arXiv subjects

Arno Förster

Publications and source records attributed to Arno Förster.

At least 19 recordsLinked to original sources

arXiv2026

Third-order Algebraic Diagrammatic Construction Renormalized by Particle-Particle Ladders

The algebraic diagrammatic construction (ADC) of the electronic self-energy is based on Moller-Plesset perturbation theory. Its vertices contain bare energy denominators that do not capture renormalization of Hartree-Fock excitations through excited-state correlations. As we show here, Epstein-Nesbet (EN) partitioning of the electronic Hamiltonian overcomes this deficiency at zero extra cost by introducing dressed denominators that resum to infinite order the diagonal elements of ladder diagrams described by the pair propagator in the particle-particle $T$-matrix approximation. Third-order ADC with EN-dressed denominators leads to an almost fourfold increase in accuracy compared to standard ADC(3) on a challenging benchmark set for IPs of closed-shell molecules, reaching an accuracy between EOM-CCSD and EOM-CCSDT. For open-shell systems, the gains in accuracy are more modest, but standard ADC is nevertheless outperformed.

physics.chem-ph↗

arXiv2026

Benchmark of Multi-Channel Dyson Equation and Algebraic Diagrammatic Construction Methods for molecules

The Dyson-algebraic diagrammatic construction (ADC) and the multi-channel Dyson equation (MCDE) formalisms explicitly leverage multi-particle channels to formulate correlated theories of the single-particle Green's function that produce positive semi-definite spectral functions by construction. While the MCDE is strictly rooted in the Dyson formalism, most ADC calculations are performed in the non-Dyson (nD) framework that decouples electron attachment and detachment sectors. We benchmark the Dyson-ADC(2)-X [that is equivalent to the (3,1)-MCDE] and ADC(3) approximations on a set of 58 ionization potentials of 23 small molecules for which near-full configuration interaction reference data exist. Comparison of Dyson- to nD-ADC(3) reveals deviations of the order of 0.1 eV between both methods, calling into question the reliability of the nD approximation. We show that Dyson-ADC gives similar accuracy for first IPs as for semi-valence and semi-core transitions. Finally, we also benchmark the screened (3,1)-MCDE that screens all ladder interactions, and show that it improves over its unscreened counterpart.

physics.chem-ph↗

arXiv2026

Static Effective Hamiltonians for Molecular Systems through RPA-based Downfolding

Green's function-based downfolding methods construct effective Hamiltonians of reduced dimension that capture dynamical correlations of an electronic environment through effective potentials acting on the active space only. Using methods based on the constrained random phase approximation (cRPA) and moment RPA (mRPA), we construct static effective Hamiltonians that include screening through the environment. We derive expressions for the energy contribution from the environment and for the effective one- and two-body terms, taking into account double-counting corrections. cRPA requires additional consideration due to its frequency dependence, while mRPA provides a static Hamiltonian by construction. For the ground state energy of benzene and bond dissociation curves, we discuss the differences and similarities between the different flavors of RPA-based screening. We show that downfolding using cRPA describes both dynamical and strong correlation well, while mRPA and cRPA restricted to screening the particle-hole matrix elements can fail to describe bond dissociation due to a dominating dynamical correlation term. In the static limit, these two methods are shown to be almost indistinguishable.

physics.chem-ph↗

arXiv2026

Approaching Coupled Cluster Accuracy with Positive Semidefinite Vertex Corrected Self-Energies

Hedin's formalism of functional derivatives is the best-known method for systematically constructing correlated electronic theories, largely due to the success of its lowest-order self-energy expansion, the $GW$ approximation. Beyond $GW$, diagrammatic resummation schemes attempt to mix correlations simultaneously across all particle-particle and particle-hole channels. Because such a comprehensive treatment is computationally prohibitive for realistic molecular systems, a highly effective alternative is to fully account for electronic correlations in one specific channel, typically the particle-hole channel. This idea was recently implemented for molecular systems [1], yielding a self-energy expressed in terms of excited-state energies and transition amplitudes from the solution of the Bethe-Salpeter equation, rather than the random phase approximation used in $GW$. While this approach is predictive and numerically efficient, it violates the fundamental positive-definiteness constraint of the electron spectral function in certain energy ranges. In this study, we resolve this physical flaw by deriving a positive semidefinite (PSD) extension of the theory using a rigorous framework based on the nonequilibrium Green's function formalism. The PSD constraint introduces new scattering channels and triplet intermediate states and restores the correct physical behavior. We demonstrate that it consistently improves quasiparticle energies across standard molecular benchmarks, with an accuracy comparable to coupled-cluster reference calculations.

physics.chem-ph↗

arXiv2026

$GW$ reduced density matrix from iterated linearized Dyson equation

Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here we apply the procedure to Hedin's $GW$ approximation. The non-iterated $GW$ based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the Random-Phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations (CCSDT) quantitatively changes the conclusions of the benchmark as compared to single and double excitations coupled-cluster (CCSD).

