(6/6)CASSCF and CASPTU6-31G* calculations have been performed to understand the experimental finding of Goldstein and Benzon (J. Ant. Chern. Sec. 1972, 94, 5119) that exo-bicyclo[2.2.0]hexane-d(4) (1b) undergoes ring inversion to form endo-bicyclo[2.2.0]hexane-d(4) (4b) faster than it undergoes cleavage to form cis, trans-1,5-hexadiene-d(4) (3b). Goldstein and Benzon also found that the latter reaction, which must occur via a chairlike transition structure (TS), is much faster than cleavage of Ib to trans, trans-1,5-hexadiene-d(4) (2b) via a boatlike TS. Our calculations reveal that all three of these reactions involve ring opening of 1, through a boat diradical TS (BDTS), to form a twist-boat diradical intermediate (TBDI). TBDI can reclose to 4 via a stereoisomeric boat diradical TS (BDTS'), or TBDI can cleave, either via a half-chair diradical TS (HCDTS) to form 3 or via a boat TS (BTS) to form 2. The calculated values of DeltaH(double dagger) = 34.6 kcal/mol, DeltaS(double dagger) = -1.6 eu, and DeltaH(double dagger) = 35.2 kcal/mol, DeltaS(double dagger) = 2.0 eu for ring inversion of 1 to 4 and cleavage of 1 to 3, respectively, are in excellent agreement with the values measured by Goldstein and Benzon. The higher value of DeltaH(double dagger) = 37.6 kcal/mol, computed for cleavage of TBDI to 2, is consistent-with the experimental finding that very little 2b is formed when Ib is pyrolyzed. The relationships between BDTS, HCDTS, and BTS and the chair and boat Cope rearrangement TSs (CCTS and BCTS) are discussed.