Squaraine dye molecules present a route to semiconducting polymers wit
h small band gaps. We use ab initio calculations to study polysquarain
es systematically, and find band gaps that range from 2.3 down to 0.2
eV. Simple arguments based upon a Huckel analysis of the ab initio res
ults enable us to identify the factors that control the size of the ba
nd gap. General design rules can be based on polymer topology and symm
etry. The band gap can be tuned by chemical substitutions.