Vertical transition energies vs. absorption maxima: Illustration with the UV absorption spectrum of ethylene

• Calibrating vertical transition energy calculations against experimental absorption maxima is not always adequate.
• The discrepancy between both quantities can be larger than the expected accuracy of 0.1 eV even in the harmonic case.
• The first Rydberg and valence transitions of ethylene are two examples of such a discrepancy.
• The valence transition is nonvertical and too anharmonic, and the average transition energy is a safer estimate.
• The band origin of the Rydberg transition seems to have been confused for the absorption maximum.

We revisit the validity of making a direct comparison between measured absorption maxima and computed vertical transition energies within 0.1 eV to calibrate an excited-state level of theory. This is illustrated on the UV absorption spectrum of ethylene for which the usual experimental values of 7.66 eV (V ← N) and 7.11 eV (R(3s) ← N) cannot be compared directly to the results of electronic structure calculations for two very different reasons. After validation of our level of theory against experimental data, a new experimental reference of 7.28 eV is suggested for benchmarking the Rydberg state, and the often-cited average transition energy (7.80 eV) is confirmed as a safer estimate for the valence state.

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