Schematic state diagram showing the frontier orbitals in ground-state DFT, simple ΔSCF, leΔSCF with a ground-state reference, and leΔSCF with an excited-state reference. Projected reference states are in red. The excitation is visualized with an electron hole pair (filled and unfilled circles). Schematic orbital positions are shown for the non-self-consistent (non-sc) and the self-consistent (sc) case.
Gas-phase Azobenzene PESs along rotation (left) and inversion (right) degrees of freedom for the ground state (black), the first excited n → π* state (red), and the second excited π → π* state (blue). The excited-state curves were calculated with simple ΔSCF (no lines, gray circles), leΔSCF with ground-state reference orbitals (dashed lines, squares), and leΔSCF with excited-state reference orbitals (straight lines, crosses). The insets illustrate the corresponding Azobenzene degrees of freedom of dihedral rotation ω and inversion along one CNN angle α.
(Upper panels) Minimum-energy paths of Azobenzene adsorbed on Ag(111) following rotation (left) or inversion (right). Shown are the ground-state energy (black), the first (S1, red) and second (S2, blue) excited states as well as the corresponding gas-phase potential energy curves (in gray). Regions marked with dashes are of increased inaccuracy due to methodological restrictions further outlined in the text. Vertical dashed and dotted lines on the sides depict the position of E-Ab and Z-Ab minima for the adsorbed molecule. (Lower panels) For both degrees of freedom, rotation and inversion, the integrated occupation of the projected gas-phase HOMO (dashed line) and LUMO (dotted line) in the ground state are shown. The horizontal line marks half filling of an orbital.
Same as Fig. 3 , but for Azobenzene on Au(111).
Vertical excitation energies (in eV) for the first singlet excited state of Z-Ab (S1) and the second singlet excited state of E-Ab (S2), as well as the difference between them. Reference values shown are taken from experiments in solvent 67,88 and from high-level quantum chemical (RI-CC2) calculations for the isolated molecule. 37
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