Benchmarking the performance of time-dependent density functional methods

Abstract

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small-to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydbergexcited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0. The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small-to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.

On the Participation of Photoinduced N–H Bond Fission in Aqueous Adenine at 266 and 220 nm: A Combined Ultrafast Transient Electronic and Vibrational Absorption Spectroscopy Study

“…Electrostatic effects of aqueous solvation was taken into account using a polarizable continuum model, while the PBE0 functional 61 was selected for its balanced description of both excited valence and charge-transfer/Rydberg states, as shown by Leang et al, 62 and its reasonable description of electronic transitions in Ade. 29 All calculations were performed using the Gaussian09 computational package.…”

Dipole-Mediated Rectification of Intramolecular Photoinduced Charge Separation and Charge Recombination

“…The errors relative to the experimental spectrum lie well within the few tenths of an eV accuracy (which maps to a few tens of nanometers here) typically expected for valence excited states in TDDFT. 70 The lowest singlet excited state S 1 is predicted to occur at 353 nm in DCM. This excitation, which corresponds to a HOMO−LUMO transition, is the state accessed experimentally with 400 nm radiation.…”

Absorption and Emission Spectra of a Flexible Dye in Solution: A Computational Time-Dependent Approach

“…19 Although some problems have yet to be fully solved for multiple excitations, charge transfer and Rydberg states, for conventional valence excitations TDDFT based on hybrid (possibly rangeseparated) density functionals shows a nearly optimal balance between accuracy (related also to the continuous improvement of functionals) and computational inexpensiveness. [19][20][21][22] In this framework, the energy difference (or vertical energy, VE) between the ground (GS) and the electronically excited state (EES), which leads to the the VE absorption ( , computed at the GS equilibrium geometry) or emission ( calculated at the EES equilibrium geometry) wavelengths, can be calculated rather straightforwardly. 19 Unfortunately, these quantities alone are not always sufficient to reproduce the experimental band shapes and they cannot be directly compared to the measured maximal absorption ( ) or emission ( ) wavelengths.…”