Schematic overview of two possible photoisomerization mechanisms for azobenzene: rotation around the central CNNC dihedral angle ω (upper panel) and inversion around one of the NNC angles α (lower panel).
Two-dimensional relaxed ΔSCF(GGA-PBE) PES scans of rotation around the dihedral CNNC angle ω and inversion around one of the two CNN angles α, cf. Fig. 1. Shown are the ground-state S0 (left), the first excited state S1 (center), and the second excited state S2 (right). Energies relative to the zero reference E-Ab ground state energy are given in eV.
PES scans along the rotational (left) and inversion (right) pathway, cf. Fig. 1. Shown are the ground-state (S0, black), first (S1, red), and second (S2, blue) excited states, calculated each time with ΔSCF(GGA-PBE) (solid line), TDDFT(GGA-PBE) (dotted line) and RI-CC2 (dashed line).
PES scan along the inversion pathway, calculated with ΔSCF (left side) and TDDFT (right side). Shown are the ground-state (S0, black), first (S1, red), and second (S2, blue) excited states, calculated each time with an LDA (dashed line), GGA-PBE (straight line), and B3LYP (dotted line) functional. Also shown for the TD-DFT case is the pathway calculated with the CAM-B3LYP functional (dashed-dotted line).
Scan along the inversion pathway, comparing the S2 PES as calculated with TD-DFT(GGA-PBE) when following the HOMO-1→LUMO excitation (red dotted line) and when following the transition with predominant π → π* character (green dotted line). Only the latter approach yields the correct PES topology with sizable barrier around mid-inversion as compared to RI-CC2 (dashed line) and ΔSCF(GGA-PBE) (solid line). Also shown are the CT Λ-values94 for the two TD-DFT curves (see text), as well as the LUMO and the “wrong” HOMO-1 orbital at mid-inversion. The latter nicely reveals the pronounced CT-character of this transition.
Energetic positions of GGA-PBE KS frontier orbitals along the inversion pathway as resulting from a self-consistent ground-state calculation (upper panel) and as resulting from a self-consistent ΔSCF calculation for the S2 excitation (lower panel). Additionally shown are the corresponding KS ground-state orbital shapes at Z-Ab (left) and E-Ab (right).
Optimized geometry parameters of E and Z azobenzene in ground (S0) and excited (S1 and S2) states, cf. Fig. 1 for the definition of the azo-bridge bond length d NN and the two angles ω and α. Additionally shown are the relative energies ΔE of the corresponding states with respect to the ground-state E-Ab zero reference. None of the methods identified a stable minimum after optimization from S1 Z-Ab, which is why the corresponding entries have been left blank in the table.
Vertical excitation energies for S1 and S2 excitation at E-Ab and Z-Ab at the different levels of theory and from experiment.
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