  The equation of motion coupled cluster singles and doubles model (EOM-CCSD)
is an accurate, black-box correlated electronic structure approach to
investigate electronically excited states and electron attachment or detachment
processes. It has also served as a basis for developing less computationally
expensive approximate models such as partitioned EOM-CCSD (P-EOM-CCSD), the
second-order many-body perturbation theory EOM (EOM-MBPT(2)), and their
combination (P-EOM-MBPT(2)) [S. Gwaltney et al., Chem. Phys. Lett. 248, 189-198
(1996)]. In this work we outline an implementation of these approximations for
four-component based Hamiltonians and investigate their accuracy relative to
EOM-CCSD for valence excitations, valence and core ionizations and electron
attachment, and this for a number of systems of atmospheric or astrophysical
interest containing elements across the periodic table. We have found that
across the different systems and electronic states of different nature
considered, partition EOM-CCSD yields results with the largest deviations from
the reference, whereas second-order based approaches tend show a generally
better agreement with EOM-CCSD. We trace this behavior to the imbalance brought
about by the removal of excited state relaxation in the partition approaches,
with respect to degree of electron correlation recovered.
