Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation

In this work we carefully investigate the relationship between computed data and experimental electronic spectra. To that end, we compare both vertical transition energies, E-v, and characteristic frequencies of the spectrum like the maximum, V-max, and the center of gravity, M-1, taking advantage of an analytical expression of M-1 in terms of the parameters of the initial- and final-state potential energy surfaces. After pointing out that, for an accurate comparison, experimental spectra should be preliminarily mapped from wavelength to frequency domain and transformed to normalized lineshapes, we simulate the absorption and emission spectra of several prototypical chromophores, obtaining lineshapes in very good agreement with experimental data. Our results indicate that the customary comparison of experimental V-max and computational E-v, without taking into account vibrational effects, is not an adequate measure of the performance of an electronic method. In fact, it introduces systematic errors that, in the investigated systems, are on the order of 0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of experimental and computed M-1 and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs are proposed to help rationalize which kind of correction one should expect when comparing E-v, M-1, and V-max.