Article pubs.acs.org/JCTC
Investigation of Multiconfigurational Short-Range Density Functional Theory for Electronic Excitations in Organic Molecules Mickael̈ Hubert,† Erik D. Hedegård,‡ and Hans Jørgen Aa. Jensen*,† †
Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
‡
S Supporting Information *
ABSTRACT: Computational methods that can accurately and effectively predict all types of electronic excitations for any molecular system are missing in the toolbox of the computational chemist. Although various Kohn−Sham density-functional methods (KS-DFT) fulfill this aim in some cases, they become inadequate when the molecule has near-degeneracies and/or low-lying double-excited states. To address these issues we have recently proposed multiconfiguration short-range density-functional theoryMC-srDFTas a new tool in the toolbox. While initial applications for systems with multireference character and double excitations have been promising, it is nevertheless important that the accuracy of MC-srDFT is at least comparable to the best KS-DFT methods also for organic molecules that are typically of single-reference character. In this paper we therefore systematically investigate the performance of MC-srDFT for a selected benchmark set of electronic excitations of organic molecules, covering the most common types of organic chromophores. This investigation confirms the expectation that the MC-srDFT method is accurate for a broad range of excitations and comparable to accurate wave function methods such as CASPT2, NEVPT2, and the coupled cluster based CC2 and CC3.
1. INTRODUCTION Kohn−Sham density-functional theory (KS-DFT) altered the role of computational chemistry up through the 1990s due to its computational efficiency combined with its often sufficiently accurate results.1−5 This is also true for predictions of electronic excitations and their associated oscillator strengths, for which time-dependent KS-DFT variants have been used extensively, and for many molecules with good results.6 Now, two decades later, it is clear that KS-DFT is not without inherent problems. We here want to draw the attention to two problems. First, KSDFT is known to break down for degenerate or neardegenerate electronic ground states, where a correct description requires a multiconfigurational ansatz.7,8 Second, the use of the time-dependent KS-DFT formalism is problematic for several types of electronic excitations. A particular problem is that in standard calculations the adiabatic approximation is employed, leading to that double excitations cannot be treated. Earlier, other well-known problems were charge transfer (CT) and Rydberg type excitations,9−14 which were often severely underestimated, due to an incorrect long-range asymptotic behavior in many approximate KS-DFT functionals. For CT excitations, one strategy is to vary the amount of exact Hartree−Fock (HF) exchange with the interelectronic distance.15−19 Correction schemes have also been devised for Rydberg-type excitations.14 However, these methods cannot alleviate KS-DFT in the multiconfigurational case, nor can they include excitations with double-excitation character. With © 2016 American Chemical Society
respect to the latter, we should mention two other methods we know are currently under development: dressed KSDFT20−23 and spin-flip KS-DFT.24−27 We have proposed to use linear response excitation energies and oscillator strengths28 based on a hybrid between multiconfigurational (MC) self-consistent field methods and KSDFT.29 Several forms of such hybrids have been suggested.30,31 In our work we use a range-separated electron-repulsion operator, suggested first by Savin32,33 and later extended by several other groups.28,29,34−39 This long-range MCSCF shortrange DFT (MC-srDFT) method can include double excitations, and it employs a multireference wave function for the partially interacting reference system. We have shown that the method indeed can yield good results for excitations of both double-excitation and charge-transfer character, as well as for molecules with significant multireference character.40 With its recent extension to include large environments through the polarizable embedding scheme,41 it contains all the needed ingredients for applications to biological chromophores. However, before we aim at complex biomolecular and condensed phase molecular systems, it is necessary to establish firmly the accuracy one can expect of MC-srDFT excitation properties for typical chromophores without multireference character and without low-lying double excitations. Therefore, Received: December 2, 2015 Published: April 8, 2016 2203
DOI: 10.1021/acs.jctc.5b01141 J. Chem. Theory Comput. 2016, 12, 2203−2213
Article
Journal of Chemical Theory and Computation
Figure 1. Thirteen organic molecules selected as the benchmark set.
in this work we investigate valence singlet excitations for a considerably larger benchmark set of molecules than previously,40 using also an extended number of excited states for each molecule. This is to ensure that the MC-srDFT method is indeed applicable and predictive for all types of excitations, both in single reference and multi reference cases. We also aim at spotting potential weaknesses for the method. For this purpose, we have as reference values chosen the detailed investigations of vertical excitation energies in various organic molecules by Sauer, Thiel, and co-workers.42−44 Our assessment of MC-srDFT in this work is based on their data using a subset of their molecules, selected to cover all typical chromophores in their set. In addition, we have also investigated basis set effects and dependence on the value of the range-separation parameter, and we have compared two different methods of constructing the short-range DFT functionals. The manuscript is organized as follows: In Section 2 we briefly present the working equations for the MC-srDFT method. The computational details are summarized in Section 3, and our results are presented and discussed in Section 4. Finally, concluding remarks are given in Section 5.
weelr, μ(r12) =
(2)
and μ is the parameter that controls the range separation. This parameter is given in bohr−1. The energy of the ground state can be obtained via the variational principle as sr, μ ̂ + Ŵ eelr, μ|Ψμ⟩ + E Hxc Eμ = min{ ⟨Ψμ|T̂ + Vne [ρΨμ ]} μ Ψ
(3)
In this equation, T̂ is the standard nonrelativistic kinetic energy operator, while V̂ ne = ∑ivne(ri) is the standard nuclear-electron lr,μ attraction potential and Ŵ lr,μ ee = ∑i
