In the last decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favourable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of non-dynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular N$_2$, Cr$_2$ molecules and also oxo-Mn(Salen) for which we have performed the first "post-DMRG" computations in order to shed light on the energy ordering of the lowest spin states.
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.
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…
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…
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 investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without any use of response theory or equation-of-motion formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the m…
Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various tailored coupled cluster methods externally corrected by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled-cluster (fpCC) methods, which are externally corrected by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system…
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…
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-…
Double Electron Attachment and Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with Full and Active-Space Treatments of 4-Particle-2-Hole and 4-Hole-2-Particle Excitations and Three-Body Clusters
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…
The accurate calculation of excited state properties of interacting electrons in the condensed phase is an immense challenge in computational physics. Here, we use state-of-the-art equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) to calculate the dynamic structure factor, which can be experimentally measured by inelastic x-ray and electron scattering. Our calculations are performed on the uniform electron gas at densities corresponding to Wigner-Seitz radii of $r_s=5$, 4, and 3 corresponding to the valence electron densities of common metals. We compare o…
The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve results of the coupled cluster with singles, doubles and triples. The resulting method has a nominal computational scaling of ${\cal O}(N^7)$ in the real-space representation, is orbital invariant, size extensive, and exact for three electrons.
We continue our work on the long-range corrected double-hybrid density functionals (LC-DHDFs) ωB2PLYP and ωB2GP-PLYP that we developed in the context of time-dependent (TD) Density Functional Theory (DFT) to enable the robust description of singlet-singlet excitations [J. Chem. Theory Comput. 15, 4735 (2019)]. In our initial study, we only assessed the impact of a long-range correction (LC) on BLYP-based DHDFs, and herein we extend our understanding by providing the first test of PBE-based LC-DHDFs within the established TD-DHDF scheme. Moreover, this study is one of few that provides a direct…
