Through the development of a new benchmark excitation set using EOM-CCSD excited states and the subsequent assessment of several representative exchange–correlation functionals, this paper brings together our work on two topics: orbital overlap and triplet instability problems in TDDFT. The first problem we quantify using Lambda, as defined in the 2008 Lambda paper. The second we quantify by computing triplet stability measures, as we did previously in our 2011 paper on triplet excited states. In this new work, we extend the application of Lambda to triplet excited states, and go on to show the implicit connection between Lambda and triplet instabilities: triplet stabilities must be associated with high orbital overlap (often caused by excitations between highly localised orbitals centred on the same area of a molecule, such as the low-lying excitations in aromatic systems). It is therefore not possible to have simultaneous failures of orbital overlap and triplet stability for the same excited state, although both problems can be seen in the same molecule.

Intuitively, the Tamm–Dancoff approximation also has a larger effect as the overlap increases (for small overlap, conventional and TDA excitation energies are identical). We illustrate that particularly high accuracy can be achieved using a combined Coulomb-attenuated Tamm–Dancoff approach.

Further information, including details of subsequent work in this area, can be found on the TDDFT diagnostic research page. For the abstract, and access to the full text, see below.

Low orbital overlap and triplet instability problems in TDDFT are investigated for a new benchmark set, encompassing challenging singlet and triplet excitation energies of local, charge-transfer and Rydberg character. The low orbital overlap problem is largely overcome for both singlet and triplet states by the use of a Coulomb-attenuated functional. For all the categories of functional considered, however, errors associated with triplet instability problems plague high overlap excitations, as exemplified by the excited states of acenes and polyacetylene oligomers. Application of the Tamm–Dancoff approximation reduces these errors for both singlet and triplet states, whilst leaving low-overlap excitations unaffected. The study illustrates the synergy between overlap and stability and highlights the success of a combined, Coulomb-attenuated Tamm–Dancoff approach.