Quantifying the Performances of DFT for Predicting Vibrationally Resolved Optical Spectra: Asymmetric Fluoroborate Dyes as Working Examples

This article aims at a quantitative assessment of the performances of a panel of exchange-correlation functionals, including semilocal (BLYP and PBE), global hybrids (B3LYP, PBE0, M06, BHandHLYP, M06-2X, and M06-HF), and range-separated hybrids (CAM-B3LYP, LC-ωPBE, LC-BLYP, ωB97X, and ωB97X-D), in predicting the vibrationally resolved absorption spectra of BF₂-carrying compounds. To this end, for 19 difluoroborates as examples, we use, as a metric, the vibrational reorganization energy (λ_vib) that can be determined based on the computationally efficient linear coupling model (a.k.a. vertical gradient method). The reference values of λ_vib were determined by employing the CC2 method combined with the cc-pVTZ basis set for a representative subset of molecules. To validate the performances of CC2, comparisons with experimental data have been carried out as well. This study shows that the vibrational reorganization energy, involving Huang–Rhys factors and normal-mode frequencies, can indeed be used to quantify the reliability of functionals in the calculations of the vibrational fine structure of absorption bands, i.e., an accurate prediction of the vibrational reorganization energy leads to absorption band shapes better fitting the selected reference. The CAM-B3LYP, M06-2X, ωB97X-D, ωB97X, and BHandHLYP functionals all deliver vibrational reorganization energies with absolute relative errors smaller than 20% compared to CC2, whereas 10% accuracy can be achieved with the first three functionals. Indeed, the set of examined exchange-correlation functionals can be divided into three groups: (i) BLYP, B3LYP, PBE, PBE0, and M06 yield inaccurate band shapes (λ_vib,TDDFT < λ_vib,CC2), (ii) BHandHLYP, CAM-B3LYP, M06-2X, ωB97X, and ωB97X-D provide accurate band shapes (λ_vib,TDDFT ≈ λ_vib,CC2), and (iii) LC-ωPBE, LC-BLYP, and M06-HF deliver rather poor band topologies (λ_vib,TDDFT > λ_vib,CC2). This study also demonstrates that λ_vib can be reliably estimated using the CC2 model and the relatively small cc-pVDZ basis set. Therefore, the linear coupling model combined with the CC2/cc-pVDZ level of theory can be used as a very efficient approach to determine λ_vib values that can be used to select the most adequate functional for more accurate vibronic calculations, e.g., including more refined models and environmental effects