  While most binary inspirals are expected to have circularized before they
enter the LIGO/Virgo frequency band, a small fraction of those binaries could
have non-negligible orbital eccentricity depending on their formation channel.
Hence, it is important to accurately model eccentricity effects in waveform
models used to detect those binaries, infer their properties, and shed light on
their astrophysical environment. We develop a multipolar effective-one-body
(EOB) eccentric waveform model for compact binaries whose components have spins
aligned or anti-aligned with the orbital angular momentum. The waveform model
contains eccentricity effects in the radiation-reaction force and gravitational
modes through second post-Newtonian (PN) order, including tail effects, and
spin-orbit and spin-spin couplings. We recast the PN-expanded, eccentric
radiation-reaction force and modes in factorized form so that the newly derived
terms can be directly included in the state-of-the-art, quasi-circular--orbit
EOB model currently used in LIGO/Virgo analyses (i.e., the SEOBNRv4HM model).
