The G3W2 approximation─the second-order self-energy beyond GW─is known to violate some fundamental analytic properties of the self-energy. In particular, its lack of positive semidefiniteness leads to...

We introduce a systematic hierarchy of one-body Green's function methods derived from the $GW$ approximation, constructed by progressively reducing the dynamical content of the self-energy. Starting from the fully dynamical Dyson formulation, we generate a family of approximations that interpolates between the standard $GW$ approximation to purely static effective single-particle Hamiltonians. This framework enables a controlled investigation of the role of dynamical effects and particle-hole coupling in the description of ionization potentials. Within this unified formalism, the hole and particle branches can be selectively decoupled through downfolding strategies into reduced one-particle spaces. By benchmarking the different members of this hierarchy on molecular ionization energies, we assess their accuracy, numerical robustness, and algorithmic complexity. We demonstrate that consistently derived partially static schemes can yield reliable quasiparticle energies while significantly simplifying the underlying eigenvalue problem. We further introduce a novel static Hermitian self-energy obtained as the static limit of this hierarchy. Despite its conceptually distinct origin, it produces results remarkably close to those of qs$GW$, thereby providing an alternative static route toward partial self-consistency.

Deep-lying core electrons carry highly localized, site-specific information that forms the basis of X-ray photoelectron spectroscopy. Accurately predicting their associated core ionization potentials ...

Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) have long evolved as distinct yet complementary frameworks for describing electronic correlation. While CC methods...

Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-

The GW approximation has become a method of choice for predicting quasiparticle properties in solids and large molecular systems, owing to its favorable accurac

The complex absorbing potential (CAP) formalism has been successfully employed in various wave function-based methods to study electronic resonance states. In contrast, Green’s function-based methods ...

The accurate prediction of ionization potentials (IPs) is central to understanding molecular reactivity, redox behavior, and spectroscopic properties. While vertical IPs can be accessed directly from ...

The Bethe–Salpeter equation (BSE) formalism, combined with the GW approximation for ionization energies and electron affinities, is emerging as an efficient and accurate method for predicting optical excitations in molecules. In this Letter, we present the first derivation and implementation of fully analytic nuclear gradients for the BSE@G0W0 method. Building on recent developments for G0W0 nuclear gradients, we derive analytic nuclear gradients for several BSE@G0W0 variants. We validate our implementation against numerical gradients and compare excited-state geometries and adiabatic excitation energies obtained from different BSE@G0W0 variants with those from state-of-the-art wave function methods.

Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-based theories, by contrast, naturally c...

Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-based theories, by contrast, naturally c...

The $GW$ approximation has become a method of choice for predicting quasiparticle properties in solids and large molecular systems, owing to its favorable accuracy-cost balance. However, its accuracy ...

We report theoretical best estimates of vertical transition energies (VTEs) for a large number of excited states and molecules: the quest database. This database includes 1489 aug-cc-pVTZ VTEs (731 singlets, 233 doublets, 461 triplets, and 64 quartets) for both valence and Rydberg transitions occurring in molecules containing from 1 to 16 non-hydrogen atoms. Quest also includes a significant list of VTEs for states characterized by a partial or genuine double-excitation character, known to be particularly challenging for many computational methods. The vast majority of the reported values are deemed chemically accurate, that is, are within ±0.05 eV of the FCI/aug-cc-pVTZ estimate. This allows for a balanced assessment of the performance of popular excited-state methodologies. We report the results of such benchmarks for various single- and multireference wave function approaches, and provide extensive Supporting Information allowing testing of other models. All corresponding data associated with the quest database, along with analysis tools, can be found in the associated GitHub repository at the following URL: https://github.com/pfloos/QUESTDB.

The complex absorbing potential (CAP) formalism has been successfully employed in various wavefunction-based methods to study electronic resonance states. In contrast, Green's function-based methods a...

The Bethe-Salpeter equation (BSE) formalism, combined with the $GW$ approximation for ionization energies and electron affinities, is emerging as an efficient and accurate method for predicting optica...

We report theoretical best estimates of vertical transition energies (VTEs) for a large number of excited states and molecules: the \textsc{quest} database. This database includes 1489 \emph{aug}-cc-p...

Strongly correlated systems are well described as a configuration interaction of Slater determinants classified by their number of unpaired electrons. This treatment is however unfeasible. In this man...

