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  Double-hybrid density functional theory for excited electronic states of molecules

Grimme, S., & Neese, F. (2007). Double-hybrid density functional theory for excited electronic states of molecules. The Journal of Chemical Physics, 127(15): 154116. doi:10.1063/1.2772854.

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Grimme, Stefan1, Author
Neese, Frank2, Author           
1Theoretische Organische Chemie, Organisch-Chemisches Institut der Universität Münster, Corrensstraße 40, D-48149 Münster, Germany, ou_persistent22              
2Lehrstuhl für Theoretische Chemie, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany, ou_persistent22              


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 Abstract: Double-hybrid density functionals are based on a mixing of standard generalized gradient approximations (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), respectively. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chemistry applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent density functional theory (TD-DFT) or the closely related Tamm-Dancoff approximation (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to configuration interaction with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. [Chem. Phys. Lett. 219, 21 (1994)] is computed on the basis of density functional data and added to the TD(A)-DFT∕GGA excitation energy. The method is implemented by applying the resolution of the identity approximation and the efficiency of the code is discussed. Extensive tests for a wide variety of molecules and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from reference data typically <0.2eV) are obtained that are mostly better than those from standard functionals. Still, systematic errors are obtained for Rydberg (too low on average by about 0.3eV) and charge-transfer transitions but due to the relatively large ax
parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases.


Language(s): eng - English
 Dates: 2007-05-242007-10-192007-10-21
 Publication Status: Issued
 Pages: 18
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1063/1.2772854
 Degree: -



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Title: The Journal of Chemical Physics
  Abbreviation : J. Chem. Phys.
Source Genre: Journal
Publ. Info: Woodbury, N.Y. : American Institute of Physics
Pages: - Volume / Issue: 127 (15) Sequence Number: 154116 Start / End Page: - Identifier: ISSN: 0021-9606
CoNE: https://pure.mpg.de/cone/journals/resource/954922836226