Molecular orbital computations using the configuration interaction singles method and complete active space self-consistent field method were used to map out the electronic ground and excited states of 1,3-dimethylallene. Both open-shell and closed-shell singlet configurations were taken into account. Potential Energy Surfaces (PES) for the ground and the first two excited states were obtained over a two-mode grid composed of the C-C-C bending angle and the dihedral angle between the planes defined by the carbon atoms of the H3C-C double bondC and C double bondC-CH3 groups. Several critical points located on the ground and first-excited PES were fully optimized by allowing all degrees of freedom to relax. The ground-state racemization reaction from the left-handed enantiomer to the right-handed was found to proceed via a barrier of 41 kcal/mol, in excellent agreement with the experimental value of 45.1 kcal/mol for the enthalpy of racemization. The ground-state transition-state geometry is shown to be planar-bent. The results indicate that 1,3-dimethylallene shows chiral structures in the ground state and achiral structures in the first-excited state. Coupled with the reported dipole-moment function, 1,3-dimethylallene is shown to be a useful molecule for coherently controlled racemic purification using our "laser distillation" scheme.