PAHs have been suggested as possible molecular carriers of the diffuse interstellar bands (DIBs) that were first discovered in 1921. Notwithstanding the significant efforts that have been devoted to this problem in the past two decades, no individual PAHs have ever been identified as DIB carriers due to the lack of a reliable method to pre-select PAH candidates out of the infinite pool of PAH molecules. In an attempt to solve this difficult PAH-DIB problem, I designed a novel approach to generate a "complete" electronic database of PAHs. In the first phase of this approach, a computer code is used to enumerate all possible carbon skeletons of PAHs with a given number of fused benzene rings. In the second phase, a ultrafast semi-empirical ab initio method is employed to generate the vibronic energies and rotational constants of all the PAHs generated in the phase one. An electronic database of all PAHs with up to 10 fused benzene rings (~39,000 molecules) has been generated this way. Possible PAH carriers are then pre-selected according to their transition wavelengths, intensities, and the simulated band profiles. High level quantum chemical calculations are then performed to further narrow down the candidate list. A survey of all PAHs in the current database shows that two closed-shell PAH cations meet all constraints put on the strong lambda-^U6614 DIB (wavelength, intensity, band profile, and ionization potential). This approach holds great power in solving the PAH–DIB problem.