In this study, based on new designed and reported molecules with chemical formula of C13H13B2N, novel electrically and optically active oligomers with different size were suggested. It was shown that the suggested structures have no imaginary frequency and have high negative values of the cohesive energies which show feasibility of their formation. Additionally, increasing the numbers of unit in oligomers created the narrower values of Eg. Similar results were obtained in calculating the optical properties of oligomers using two different methods. Considerable improvements in optical properties of oligomers were observed by increasing numbers of units in their structures. The feasibility of formation of cyclic oligomers with 8 units was studied, and it was shown that formation of this structure is possible which has considerable optical properties. A noteworthy result is that the circular oligomer comprised 8 units has cup-like structure which is very attractive.