This work presents crystal orbital studies on novel one-dimensional (1D) nanoscale materials derived from a Si-diyne sheet, based on the density functional theory. The two-dimensional (2D) Si-diyne layer is observed to be carbo-merized silicene, with a similar structure to graphdiyne. The 2D Si-diyne and its 1D ribbons and tubes, of different size and chirality, have been addressed systematically. The low dimensional Si-diyne materials studied exhibit relatively high stability, according to phonon-frequency calculations and molecular dynamics simulations. With comparable diameters, the Si-diyne tubes have lower strain energies than silicene and silicon carbide nanotubes. The Si-diyne layer and its 1D derivatives are all semiconductors, regardless of the size and chirality of the strips and tubes. In addition, the band gaps of the 1D Si-diyne nanoribbons and nanotubes with different chirality, always monotonically decrease as their sizes increases. A quantitative relationship between the band gap and the size of the ribbons and tubes was obtained. The mobility of charge carriers for the 1D Si-diyne structures was also investigated. It was found that both hole and electron mobility of the ribbons and tubes exhibit linear increase with increasing size. The electrons have greater mobility than the holes for each strip and tube. In addition, the mechanical properties of the Si-diyne nanostructures were also investigated by calculation of the Young's modulus and the Poisson's ratio.