The optimum valence bond scheme is a new theoretical method in generating the initial geometric configurations in molecular dynamics simulations of cluster systems. We will present the application of such a new method to the prediction of nano-structures and the study of matter properties, especially for the low-dimensional nano-structures, such as clusters and nano wires. The optimum valence bond scheme uses the atomic geometry of structures and the space distribution of the valence electrons (mainly the molecular orbitals near the Fermi levels, i.e., the generalized frontier orbitals) to determine the possible stable geometric configurations of nano-structures. Silicon clusters are used to demonstrate the features of the optimum valence bond scheme. Metallic clusters such as those of lithium, sodium, beryllium and magnesium are used as examples to illustrate the application of the scheme to the prediction of structures and the studies of the evolution of the material properties with the sizes of clusters. We will use the adsorption process of lithium ion and MoS nano wire to illustrate the application of the optimum valence bond scheme in the studies of the ionic conduction mechanism of the energy storage materials. We will finish the paper by summarizing the direction for further development of the optimum valence bond scheme.