The geometry and the electronic structure of the tetracyclo-[6. 2.2.1(3,6).0(2,7)]trideca-4,9,11-triene-9,10-dicarboxylic anhydride (TTDA) have been investigated by DFT/B3LYP and DFT/B3PW91 methods using the 6-31G(d,p) and 6-311G(d,p) basis sets. Anhydride double bond of TTDA molecule is antipyramidalized. Potential energy surface of addition reaction of fulvene to 1:1DA molecule (syn,endo-, syn,exo-, anti,endo- and anti, exo-addition) is calculated by B3LYP/6-31G(d,p) method and configurations (transition state and product) corresponding to stationary points (saddle point and minima) are determined. Kinetic and thermodynamic parameters of cycloaddition reactions have also been calculated. Syn addition reactions have lower activation energies, enthalpies, entropies and free energies than anti addition reactions. Activation energies of syn,endo- and syn, exo-addition reactions are 25.032 and 23.210 kcal mai, respectively, while the anti, endo-addition reaction has the largest activation energy (28.763 kcal mol(-1)). According to theoretical calculations, syn addition reactions should take place in line with experimental conditions. There is a correlation between the syn-mface selectivity of the cycloaddition reaction and the pyramidalization of anhydride double bond of the TTDA molecule.