Separability properties of reduced and effective density matrices in the equation-of-motion coupled cluster method

Certain aspects of final state descriptions provided by the equation-of-motion coupled cluster (EOM-CC) method are analyzed, particularly the asymptotic separability of density matrices. Specific attention is focused on a supermolecule system that consists of two fragments, one of which is in an excited electronic state. For this example, the reduced n-particle density matrix [ρ(n)] associated with EOM-CC theory exhibits unphysical long range behavior due to a lack of bra state multiplicative separability. More satisfactory is the effective density [D(n)] which includes the first order response of ground state correlation. In particular, local components of D(n) reduce to the corresponding monomer quantities in the limit of infinite separation. This feature guarantees that observables calculated by contracting D(n) with local operators are size consistent. However, the situation with respect to physical phenomena associated with nonlocal operators is less clear, as multicenter matrix elements of both ρ(n) and D(n) behave incorrectly for n≥2 in the separated limit. The latter consideration should not be misconstrued as an inherent failure of the EOM-CC approximation, as problems associated with nonlocal parts of the density are already present in the normal coupled cluster treatment of the ground state.