Theoretical Insights of the Non-Rigid Behavior of Benzophenone by Franck-Condon Factors Approach

Abstract

Benzophenone is a molecule with several extremely relevant characteristics, widely used as a type-2 photoinitiator due to its unique electronic properties and a very efficient intersystem crossing. In general, benzophenone can absorb directly to S₁ or S₂ states, but S₀ → S₁ transition is weak. Also, benzophenone has symmetric activity of the torsional modes of the phenyl groups, suggesting that is a non-rigid molecule. This work has two fundamental purposes. The first is to examine the ground state (S₀) and first singlet excited state (S₁) of benzophenone using TD-DFT methodology to generate the potential energy surface (PES) to understand its non-rigid behavior; and the second, to examine the Franck-Condon factors (FC factors) between the transition S₀ → S₁. From our results, the most accurate was the hybrid functional PBE0. From the PES analysis of S₀ and S₁ states, we observe that several minima were located and that they are separated by relative low energy barriers. The global minimum of S₀ is found at θ₁/θ₂ = 28.15° and for S₁ at θ₁/θ₂ = 20.71°. Interestingly, the PES of S₁ state shows a very extensive area of minimum energy and a local minimum located at θ₁ = 90.71°/θ₂ = 0.71°. From the vibrational spectra, we observe two intense signals that correspond to the symmetric phenyl twisting of normal mode 2 (2³ and 2⁴), and a combination between the symmetric hydrogen scissoring of 44¹ and 2³. As the vibronic spectrum tells, this transition is forbidden by the orbital theory but it is electronically allowed. Also, from the Duschinksy matrix, we observe a high mixing of vibrational modes.