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We present a comprehensive and integrated model-independent ab initio study of the structural, cohesive, electronic, and optical properties of silicon quantum dots of various morphologies and sizes in the framework of all-electron "static" and time-dependent density functional theory (DFT, TDFT), using the well-tested B3LYP and other properly chosen functional(s). Our raw ab initio results for all these properties for hydrogen passivated nanocrystals of various growth models and sizes from 1 to 32 Ångstroms, are subsequently fitted, using power-law dependence with judicially selected exponents, based on dimensional and other plausibility arguments. As a result, we can reproduce with excellent accuracy not only known experimental and well-tested theoretical results in the regions of overlap, but we can also extrapolate successfully all the way to infinity, reproducing the band gap of crystalline silicon with almost chemical accuracy as well as the cohesive energy of the infinite crystal with very good accuracy. Thus, our results could be safely used, among others, as interpolation and extrapolation formulas not only for cohesive energy and band gap, but also for interrelated properties, such as dielectric constant and index of refraction of silicon nanocrystals of various sizes all the way up to infinity

We investigate the superluminal effect of transmitted probe field in three‐level quantum dot molecules (QDMs) assisted optomechanical system which consist of mechanical resonator. We show that the superluminal behavior of transmitted probe field can be controlled by changing the tunneling strength and number of QDMs inside the cavity. Furthermore, it is shown that in the absence of tunneling strength, the transmitted probe field shows the fast light effect and by increasing the number of QDMs, the enhancement in superluminal behavior is decreased and converts into slow light. While, in the presence of the tunneling strength, with the increase of the number of QDMs the superluminal behavior of transmitted field is obtained at smaller detuning frequency. The influence of tunneling strength and number of QDMs on superluminal part of the transmitted probe field is quite useful in optical memory, optical buffers, and quantum information processing.

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