  Triplet excitonic state in the organic molecule may arise from a singlet
excitation and the following inter-system crossing. Especially for a
spin-bearing molecule, an exchange interaction between the triplet exciton and
the original spin on the molecule can be expected. In this paper, such exchange
interaction in copper-phthalocyanine (CuPc, spin-$\frac{1}{2}$) was
investigated from first-principles by using density-functional theory within a
variety of approximations to the exchange correlation, ranging from
local-density approximation to long-range corrected hybrid-exchange functional.
The magnitude of the computed exchange interaction is in the order of meV with
the minimum value (1.5 meV, ferromagnetic) given by the long-range corrected
hybrid-exchange functional CAM-B3LYP. This exchange interaction can therefore
give rise to a spin coherence with an oscillation period in the order of
picoseconds, which is much shorter than the triplet lifetime in CuPc (typically
tens of nanoseconds). This implies that it might be possible to manipulate the
localised spin on Cu experimentally using optical excitation and inter-system
crossing well before the triplet state disappears.
