Abstract
The photodimers with cyclobutane rings and C$_2$ symmetry, derived from coumarin (syn, head to tail and anti, head to head) have been calculated by PM3-UHF-CI and Molecular Mechanics force field. The photocycloaddition to coumarin and 5,7-dimethoxycoumarin(DMC) dimers were deduced to be formed by their preferable frontier orbital interactions and via more stable cycloaddition by the C$_3$, C$_4$ bond. These results are consistent with the coumarin dimer model that the theoretical C$_4$-photocyclodimer of coumarin is predicted much more than the experimental C$_4$-photocyclodimer.