State-average complete active space self-consistent field (SA-CASSCF) calculations are performed on the energetically lowest two electronic states of a novel alkyl-substituted 4-quinopyran twisted pi-system electro-optic chromophore. In the gas phase, the ground-state electronic configuration is diradicaloid (D), and the first excited state is zwitterionic (Z). When an external dipolar field is applied to simulate polar solvation, the relative energies of D and Z are dramatically perturbed. At sufficient field strengths, the relative ordering of the states is inverted so that Z becomes the ground state. As the energy difference between the D and Z states falls, the magnitudes of the longitudinal static polarizability (alpha) and hyperpolarizability (beta) increase appreciably-in certain cases, by 2 orders of magnitude. These computational results are interpreted and supported by qualitative state correlation diagrams constructed from qualitative molecular orbital theory and are in agreement with recent experimental results on twisted pi-system electro-optic chromophores (Kang, H. et al. J. Am. Chem. Soc. 2007, 129, 3267). The computational results also suggest that changing the environmental polarity is a promising strategy for tuning alpha and beta in such types of chromophores, which experimentally exhibit large nonlinear optical response.