From the system Hamiltonians an open quantum system can be constructed through coupling to the environment spectral density. This makes use of the HEOM -which is intrinsically dependent on its spectral function -the details of which can be found in our previous work, and in the original derivation by Tanimura and Kubo. All environmental degrees of freedom, including all memory effects due to non-Markovianity, are described by the correlation function associated with the fluctuation-dissipation theorem: