  We overview nonequilibrium Green function combined with density functional
theory (NEGF-DFT) modeling of independent electron and phonon transport in
nanojunctions with applications focused on a new class of thermoelectric
devices where a single molecule is attached to two metallic zigzag graphene
nanoribbons (ZGNRs) via highly transparent contacts. Such contacts make
possible injection of evanescent wavefunctions from ZGNRs, so that their
overlap within the molecular region generates a peak in the electronic
transmission. Additionally, the spatial symmetry properties of the transverse
propagating states in the ZGNR electrodes suppress hole-like contributions to
the thermopower. Thus optimized thermopower, together with diminished phonon
conductance through a ZGNR/molecule/ZGNR inhomogeneous structure, yields the
thermoelectric figure of merit ZT~0.5 at room temperature and 0.5<ZT<2.5 below
liquid nitrogen temperature. The reliance on evanescent mode transport and
symmetry of propagating states in the electrodes makes the
electronic-transport-determined power factor in this class of devices largely
insensitive to the type of sufficiently short conjugated organic molecule,
which we demonstrate by showing that both 18-annulene and C10 molecule
sandwiched by the two ZGNR electrodes yield similar thermopower. Thus, one can
search for molecules that will further reduce the phonon thermal conductance
(in the denominator of ZT) while keeping the electronic power factor (in the
nominator of ZT) optimized. We also show how often employed Brenner empirical
interatomic potential for hydrocarbon systems fails to describe phonon
transport in our single-molecule nanojunctions when contrasted with
first-principles results obtained via NEGF-DFT methodology.
