Exploring potential crossing seams in periodic systems: Intersystem crossing pathways in the benzene crystal

The intersystem crossing (ISC) pathways of triplet benzene molecules in a benzene crystal were investigated theoretically. A combination of the gradient projection (GP) method, which is a standard method for optimizing the crossing seam of two potential energy surfaces, and the single-component artificial-force-induced reaction (SC-AFIR) method (GP/SC-AFIR) was used. This is the first reported use of a GP/SC-AFIR calculation using a density functional theory calculation with periodic boundary conditions. A systematic search for the minimum-energy structures in the seams of crossing of the singlet (S₀) and triplet (T₁) potential energy surfaces (S₀/T₁-MESX structures) found 39 independent S₀/T₁-MESX structures. Energy barriers between the S₀/T₁-MESX and the stationary structure of the triplet state (T₁-MIN) were computed, and then two competing ISC pathways were extracted; the calculated overall energy barrier to the intermolecular C-C-bonded type (SX3) and the out-of-plane bent C-H type (SX15) S₀/T₁-MESX structures from T₁-MIN were 0.26 and 0.27 eV, respectively. The rate constants for SX3 and SX15 formation were estimated to be 5.07 × 10⁸ and 2.17 × 10⁸ s^-1 (at 273 K), respectively, or 9.73 × 10^-5 and 4.78 × 10^-6 s^-1 (at 77 K), respectively. At 273 K, which is close to the melting point of the benzene crystal (278.5 K), SX3 and SX15 are easily accessible from T₁-MIN, and ISC could occur through the S₀/T₁-MESX points. By contrast, at 77 K, T₁-MIN survives long enough for phosphorescence to compete with ISC.