Excitation energies in DFT: An evaluation and a diagnostic test

Michael J. G. Peach, Peter Benfield, Trygve Helgaker, David J. Tozer, J. Chem. Phys. 128 044118 (2008)


In my most-widely known paper, which started as a 4th year Masters project for a student working in our research group, we developed the ‘Lambda diagnostic’ that has subsequently been implemented in several major electronic structure codes. This paper includes an extensive assessment of several representative exchange–correlation functionals, for the evaluation of theoretically challenging vertical excitation energies. It also introduced the ‘Lambda diagnostic’ that may be used to determine when TDDFT singlet excitation energies are liable to be significantly in error.

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.


Electronic excitation energies are determined using the CAM-B3LYP Coulomb-attenuated functional [ T. Yanai et al. Chem. Phys. Lett. 393, 51 (2004) ], together with a standard generalized gradient approximation (GGA) and hybrid functional. The degree of spatial overlap between the occupied and virtual orbitals involved in an excitation is measured using a quantity Λ, and the extent to which excitation energy errors correlate with Λ is quantified. For a set of 59 excitations of local, Rydberg, and intramolecular charge-transfer character in 18 theoretically challenging main-group molecules, CAM-B3LYP provides by far the best overall performance; no correlation is observed between excitation energy errors and Λ, reflecting the good quality, balanced description of all three categories of excitation. By contrast, a clear correlation is observed for the GGA and, to a lesser extent, the hybrid functional, allowing a simple diagnostic test to be proposed for judging the reliability of a general excitation from these functionals—when Λ falls below a prescribed threshold, excitations are likely to be in very significant error. The study highlights the ambiguous nature of the term “charge transfer,” providing insight into the observation that while many charge-transfer excitations are poorly described by GGA and hybrid functionals, others are accurately reproduced.

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