Bis(benzofuranonyl)methanolate (BM4i4i) dye and croconate dyes (derivatives of oxyallyl molecules) in general are known to have intense transitions in the near-infrared (NIR) region, indicating small transition energies and large transition dipole moments. These molecules have been reported in the literature to have very large resonant third-order nonlinear optical (NLO) susceptibilities and molecular hyperpolarizabilities (gamma). In this work we investigate using density functional theory (DFT)/ab initio/symmetry adapted cluster-configuration interaction (SAC-CI) techniques the oxyallyl substructure and attribute the NIR transition and the NLO activity to this substructure, which is common in all these molecules. Using valence bond (VB) theory, an analysis of a three-state model of this substructure is carried out. It is seen that the mixture of an intermediate diradical character and some zwitterionic character in the molecule and a large coupling between these two VB resonance forms is responsible for large gamma values. This can be used as a design principle for increasing NLO activity in oxyallyl derivatives.