An example of the procedure to define the “mother” states. On the left we report the initial states of a hypothetical molecule with a Boltzmann population higher than a given threshold. On the right we report how they are grouped into the “mother states.” Note that a full grouping would have lead to the unique mother state ∣3, 2, 1, 0, 0,…⟩, with the implicit inclusion of six initial states (e.g., ∣3, 1, 0, 0, 0,…⟩) with a negligible Boltzmann population). Only one negligible state ∣2, 2, 0, 0, 0, …⟩) is included according to our strategy.
Schematic drawing of the anti conformer of C153 (a), of porphyrazine (b), and of the trans-isomer of stilbene (c).
Absorption spectrum of the anti isomer of C153 in cyclohexane convoluted with a Gaussian with . Panel a: convergence with , panel b: stick and convoluted spectra at , and panel c: stick and convoluted spectra at .
Computed phosphorescence spectrum of porphyrazine in gas phase at (short-dashed line) and with two different thresholds of the Boltzmann population for the inclusion of the initial states (0.4 and 0.3, respectively, dash-dotted and solid lines). The spectra have been convoluted with a Gaussian with .
(a) Absorption spectrum of trans-stilbene computed in cyclohexane at (solid line), 77 (dotted line), and (dot-dashed line), convoluted with a Gaussian with and normalized so that the maximum of their second band is equal. (b) Comparison of the computed spectrum (blueshifted by ) with the experimental spectrum in 3-methylpentane at 35. (c) Comparison of the computed spectrum (blue-shifted by ) with the experimental spectrum in cyclohexane at 34.
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