Excited State Absorption: Reference Oscillator Strengths, Wavefunction and TD-DFT Benchmarks

Abstract: Excited-state absorption (ESA) corresponds to the transition between two electronic excited states and is a fundamental process for probing and understanding light-matter interactions. Accurate modeling of ESA is indeed often required to interpret time-resolved experiments. In this contribution, we present a dataset of 53 ESA oscillator strengths in three different gauges and the associated vertical transition energies between 71 excited states of 23 small- and medium-sized molecules from the QUEST database. The reference values were obtained within the quadratic-response (QR) CC3 formalism using eight different Dunning basis sets. We found that the d-aug-cc-pVTZ basis set is always adequate while its more compact double-$\zeta$ counterpart, d-aug-cc-pVDZ, performs well in most applications. These QR-CC3 data allow us to assess the performance of QR-TDDFT, with and without applying the Tamm-Dancoff approximation, using a panel of global and range-separated hybrids (B3LYP, BH{&}HLYP, CAM-B3LYP, LC-BLYP33, and LC-BLYP47), as well as several lower-order wavefunction methods, i.e., QR-CCSD, QR-CC2, EOM-CCSD, ISR-ADC(2), and ISR-ADC(3). We show that QR-TDDFT delivers acceptable errors for ESA oscillator strengths, with CAM-B3LYP showing particular promise, especially for the largest molecules of our set. We also find that ISR-ADC(3) exhibits excellent performance

• The paper compiled a dataset of 53 excited state absorption oscillator strengths for 21 molecules to benchmark computational methods.
• Reference values were computed using QR-CC3, finding that QR-TDDFT with CAM-B3LYP and ISR-ADC(3) offer promising accuracy for ESA calculations.
• The benchmark dataset and method evaluations provide a valuable resource for selecting computational approaches in studies leveraging excited state absorption.

Excited State Absorption: Evaluation of Reference Oscillator Strengths, Wavefunction, and TD-DFT Benchmarks

The paper undertakes a comprehensive study of excited-state absorption (ESA) processes and their significance in understanding light-matter interactions. ESA, characterized by transitions between two excited states, plays a pivotal role in various photophysical and technological applications, including solar energy, lasers, and optical sensors. This study is focused on developing a dataset that can be used to benchmark various electronic structure methods for modeling ESA.

Methodological Overview

• Dataset Development: The authors have compiled a dataset containing 53 ESA oscillator strengths for 71 transitions among excited states of 21 molecules. The dataset spans valence and Rydberg excited states with a predominant single excitation character.
• Computational Techniques: The reference values were obtained through quadratic-response (QR) coupled-cluster singles, doubles, and triples (CC3) methods using the d-augmented Dunning basis sets, particularly favoring dAVDZ and dAVTZ for computational efficiency and accuracy.
• Wavefunction and TD-DFT Benchmarks: The dataset was used to evaluate the performance of various methods, including QR-TDDFT with and without the Tamm-Dancoff approximation (TDA) and several lower-order wavefunction methods. The methods analyzed comprise QR-CCSD, QR-CC2, EOM-CCSD, ISR-ADC(2), and ISR-ADC(3), as well as global and range-separated hybrid functionals (B3LYP, CAM-B3LYP, among others).

Numerical Analysis and Results

• Basis Set Effects: The study identifies the importance of including diffuse functions in the basis sets for accurate oscillator strength calculations, especially when dealing with Rydberg states. Double augmentation (dAVDZ) was found to provide a balance between computational cost and accuracy.
• Method Comparison: QR-TDDFT with CAM-B3LYP demonstrated promise in delivering acceptably low errors for ESA oscillator strengths, particularly for larger molecules. ISR-ADC(3) also exhibited competitive performance compared to higher computational cost methods like QR-CCSD.
• Insights on Methodologies Tested:
  • QR-CC Methods: QR-CC3 served as a reference, with excellent agreement observed among different gauges, corroborating the accuracy and reliability of this level of theory.
  • ISC-ADC Methods: These show potential, particularly at the ADC(3) level, for calculating ESA properties with accuracy close to the benchmark level.
  • TD-DFT and TDA: The application of TDA generally led to degraded performance, although full TD-DFT results are sensitive to the exchange-correlation functional used.
• Error Trends: The study identifies error magnitudes and trends across methods for different transition types (Rydberg-Rydberg, Rydberg-Valence, Valence-Valence), revealing where specific methodologies may excel or require caution.

Implications and Future Directions

The compilation of this dataset and the subsequent benchmarks hold substantial value for future studies on ESA, providing a strong foundation for method development and validation. The insights regarding basis sets and method accuracy can drive the choice of computational approaches in practical applications, aiding in the design and development of materials where ESA is leveraged.

Speculatively, future advancements may include broader exploration into multireference methods for states with substantial non-single-excitation character or further refinement of TD-DFT approaches to capitalize on their computational efficiency for larger systems. Additionally, the development of solvation models for QR methods would significantly extend the applicability of these techniques to more complex and realistic scenarios, encompassing the condensed phase or biological environments.

In conclusion, the research presented underscores the robustness of QR-CC3 as a reference standard, while showcasing the viability of certain TD-DFT and ADC implementations as cost-effective alternatives, particularly for larger scale analyses where computational resources may be limited.