Influence of triplet instabilities in TDDFT

Michael J. G. Peach, Matthew J. Williamson, David J. Tozer, J. Chem. Theory Comput., 7, 3578–3585, 2011.


In our first major investigation of triplet excited states, we considered the difference in behaviour highlighted by Jacquemin and co-workers, between the exact exchange-dependence of singlet and triplet excited states. We showed (in a re-discovery of problems known from Hartree–Fock theory) that triplet states are plagued by instabilities (or near-instabilities) from the ground-state wavefunction. The problems are exacerbated as the amount of exact exchange in a functional increases. The Tamm–Dancoff approximation was shown to provide significant improvements for both singlet and triplet states of character similar to the wavefunction instabilities.

We are currently following up this work on a more demanding, newly developed benchmark set, and we link the instability problem to Lambda. Watch this space!

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.


Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange–correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree–Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm–Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.

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