Accurate calculations of molecular crystals are crucial for drug design and
crystal engineering. However, periodic high-level density functional
calculations using hybrid functionals are often prohibitively expensive for
relevant systems. These expensive periodic calculations can be circumvented by
the usage of embedding methods in which for instance the periodic calculation
is only performed at a lower-cost level and then monomer energies and dimer
interactions are replaced by those of the higher-level method. Herein, we
extend upon such a multimer embedding approach to enable energy corrections for
trimer interactions and the calculation of harmonic vibrational properties up
to the dimer level. We evaluate this approach for the X23 benchmark set of
molecular crystals by approximating a periodic hybrid density functional
(PBE0+MBD) by embedding multimers into less expensive calculations using a
generalized-gradient approximation (GGA) functional (PBE+MBD). We show that
trimer interactions are crucial for accurately approximating lattice energies
within 1 kJ/mol and might also be needed for further improvement of lattice
constants and hence cell volumes. Finally, vibrational properties are already
very well captured at the monomer and dimer level, making it possible to
approximate vibrational free energies at room temperature within 1 kJ/mol