The uniform electron gas (UEG) is a cornerstone of density-functional theory (DFT) and the foundation of the local-density approximation, one of the most succes

Unitary coupled cluster (UCC) theory offers a promising Hermitian alternative to conventional coupled cluster (CC) theory, but its practical implementation is hindered by the non-truncating nature of ...

We present a new implementation of the driven similarity renormalization group (DSRG) based on a density matrix renormalization group (DMRG) reference. The explicit build of high-order reduced density...

We investigate the application of the canonical polyadic decomposition (CPD) to the tensor hypercontraction (THC) and Laplace transform (LT) approximated second-order Møller-Plesset (MP2) method. By i...

The Bethe-Salpeter equation (BSE) combined with the Green's function GW method has successfully transformed into a robust computational tool to describe light-matter interactions and excitation spectr...

Diffuse atomic orbital basis sets have proven to be essential to obtain accurate interaction energies, especially in regard to non-covalent interactions. However, they also have a detrimental impact o...

We introduce affordable computational strategies for calculating orbital and pair-orbital energies in atomic and molecular systems. Our methods are based on the pair Coupled Cluster Doubles (pCCD) ans...

The uniform electron gas (UEG) is a cornerstone of density-functional theory (DFT) and the foundation of the local-density approximation (LDA), one of the most successful approximations in DFT. In thi...

Reduced density matrix functional theory (RDMFT) and coupled cluster theory restricted to paired double excitations (pCCD) are emerging as efficient methodologi

While the periodic equation-of-motion coupled-cluster (EOM-CC) method promises systematic improvement of electronic band gap calculations in solids, its practical application at the singles and double...

Many electronic structure methods rely on the minimization of the energy of the system with respect to the one-body reduced density matrix (1RDM). To formulate a minimization algorithm, the 1RDM is of...

A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular ...

Accurate yet efficient modeling of chemical systems with pronounced static correlation in their excited states remains a significant challenge in quantum chemistry, as most electronic structure method...

Time-independent, orbital-optimized density functional approaches outperform time-dependent density functional theory (TDDFT) in calculations of excited electronic states involving a large rearrangeme...

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we int...

Excited-state absorption (ESA) corresponds to the transition between two electronic excited states and is a fundamental process for probing and understanding light-matter interactions. Accurate modeli...

For optimal accuracy, auxiliary-field quantum Monte Carlo (AFQMC) requires trial states consisting of multiple Slater determinants. We develop an efficient algorithm to select the determinants from an AFQMC random walk eliminating the need for other methods. When determinants contribute significantly to the non-orthogonal configuration interaction energy, we include them in the trial state. These refined trial wave functions significantly reduce the phaseless bias and sampling variance of the local energy estimator. With 100 to 200 determinants, we lower the error of AFQMC by up to a factor of 10 for second row elements that are not accurately described with a Hartree-Fock trial wave function. For the HEAT set, we improve the average error to within the chemical accuracy. For benzene, the largest studied system, we reduce AFQMC error by 80% with 214 Slater determinants and find a 10-fold increase of the time to solution. We show that the remaining error of the method prevails in systems with static correlation or strong spin contamination.

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely-trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Fu...

Guided by perturbative analysis, we improve the accuracy of Aufbau suppressed coupled cluster theory in simple single excitations, multi-configurational single excitations, and charge transfer excitat...

Orbital-optimized density functional theory (DFT) has emerged as an alternative to time-dependent (TD) DFT capable of describing difficult excited states with significant electron density redistributi...

This article summarizes recent updates to the p$^\dagger$q package, which is a C++ accelerated Python library for generating equations and computer code corresponding to singly-reference many-body qua...

Seniority-zero wavefunctions describe bond-breaking processes qualitatively. As eigenvectors of a model Hamiltonian, Richardson-Gaudin states provide a clear physical picture and allow for systematic ...

Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light an...

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The pairing hierarchy of perfect pairing (PP), perfect quadruples (PQ) and perfect hextuples (PH) are sparsified coupled cluster models that are exact in a pairing active space for 2, 4, and 6 electro...

We present our computational implementation of the equation-of-motion (EOM) coupled-cluster (CC) singles, doubles, and triples (SDT) method for computing doubly ionized (DIP) and two-electron attached...