Failure of density-functional theory and time-dependent density-functional theory for large extended π systems

Abstract

Density-functional theory ͑DFT͒ is widely used for studying large systems such as metals, semiconductors, and large molecules, with time-dependent density-functional theory becoming a very powerful tool for investigating molecular excited states. As part of a systematic study of both the intrinsic weaknesses of DFT and the weaknesses of present implementations, we consider its application to the one and two-dimensional conjugated systems: polyacetylene fragments and oligoporphyrins, respectively. Very poor results are obtained for the calculated spectra, and polyacetylene is predicted by all functionals considered, including gradient-corrected functionals, to have a triplet ground state. The cause of this is linked to known problems of existing density functionals concerning nonlocality and asymptotic behavior which result in the highest-occupied molecular-orbital being too high in energy so that semiconductors and low-band-gap insulators are predicted to have metal-like properties. The failure of modern density functionals to predict qualitatively realistic molecular hyperpolarizabilities for extended systems is closely related.

Theoretical Investigation of Excited States of Large Polyene Cations as Model Systems for Lightly Doped Polyacetylene

“…43,44,85 TDDFT, pure as well as hybrid, increasingly underestimates excitation energies of conjugated systems with increasing chain length. 42,45,46,[86][87][88] Since high level ab initio methods become prohibitively expensive for long chain cations, TDHF and TDDFT will be tested here for excited-state calculations on polyene cations.…”

Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters

“…[1][2][3] At the same time, the failure of TDDFT to correctly describe charge-transfer (CT) states is well-known. [4][5][6] Also Rydberg states, excited states of extended π-conjugated systems, 7,8 and multiply excited states 9,10 cause difficulties. To solve conceptual short-comings, great effort has been made to search for improved functionals that reliably describe CT states, and in particular, long-range corrected (LRC) functionals featuring varying amounts of non-local exchange were developed for this purpose.…”

“…However, some cases like extended symmetric π-conjugated systems, e.g., acenes, cause significant but hard-to-detect errors. 7,8,20 For these systems, the overlap of the canonical orbitals is not a good predictor of the performance of TDDFT [20][21][22][23] and a more complex dynamical view has to be adopted.…”

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree–Fock

“…If the products of occupied times unoccupied orbitals, or more precisely the products W ia (r) = ε −1/2 ia λ ia (ω)ϕ ia (r) were linear independent then Eq. (14) would imply the matrix equation…”

“…(iii) Excitation energies of long chain-like aromatic molecules [12][13][14][15][16] are systematically underestimated by conventional TDDFT response methods.…”