The recent use of a new ensemble in density functional theory (DFT) to yield direct corrections to the Kohn-Sham transitions yields the elusive double excitations that are missed by time-dependent DFT with the standard adiabatic approximation. But accuracies are lower than for single excitations, and formal arguments suggest that direct corrections at the exchange level should not be sufficient. We show that in principle, EDFT with direct corrections can yield accurate doubles and explain the error in naive formal arguments about TDDFT. Exact calculations and analytic results on a simple model, the Hubbard dimer, illustrate the results, showing that the answer to the title question is typically yes.
By studying the lowest excitations of an exactly solvable one-dimensional molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfers. Furthermore, we compute the approximate excitation energies obtained by using thee exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [Gould and Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to stro…
Charged excitations made neutral: N-centered ensemble density functional theory of Fukui functions
Laboratoire de Chimie Quantique, Institut de Chimie, CNRS / Université de Strasbourg（斯特拉斯堡大学化学研究所量子化学实验室）；University of Strasbourg Institute for Advanced Study（斯特拉斯堡大学高等研究院）
The efficiency of natural light harvesting systems is largely determined by their ability to transfer excitations from the antenna to the energy trapping center before recombination. Exciton diffusion length similarly limits organic photovoltaics and demands bulk heterojunction architectures. Dark state protection, achieved by coherent coupling between subunits within the antenna, can significantly reduce radiative recombination and enhance the efficiency of energy trapping. In this work we extend the dark state concept to the double-excitation manifold by studying the dynamical flow of excita…
We present analytic gradients and derivative couplings for the simplest possible multireference configuration interaction method, CIS-1D, an electronic structure ansatz that includes all single excitations and one lone double excitation on top of a Hartree-Fock reference state. We show that the resulting equations are numerically stable and require the evaluation of a similar number of integrals as compared to standard CIS theory; one can easily differentiate the required frontier orbitals ($\mathtt{h}$ and $\mathtt{l}$) with minimal cost. The resulting algorithm has been implemented within th…
A very specific ensemble of ground and excited states is shown to yield an exact formula for any excitation energy as a simple correction to the energy difference between orbitals of the Kohn-Sham ground state. This alternative scheme avoids either the need to calculate many unoccupied levels as in time-dependent density functional theory (TDDFT) or the need for many self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange (SEHX) approximation yields results comparable to standard TDDFT for atoms. With this formalism, SEHX yields approximate double-excitations, which are…
The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble density-functional approximations, with the extrapolation scheme of Savin [J. Chem. Phys. 140, 18A509 (2014)] is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter mu when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, …
We derive the second-order approximation (PT2) to the ensemble correlation energy functional by applying the Görling-Levy perturbation theory on the ensemble density-functional theory (EDFT). Its performance is checked by calculating excitation energies with the direct ensemble correction method in 1D model systems and 3D atoms using numerically exact Kohn-Sham orbitals and potentials. Comparing with the exchange-only approximation, the inclusion of the ensemble PT2 correlation improves the excitation energies in 1D model systems in most cases, including double excitations and charge-transfer …
Gross-Oliveira-Kohn density functional theory (GOK-DFT) for ensembles is in principle very attractive, but has been hard to use in practice. A novel, practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The new model relies on two modifications of GOK-DFT: use of range separation and use of the slope of the linearly-interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range densit…
The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interaction-corrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as $μ^{-2}$ in the large range-separation-parameter $μ$ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as $μ^{-3}$) towards their pure wavefunction theory values ($μ\rightarro…
Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{independent} extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a \textit{weight-dependent} exchange-correlation functional in order to model the infamous ensemble derivative contribution to the exc…
Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results like, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational eval…
We show that recently developed quantum Monte Carlo methods, which provide accurate vertical transition energies for single excitations, also successfully treat double excitations. We study the double excitations in medium-sized molecules, some of which are challenging for high level coupled-cluster calculations to model accurately. Our fixed-node diffusion Monte Carlo excitation energies are in very good agreement with reliable benchmarks, when available, and provide accurate predictions for excitation energies of difficult systems where reference values are lacking.
Femtosecond induced transparency and absorption in the extreme ultraviolet by coherent coupling of the He 2s2p (1P0) and 2p2 (1Se) double excitation states with 800 nm light
The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations. In particular, this equivalence requires keeping only those terms that generate time-independent ring diagrams, in the Goldstone sense. Here I show that this equivalence extends to neutral excitation energies, for which those calculated in the RPA are identical to those calculated using an approximation to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD).…
The Bethe-Salpeter equation (BSE) that results from the GW approximation to the self-energy is a frequency-dependent (nonlinear) eigenvalue problem due to the dynamically screened Coulomb interaction between electrons and holes. The computational time required for a numerically exact treatment of this frequency dependence is $O(N^6)$, where $N$ is the system size. To avoid the common static screening approximation, we show that the full-frequency dynamical BSE can be exactly reformulated as a frequency-independent eigenvalue problem in an expanded space of single and double excitations. When c…
The accurate description of doubly-excited states using conventional electronic structure methods is remarkably challenging, primarily because such excited states require the inclusion of doubly or higher excited configurations or the application of multi-reference methods. We present a new approach to target electronically excited states that feature a double-electron transfer. Our method uses the equation of motion (EOM) formalism with a pair coupled cluster doubles (pCCD) reference function, where dynamical correlation is accounted for by a linearized coupled cluster correction with singles…
We report a local, weight-dependent correlation density-functional approximation that incorporates information about both ground and excited states in the context of density-functional theory for ensembles (eDFT). This density-functional approximation for ensembles is specially designed for the computation of single and double excitations within Gross--Oliveira--Kohn (GOK) DFT (i.e., eDFT for neutral excitations), and can be seen as a natural extension of the ubiquitous local-density approximation in the context of ensembles. The resulting density-functional approximation, based on both finite…
Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than possible otherwise. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. I review the fundamental challenges the approximate functionals have in describing double-…
Excited states exhibiting double excitation character are notoriously difficult to model using conventional single-reference methods, such as adiabatic time-dependent density-functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC). In the present work, we provide accurate reference excitation energies for transitions involving a substantial amount of double excitation using a series of increasingly large diffuse-containing atomic basis sets. Our set gathers 20 vertical transitions from 14 small- and medium-size molecule. Depending on the size of the molecule, selected configu…
