcombination of the two RPA channels does not lead to a successful computationalscheme for describing molecular dissociations.

Comparing particle-particle and particle-hole channels of random-phase approximation