[Paper Review] A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Bicyclic Systems

Pierre‐François Loos, Denis Jacquemin|arXiv (Cornell University)|Sep 28, 2021

Photochemistry and Electron Transfer Studies160 references42 citations

TL;DR

This study presents highly accurate vertical excitation energies (VTEs) for 91 excited states in 10 bicyclic organic molecules using CC3 and CCSDT methods with aug-cc-pVTZ basis sets, establishing a new benchmark set for larger systems. The reference data enable systematic benchmarking of 16 wave function methods, revealing that ADC(2) and CC2 improve in accuracy with increasing system size, while CCSD and EOM-MP2 deteriorate, offering critical guidance for selecting cost-effective methods in excited-state calculations for chromophores and fluorophores.

ABSTRACT

Pursuing our efforts to define highly-accurate estimates of the relative energies of excited states in organic molecules, we investigate, with coupled-cluster methods including iterative triples (CC3 and CCSDT), the vertical excitation energies of 10 bicyclic molecules (azulene, benzoxadiazole, benzothiadiazole, diketopyrrolopyrrole, fuofuran, phthalazine, pyrrolopyrrole, quinoxaline, tetrathiafulvalene, and thienothiophene). In total, we provide \emph{aug}-cc-pVTZ reference vertical excitation energies for 91 excited states of these relatively large systems. We use these reference values to benchmark various wave function methods, i.e., CIS(D), EOM-MP2, CC2, CCSD, STEOM-CCSD, CCSD(T)(a)*, CCSDR(3), CCSDT-3, ADC(2), ADC(2.5), ADC(3), as well as some spin-scaled variants of both CC2 and ADC(2). These results are compared to those obtained previously on smaller molecules. It turns out that while the accuracy of some methods is almost unaffected by system size, e.g., CIS(D) and CC3, the performance of others can significantly deteriorate as the systems grow, e.g., EOM-MP2 and CCSD, whereas others, e.g., ADC(2) and CC2, become more accurate for larger derivatives.

Motivation & Objective

• To extend the QUEST database by providing highly accurate theoretical best estimates (TBEs) for excited states in larger, chemically relevant bicyclic systems with 8–10 non-hydrogen atoms.
• To assess the size-dependent performance of common wave function methods (e.g., CC2, ADC(2), EOM-MP2) in predicting vertical excitation energies.
• To identify computationally efficient methods that maintain high accuracy for larger organic chromophores used in dye and fluorophore applications.
• To provide a reference dataset for validating lower-level methods, including TD-DFT functionals and approximate coupled-cluster approaches.

Proposed method

• Computed ground-state geometries at the CC3/cc-pVTZ level with symmetry constraints using CFOUR.
• Performed CCSD/aug-cc-pVTZ calculations to screen excited states and identify orbital character (valence, Rydberg, CT) via orbital analysis and transition density matrices.
• Used CC3 with multiple basis sets (6-31+G(d), aug-cc-pVDZ, aug-cc-pVTZ) and cross-validated results between CFOUR and DALTON for consistency.
• Calculated corrected VTEs for singlet states using double-𝜁 CCSDT values and basis set extrapolation, with CC3 used as reference for triplet states.
• Benchmarked 16 methods including CIS(D), EOM-MP2, CC2, ADC(2), ADC(3), STEOM-CCSD, and spin-scaled variants against the TBEs.
• Defined charge-transfer character using two metrics: electron-hole distance from ADC(2) and Le Bahers’ model with CAM-B3LYP, with CT considered significant if >1 Å.

Experimental results

Research questions

• RQ1 How does the accuracy of common wave function methods for excited states vary with increasing molecular size, particularly for systems with 8–10 non-hydrogen atoms?
• RQ2 Which low-cost methods (e.g., CC2, ADC(2)) maintain or improve accuracy for larger conjugated systems compared to smaller ones?
• RQ3 To what extent do methods like EOM-MP2 and CCSD deteriorate in accuracy as system size increases, and why?
• RQ4 Can CC3 provide reliable reference VTEs for both singlet and triplet excited states in large, complex organic molecules?
• RQ5 How do spin-scaled variants of CC2 and ADC(2) perform relative to their standard counterparts in larger systems?

Key findings

• ADC(2) and CC2 show improved accuracy with increasing system size, with MAE values halved for larger molecules compared to smaller ones.
• CCSD and EOM-MP2 exhibit deteriorating performance as molecular size increases, with EOM-MP2’s MAE quadrupling and CCSD’s MAE rising from 0.07 to 0.18 eV.
• CC3 delivers consistently high accuracy (MAE ≈ 0.02 eV) across all system sizes and excitation types, making it a robust reference for large chromophores.
• ADC(2.5) outperforms CC2, ADC(2), and STEOM-CCSD with accuracy comparable to more expensive methods like CCSD(T)(a)* and CCSDT-3, at a similar computational cost.
• Spin-scaled variants of CC2 and ADC(2) (e.g., SOS-CC2, SOS-ADC(2)) show mixed performance, with some variants improving accuracy but not consistently across all systems.
• The benchmark set includes 58 singlet, 33 triplet, 60 valence, 17 Rydberg, and 13 charge-transfer excited states, offering broad coverage for diverse electronic transitions.