Conjugation in extended systems gives rise to unique properties. For example, conjugated polymers possess unique combination of characteristics: electronic, optical, magnetic properties of semiconductors and metals; and, processing properties of plastics. Band gap control is essential in achieving those properties. Theoretical methods were first screened with available experimental data on conventional conjugated polymers and/or their oligomers, the validated methods were then used to predict and design various novel intrinsic low band gap conducting polymers, including various acetylenic coupled ladder polymers and aromatic-quinonoid copolymers. To accurately predict vibrational spectroscopy of extensively conjugated systems has been challenging to computational chemists due to the strong electron-phonon coupling in these systems. Currently available theoretical models are proved to be un-applicable for this matter, especially for the extremely conjugated system, polyyne. A novel linear/exponential hybrid force field scaling scheme is proposed in accompanying with quantum mechanical vibrational calculations to solve this problem. It has been successfully applied to polyyne and polyacetylene, and in principle can be extended to all extensively conjugated systems.