In the calculations of the HOMO-LUMO gaps for organic molecules and nonoclusters you use the same quantum molecular orbital methods such as DFT, ab initio or semi-empirical.
These calculations can be carried out using the methods installed in Gaussian 09.
Examples for such calculations are depicted in the following links and attached file:
Please, find in attach two files on NANOCLUSTERS:Their Generation and Characterization in Beams and the Bulk L.B. Kidder, C.A. Fancher, J.M. Collins, H.W. Sarkas, D.W. Robinson, c.A. Jones", and K.H. Bowen, Department of Chemistry, Johns Hopkins University, Baltimore, MD 21218, USA and about Ultraviolet and visible spectroscopy including HOMO/LUMO calculation.
In this paper, various energies and geometries of pure platinum nanoparticles and those of platinum nanoparticles with adsorbed OH were investigated. Ten different platinum clusters of up to 28 atoms were studied using spin-unrestricted density functional theory (DFT) with a double numerical plus polarization basis set. Three different shapes were presented, and the effect of cluster size on binding energy, total energy, and HOMO-LUMO energy gap was investigated. The same set of calculations was performed for selected clusters with OH adsorbate on the Pt(111) surface. The results show that the stability of both the pure clusters and the clusters with adsorbed OH molecule increases with an increase of cluster size. This fact indicates that direct influence of the size of Pt cluster on the reaction rate is possible, and the understanding of how cluster size would affect binding energy is important. The effect of cluster size on total energy of molecule was shown to be a linear function independent of cluster type, as expected. We also found that optimized (stable) Pt clusters were bigger in size than that of the initial clusters, or clusters with bulk geometry.
Please, find in attch a paper on: Metallic Clusters: Theoretical Background, Properties and Synthesis in Microemulsions David Buceta 1, Yolanda Piñeiro 1, Carlos Vázquez-Vázquez 1, José Rivas 2 and Manuel Arturo López-Quintela 1,*Catalysts 2014, 4, 356-374; doi:10.3390/catal4040356. Disccsing the quantum size effects (HOMO-LUMO gap), the small size and the specific geometry award subnanometric clusters with totally new and fascinating properties, including cluster photoluminescence, enhanced catalytic activity, etc.