An Algebraic-Diagrammatic Construction for Vertex Corrections to the GW Self-Energy

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...

pubs.acs.org

From Full Dynamic to Pure Static: A Family of $GW$-Based Approximations

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.

arxiv.org

Reference Energies for Non-Relativistic Core Ionization Potentials

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 ...

arxiv.org

Connection between $GW$ and Extended Coupled Cluster

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...

arxiv.org

Connections between Richardson–Gaudin states, perfect-pairing, and pair coupled-cluster theory

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

pubs.aip.org

Parquet theory for molecular systems: Formalism and static kernel parquet approximation

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

pubs.aip.org

Complex Absorbing Potential Green’s Function Methods for Resonances

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 ...

pubs.acs.org

Analytic $G_0W_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment

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 ...

arxiv.org

Fully Analytic Nuclear Gradients for the Bethe–Salpeter Equation

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.

pubs.acs.org

Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory

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...

arxiv.org

Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory

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...

arxiv.org

Parquet theory for molecular systems. I. Formalism and static kernel parquet approximation

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 ...

arxiv.org

QUEST Database of Highly-Accurate Excitation Energies

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.

pubs.acs.org

Complex Absorbing Potential Green's Function Methods for Resonances

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...

arxiv.org

Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation

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...

arxiv.org

The QUEST Database of Highly-Accurate Excitation Energies

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...

arxiv.org

Richardson-Gaudin states of non-zero seniority II: Single-reference treatment of strong correlation

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...

arxiv.org

Excited states of the uniform electron gas

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

pubs.aip.org

Comparing Perturbative and Commutator-Rank-Based Truncation Schemes in Unitary Coupled-Cluster Theory

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 ...

arxiv.org

Driven similarity renormalization group with a large active space: Applications to oligoacenes, zeaxanthin, and chromium dimer

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...

arxiv.org

Using Matrix-Free Tensor-Network Optimizations to Construct a Reduced-Scaling and Robust Second-Order Møller-Plesset Theory

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...

arxiv.org

A Guide to Molecular Properties from the Bethe-Salpeter Equation

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...

arxiv.org

The Conundrum of Diffuse Basis Sets: A Blessing for Accuracy yet a Curse for Sparsity

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...

arxiv.org

Simple and efficient computational strategies for calculating orbital energies and pair-orbital energies from pCCD-based methods

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...

arxiv.org

Excited States of the Uniform Electron Gas

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...

arxiv.org

Time-reversal symmetry in RDMFT and pCCD with complex-valued orbitals

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

doi.org

Exploring the accuracy of the equation-of-motion coupled-cluster band gap of solids

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...

arxiv.org