  We present an analytical proof and numerical demonstrations of the
equivalence of the correlation energy from particle-particle random phase
approximation (pp-RPA) and ladder-couple-cluster-doubles (ladder-CCD). These
two theories reduce to the identical algebraic matrix equation and correlation
energy expressions, under the assumption that the pp-RPA equation is stable.
The numerical examples illustrate that the correlation energy missed by pp-RPA
in comparison with couple-cluster single and double is largely canceled out
when considering reaction energies. This theoretical connection will be
beneficial to future pp-RPA studies based on the well established couple
cluster theory.
