The rare earth dope d nano-cluster can be a building block for the next-generation photo-electrical industry, so the imminent discovery of novel, suitable nano-functional material is urgent. Praseodymium element as a wonderful dopant, bestow a novel photoelectrochemical properties for nanomaterials especially for semiconductor, derived from its unfulfilled 4f electrons configuration and active electronic transitions between 4f to 4f and 4f to 5d. In view of this, the neutral and anionic clusters of PrSin0/- with a medium size of n = 10–20 are comprehensively investigated by the quantum chemistry method of mPW2PLYP associated with the global searching potential energy surface techniques. The geometry evolution in medium size for PrSin can be attributed to three stages of replaced (n = 10–12), linked (n = 13–19), and cage (n = 20) structure. For PrSin-, two evolution phases are obviously observed by linked (n = 10–19) and cage (n = 20) structure. The PES spectra of the anionic most stable cluster and several degeneracy structures are simulated to identify the ground state structure. Each cluster of AEA, charge transfer, and VDE values are all calculated. Combined with binding energy, HOMO-LUMO gap, molecular orbital analysis, and a series of optical properties estimated, including simulated UV–vis, IR, and Raman spectra, excitation behavior shows PrSi20- has not only prominent stability but also has a proper range of lighting absorption, higher electron-hole recombination, possible as a functional material for optoelectronic devices. •Nano-clusters PrSin0/- (n = 10–20) studied by double hybrid density functional theory.•Praseodymium doped in silicon clusters can improve the stabilities and make new unique photoelectric characteristics.•Structure evolution, photoelectron spectroscopy, HOMO-LUMO gap.•As excellent building blocks, potentially applied to multifunctional optical and electrical nanomaterials.