An assessment of the low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach

The accurate prediction of singlet and triplet excitation energies is of significant fundamental interest and is critical for many applications. An area of intense research, most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiels set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relatively to higher level theories. Finally, we find that BSE-TDA calculations built on good DFT starting points, such as those utilizing optimally-tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.