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A family of non-empirical double-hybrid (DH) density functionals, such as Perdew–Burke–Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet 1La and 1Lb states of linear oligoacenes as well as the triplet 3La and 3Lb states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S0–T1 singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive results. [ABSTRACT FROM AUTHOR]

The energy difference (ΔEST) between the lowest singlet (S1) state and the triplet (T1) excited state of a set of azaphenalene compounds, which is theoretically and experimentally known to violate Hund's rule, giving rise to the inversion of the order of those states, is calculated here with a family of double-hybrid density functionals. That excited-state inversion is known to be very challenging to reproduce for time-dependent density functional theory employing common functionals, e.g., hybrid or range-separated expressions, but not for wavefunction methods due to the inclusion of higher-than-single excitations. Therefore, we explore here if the last developed family of density functional expressions (i.e., double-hybrid models) is able to provide not only the right excited-state energy order but also accurate ΔEST values, thanks to the approximate inclusion of double excitations within these models. We herein employ standard double-hybrid (B2-PLYP, PBE-QIDH, and PBE0-2), range-separated (ωB2-PLYP and RSX-QIDH), spin-scaled (SCS/SOS-B2PLYP21, SCS-PBE-QIDH, and SOS-PBE-QIDH), and range-separated spin-scaled (SCS/SOS-ωB2-PLYP, SCS-RSX-QIDH, and SOS-RSX-QIDH) expressions to systematically assess the influence of the ingredients entering into the formulation while concomitantly providing insights for their accuracy. [ABSTRACT FROM AUTHOR]

We have systematically analyzed the performance of some representative double-hybrid density functionals (including PBE0-DH, PBE-QIDH, PBE0-2, XYG3, XYGJ-OS, and xDH-PBE0) for a recently introduced database of diene isomerization energies. Double-hybrid models outperform their corresponding hybrid forms (for example, PBE0-DH, PBE0-2, and PBE-QIDH are more accurate than PBE0) and the XYG3, XYGJ-OS, and xDH-PBE0 functionals perform excellently, providing root mean square deviation values within "calibration accuracy." XYGJ-OS and xDH-PBE0 also rival the best performing post-Hartree-Fock methods at a substantially lower cost. [ABSTRACT FROM AUTHOR]

The calculation of the bond-length alternation (BLA) in trans-polyacetylene has been chosen as benchmark to emphasize the effect of the self-interaction error within density-functional theory (DFT). In particular, the BLA of increasingly long acetylene oligomers has been computed using the Mo\ller-Plesset wave-function method truncated at the second order and several DFT models. While local-density approximation (LDA) or generalized gradient corrected (GGA) functionals strongly underestimate the BLA, approaches including self-interaction corrections (SIC) provide significant improvements. Indeed, the simple averaged-density SIC scheme (ADSIC), recently proposed by Legrand et al. [J. Phys. B 35, 1115 (2002)], provides better results for the structure of large oligomers than the more complex approach of Krieger et al. [Phys. Rev. A 45, 101 (1992)]. The ADSIC method is particularly promising since both the exchange-correlation energy and potential are improved with respect to standard LDA/GGA using a physically appealing correction, through a different route than the more popular approach through the Hartree-Fock exchange inclusion within the hybrid functionals. [ABSTRACT FROM AUTHOR]

The use of density functional theory to obtain energy differences related to magnetic coupling constants is debated with special emphasis to the claims by Ruiz et al. [J. Chem. Phys.123, 164110 (2005)] that good agreement with experiment using the B3LYP potential is obtained by ignoring spin symmetry in case self-interaction error cannot be removed. [ABSTRACT FROM AUTHOR]

We theoretically study the excited-state properties of cycloparaphenylenes ([n]CPPs) for a deeper understanding of their photochemical properties with increasing size n, being n = 6 - 12 the number of repeat units forming the nanoring. We apply hybrid (e.g., PBE0 and PBE0-1/3), double-hybrid (e.g., PBE0-DH and PBE-QIDH) and range-separated (e.g., ω B97X) functionals within a Time-Dependent (Tamm–Dancoff) Density Functional Theory framework. For the [6]CPP case, we concomitantly address changes in the set of selected excited states when going from an isolated molecule to a pair of self-assembled molecules, employing for that a dimer of parallel-like or tubular-like molecules according to the solid-state supramolecular organization found in real samples. These nanorings challenge standard theoretical methods due to the compromise needed between medium-range intramolecular (in isolated molecules) and long-range intermolecular (for weakly interacting pairs of molecules in condensed phases) interactions. [ABSTRACT FROM AUTHOR]

In a comparative study, the doublet and quartet electronic states of the 2-pyridone+ cation are calculated using the PBE0/6-311+G(d,p) technique and the CASSCF and MRCI(+Q) methods in connection with the cc-pVDZ and cc-pVTZ Dunning's basis sets. Our data show that TD-DFT describes quite well the vertical excitation energies of these electronic states, whereas, multiconfiguration methods should be used for the investigation of the fragmentation and the dynamics of this molecular species. This is related to the change of the nature of the wavefunction of these electronic states along the corresponding reactive coordinates not accounted for by TD-DFT methods. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [ABSTRACT FROM AUTHOR]

The present work assesses some recently developed double-hybrid density functionals (B2π-PLYP, PBE0-DH, and PBE0-2) using linear-response Tamm-Dancoff Time-Dependent Density Functional Theory. This assessment is achieved against experimentally derived low-lying excitation energies of large organic dyes of recent interest, including some excitations dominated by charge-transfer transitions. Comparisons are made with some of the best-performing methods established from the literature, such as PBE0 or B3LYP hybrid or the recently proposed B2-PLYP and B2GP-PLYP double-hybrid models, to ascertain their quality and robustness on equal footing. The accuracy of parameter-free or empirical forms of double-hybrid functionals is also briefly discussed. Generally speaking, it turns out that double-hybrid expressions always provide more accurate estimates than corresponding hybrid methods. Double-hybrid functionals actually reach averaged accuracies of 0.2 eV, that can be admittedly considered close to any intended accuracy limit within the present theoretical framework. [ABSTRACT FROM AUTHOR]