GaN on Si plays an important role in the integration and promotion of GaN-based wide-gap materials with Si-based integrated circuits (IC) technology. A series of GaN film materials were grown on Si (111) substrate using a unique plasma assistant molecular beam epitaxy (PA-MBE) technology and investigated using multiple characterization techniques of Nomarski microscopy (NM), high-resolution X-ray diffraction (HR-XRD), variable angular spectroscopic ellipsometry (VASE), Raman scattering, photoluminescence (PL), and synchrotron radiation (SR) near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. NM confirmed crack-free wurtzite (w-) GaN thin films in a large range of 180-1500 nm. XRD identified the w- single crystalline structure for these GaN films with the orientation along the c-axis in the normal growth direction. An optimized 700 °C growth temperature, plus other corresponding parameters, was obtained for the PA-MBE growth of GaN on Si, exhibiting strong PL emission, narrow/strong Raman phonon modes, XRD w-GaN peaks, and high crystalline perfection. VASE studies identified this set of MBE-grown GaN/Si as having very low Urbach energy of about 18 meV. UV (325 nm)-excited Raman spectra of GaN/Si samples exhibited the GaN E2(low) and E2(high) phonon modes clearly without Raman features from the Si substrate, overcoming the difficulties from visible (532 nm) Raman measurements with strong Si Raman features overwhelming the GaN signals. The combined UV excitation Raman-PL spectra revealed multiple LO phonons spread over the GaN fundamental band edge emission PL band due to the outgoing resonance effect. Calculation of the UV Raman spectra determined the carrier concentrations with excellent values. Angular-dependent NEXAFS on Ga K-edge revealed the significant anisotropy of the conduction band of w-GaN and identified the NEXAFS resonances corresponding to different final states in the hexagonal GaN films on Si. Comparative GaN material properties are investigated in depth.