We investigate here the relationship between molecular architecture and two-photon absorption (TPA) processes in a class of alkyl-substituted 4-quinopyran chromophores. We find that TPA cross sections diverge as the one-photon gap energy nears one-half of the two-photon gap. The molecular strategy proposed here to tune these two-excitation gaps for maximizing TPA cross sections is to twist the molecule about the bond connecting the chromophore donor and acceptor phenylene fragments. Extremely large TPA cross sections, determined by the absorption bandwidth, can then be realized (imaginary part of the third-order polarizability similar to 2.6 x 10(5) x 10(-36) esu) for fundamental photon energies near 1.0 eV, when the torsional angle approaches 104 degrees. The required torsional angle is achieved by introduction of sterically encumbered 2,2',2",2'" tertiary alkyl substituents.