Benchmark of Bethe-Salpeter for Triplet Excited-States

• Published in: Journal of chemical theory and computation Vol. 13; no. 2; pp. 767 - 783
• Main Authors: Jacquemin, Denis, Duchemin, Ivan, Blondel, Aymeric, Blase, Xavier
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 14.02.2017
• Subjects: Approximation; BSE; Chemical Sciences; Computation; Eigenvalues; Energy use; Excitation; Mathematical analysis; or physical chemistry; Permissible error; Theoretical and
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.6b01169

We have evaluated the accuracy of the Bethe-Salpeter singlet–triplet transition energies as well as singlet–triplet and triplet–triplet splittings for 20 organic molecules, using as reference the CC3 values determined by Thiel and co-workers with both the TZVP and aug-cc-pVTZ atomic basis sets. Our excitation energies are obtained on the basis of GW quasiparticle energy levels that are self-consistently converged with respect to the starting DFT eigenvalues. In its current form, BSE/GW is often unable to provide a balanced description of both singlet and triplet excited-states. While the singlet–singlet and triplet–triplet energy separations are obtained accurately, triplets are located too close in energy from the ground-state, by typically −0.55 eV when using standard functionals to generate the starting eigenstates. Applying the Tamm-Dancoff approximation upshifts the BSE triplet energies and allows reducing this error to ca. −0.40 eV, while using M06-HF eigenstates allows a further increase and hence a reduction of the error for triplet states, but at the cost of larger errors for the singlet excited-states. At this stage, the most accurate TD-DFT estimates therefore remain competitive for computing singlet–triplet transition energies. Indeed, with M06-2X, irrespective of the application or not of the Tamm-Dancoff approximation and of the selected atomic basis set, the deviations obtained with TD-DFT are rather small.