Gallium arsenide diamondoids structural and vibrational properties are investigated using density functional theory at the PBE/6-31(d) level and basis including polarization functions. Variation of energy gap as these diamondoids increase in size is seen to follow confinement theory for diamondoids having nearly equiaxed dimensions. Density of energy states transforms from nearly single levels to band structure as we reach larger diamondoids. Bonds of surface hydrogen with As atoms are relatively localized and shorter than that bonded to Ga atoms. Ga-As bonds have a distribution range of values due to surface reconstruction and effect of bonding to hydrogen atoms. Experimental bulk Ga-As bond length (2.45 Å) is within this distribution range. Tetrahedral and dihedral angles approach values of bulk as we go to higher diamondoids. Optical-phonon energy of larger diamondoids stabilizes at 0.037 eV (297 cm-1) compared to experimental 0.035 eV (285.2 cm-1). Ga-As force constant reaches 1.7 mDyne/Å which is comparable to Ga-Ge force constant (1.74 mDyne/Å). Hydrogen related vibrations are nearly constant and serve as a fingerprint of GaAs diamondoids while Ga-As vibrations vary with size of diamondoids.