There is a growing interest in developing low-band gap conjugated polymers via synthesis of copolymers containing alternating units of different pi-electron-donating/accepting capabilities. In this study, electronic and optical properties of conjugated copolymers containing fluorene and thiophene/cyclopentadithiophene derivatives are determined using density function theory and semiempirical ZINDO calculations. A remarkable linear correlation is found between the amount of charge transfer between the donor-acceptor pair, the band gap, the bandwidth, and the oscillator strength of S(0)-->S(1) electronic transition (ground state to first excited state) of the copolymers. Strong pi-electron withdrawing substituents, such as dicyanoethenyl and carbonyl groups, on the thiophene moiety effectively reduce the band gap of the copolymers. However, the reduction of band gap is frequently accompanied by a linear reduction in bandwidths and in the oscillator strength of S(0)-->S(1) transition. For very strong pi-electron withdrawing thiophene derivatives, the occurrence of maximum oscillator strength may even shift from S(0)-->S(1) to S(0)-->S(n>1) (ground state to a higher excited state), giving a blue shift in maxima absorption peak and a red shoulder in the UV-vis spectra as reported in recent experimental measurements. Therefore, the achievement of low band gap for conjugated polymers with alternating arrangement of pi-electron-donating/accepting moieties may be achieved at a cost of lowering electron mobility and optical efficiency and sometimes a blue-shift in the major optical (UV-vis) absorption.