  Colloidal quantum dots (QDs) of group III-V are considered as promising
candidates for next-generation environmentally friendly light emitting devices,
yet there appears to be only limited understanding of the underlying electronic
and excitonic properties. Using large-scale density functional theory with the
hybrid B3LYP functional solving the single-particle states and time-dependent
density functional theory accounting for the many-body excitonic effects, we
have identified the structural, electronic and excitonic optical properties of
InP, GaP and GaInP QDs containing up to a thousand atoms or more. The
calculated optical gap of InP QD appears in excellent agreement with available
experiments, and it scales nearly linearly with the inverse diameter. The
radiative exciton decay lifetime is found to increase surprisingly linearly
with increasing the dot size. For GaP QDs, we predict an unusual electronic
state crossover at diameter around 1.5 nm whereby the nature of the lowest
unoccupied molecular orbital (LUMO) state switches its symmetry from
$\Gamma_{5}$-like at larger diameter to $\Gamma_{1}$-like at smaller diameter.
After the crossover, the absorption intensity of the band-edge exciton states
is significantly enhanced. Finally, we find that Vegard's law holds very well
for GaInP random alloyed quantum dots down to ultra-small sizes with less than
a hundred atoms. The obtained energy gap bowing parameter of this common-cation
compound in QD regime appears positive, size-dependent and much smaller than
its bulk parentage. The volume deformation, dominating over the charge exchange
and structure relaxation effects, is mainly responsible for the QD energy gap
bowing. The present work provides a road map for a variety of electronic and
optical properties of colloidal QDs in group III-V that can guide spectroscopic
studies.
