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We present a comprehensive and integrated model-independent ab initio studyof the structural, cohesive, electronic, and optical properties of siliconquantum dots of various morphologies and sizes in the framework of all-electronstatic and time-dependent density functional theory (DFT, TDFT), using thewell-tested B3LYP and other properly chosen functional(s). Our raw ab initioresults for all these properties for hydrogen passivated nanocrystals ofvarious growth models and sizes from 1 to 32 Angstroms, are subsequentlyfitted, using power-law dependence with judicially selected exponents, based ondimensional and other plausibility arguments. As a result, we can reproducewith excellent accuracy not only known experimental and well-tested theoreticalresults in the regions of overlap, but we can also extrapolate successfully allthe way to infinity, reproducing the band gap of crystalline silicon withalmost chemical accuracy as well as the cohesive energy of the infinite crystalwith very good accuracy. Thus, our results could be safely used, among others,as interpolation and extrapolation formulas not only for cohesive energy andband gap, but also for interrelated properties, such as dielectric constant andindex of refraction of silicon nanocrystals of various sizes all the way up toinfinity.

A Comprehensive Ab Initio Study of Electronic, Optical and Cohesive  Properties of Silicon Quantum Dots of Various Morphologies and Sizes up to  Infinity