Spin-scaled double hybrids with long-range correction solve the TD-DFT overestimation problem in BODIPY dyes: benchmarking and experimental validation

Abstract

It has been established in the literature that time-dependent density functional theory (TD-DFT) methods systematically overestimate the electronic excitation energies in boron-dipyrromethene (BODIPY) dyes. Herein, we present the new SBYD31 benchmark set for BODIPY absorption energies and assess 28 different TD-DFT methods, most of which have not been tested on BODIPY dyes before. We show how functionals belonging to the class of recently developed spin-scaled double hybrids with long-range correction (J. Chem. Theory Comput., 2021, 17, 5165) overcome the overestimation problem and provide more robust results that have met the chemical accuracy threshold of 0.1 eV. To our knowledge, these are the most accurate absorption energies for BODIPY dyes reported for TD-DFT methods. In passing, we also point out how previous recommendations of "DSD" double hybrids, incl. one published in this journal (RSC. Adv., 2022, 12, 1704; Comput. Theor. Chem., 2022, 1207, 113531), were based on incorrect interpretations of the results. Our top-three recommended methods are SOS-ωB2GP-PLYP, SCS-ωB2GP-PLYP and SOS-ωB88PP86 and we verify our recommendations by making predictions, which we confirm with experimental measurements of newly synthesised BODIPY dyes. Our results add to existing evidence how time-dependent double hybrids with spin-component scaling and long-range correction solve notoriously hard cases for conventional TD-DFT methods and we are confident that our recommendations will assist in future developments of BODIPY dyes.

Fig. 1. The SBYD31 set.

Scheme 1. Synthesis of BODIPYs 1, B3, 2 and 3. Reaction conditions: (a) (i) CH₂Cl₂/TFA, 18 h, N₂, rt, (ii) DDQ, (iii) Et₃N/BF₃–OEt₂; (b) toluene, AcOH, piperidine, p-N,N-dimethylaminobenzaldehyde, MW, 20 min; (c) CH₂Cl₂/MeOH (9 : 1), NaOH, rt; (d) DMF, NHS, EDC, N₂, rt.

Fig. 2. TD-DFT results in the form of a bar chart; (a) MAE, (b) MSE and (c) error range (all in eV).

Fig. 3. (a) Comparison between the methods with best (SOS-RSX-QIDH) and worst R² values (B3LYP). (b) Radar chart showing the overall performance of select functionals.

Fig. 4. MAEs (in eV) for the assessed TDA-DFT methods.