This paper was part of a special issue honouring Professor Trygve Helgaker, of the University of Oslo. The work is a follow-up to some of my previous work on the triplet instability and how it can affect TDDFT excitation energies. In particular, this considers two aspects of this problem. One is the usefulness of using the stability of the Hartree–Fock single determinant wavefunction as an indication of when excitations will be unreliably described by conventional functionals in TDDFT. The second aspect involves the B97-2 functional, which displays a surprisingly small triplet instability problem, given the amount of exact exchange that the functional contains.

Tlhe utility of a Hartree-Fock triplet stability threshold, for identifying time-dependent d. functional theory triplet excitations for which the inclusion of exact orbital exchange is detrimental, is illustrated for a benchmark set of 63 excitations in 20 org. mols.  Following earlier spin-spin coupling observations that suggest a relatively small triplet instability problem, the accuracy of triplet excitation energies from the B97-2 hybrid functional is also quantified.  As anticipated, the results are relatively accurate and this is readily understood in terms of the stabilities.  Application of the Tamm-Dancoff approxn. dramatically improves all the triplet excitation energies corresponding to low stabilities, while also providing a modest improvement in the corresponding singlet states.