physics.chem-ph↗

arXiv2025

Transfer learning of GW-Bethe-Salpeter Equation excitation energies

A persistent challenge in machine learning for electronic-structure calculations is the sharp imbalance between abundant low-fidelity data like DFT or TDDFT results and the scarcity of high-fidelity data like many-body perturbation theory labels. We show that transfer learning provides an effective route to bridge this gap: graph neural networks pretrained on DFT and TDDFT properties can be finetuned with limited qs$GW$ and qs$GW$-BSE data to yield accurate predictions of quasiparticle and excitation energies. Assessing both full-model and readout-only finetuning across chemically diverse test sets, we find that pretraining improves accuracy, reduces reliance on costly qs$GW$ data, and mitigates large predictive outliers even for molecules larger or chemically distinct from those seen during finetuning. Our results demonstrate that multi-fidelity transfer learning can substantially extend the reach of many-body-level predictions across chemical space.

physics.chem-ph↗

arXiv2025

qs$GW$ quasiparticle and $GW$-BSE excitation energies of 133,885 molecules

Machine learning applications in the chemical sciences, especially when based on neural networks, critically depend on the availability of large quantities of high quality data. As they provide excellent accuracy for both charged and neutral excitations, a large dataset containing quasiparticle self-consistent GW (qs$GW$) and Bethe-Salpeter equation (BSE) data would be highly desirable to model excited state energies and properties. In this work, we introduce a dataset for qs$GW$-BSE excitation energies and qs$GW$ quasiparticle energies of unprecedented size. Our dataset, denoted QM9GWBSE, supplies $GW$-BSE singlet-singlet and singlet-triplet excitation energies, corresponding transition dipole moments and oscillator strengths as well as qs$GW$ quasiparticle energies for all molecules from the popular QM9 dataset. We anticipate that QM9GWBSE will provide a solid foundation to train highly accurate machine learning models for the prediction of molecular excited state properties.

physics.chem-ph↗

arXiv2025

Predicting complete basis set limit quasiparticle energies from triple-$ζ$ calculations

We present a simple linear model to estimate the basis set incompleteness errors (BSIE) of (vertex-corrected) $GW$ QP energies based on the kinetic energy of the corresponding orbital only. We parametrise the model for $G_0W_0$, quasi-particle self-consistent $GW$ (qs$GW$), and vertex-corrected ($Σ^{BSE}@L^{BSE}$) QP energies on a large set of molecules containing 10 different elements for which we calculate complete basis set (CBS) limit extrapolated reference values with correlation-consistent basis sets ranging from triple- to hextuple-$ζ$ (TZ/6Z). Based on these accurate reference values, we obtain model parameters for Gaussian-type and Slater-type orbital (GTO/STO) basis sets which allow for the extrapolation of QP energies calculated with TZ basis sets to the CBS limit with errors of 20 to 30 meV. Analysing extrapolation errors, we show the commonly used extrapolation method which assumes an inverse linear dependence of the BSIE on the inverse number of basis functions to be valid, but to produce larger errors, even when a quadruple-$ζ$ calculation is used in the extrapolation.

physics.chem-ph↗

arXiv2025

Calculation and analysis of exciton couplings via a subsystem formulation of the $GW$-Bethe-Salpeter Equation

We present a fragment-based framework for analyzing exciton couplings within the $GW$-Bethe-Salpeter Equation formalism using localized molecular orbitals, and assess how excitonic states in molecular dimers can be decomposed into local and charge-transfer (CT) sectors. Our localization procedure preserves orbital orthonormality via a block-diagonal unitary transformation, enabling a simple and interpretable analysis of excitonic interactions. Using ethylene and pyrene dimers as model systems, we identify key effects of excitonic basis truncation and coupling approximations on excitation energies. We then extend the method to chlorophyll dimers, where weak CT asymmetries emerge due to geometric distortions. This framework offers a tractable route to analyze excitonic behavior in complex systems and paves the way for future fragment-based reconstruction of full exciton coupling matrices in large molecular assemblies.

physics.chem-ph↗

arXiv2025

Periodic implementation of the random phase approximation with numerical atomic orbitals and dual reciprocal space grids

The random phase approximation (RPA) has emerged as a prominent first-principles method in material science, particularly to study the adsorption and chemisorption of small molecules on surfaces. However, its widespread application is hampered by its relatively high computational cost. Here, we present a well-parallelised implementation of the RPA with localised atomic orbitals and pair-atomic density fitting, which is especially suitable for studying two-dimensional systems. Through a dual $\textbf{k}$-grid scheme, we achieve fast and reliable convergence of RPA correlation energies to the thermodynamic limit. We demonstrate the efficacy of our implementation through an application to the adsorption of CO on MgO(001) using PBE input orbitals (RPA@PBE) Our calculated adsorption energy is in good agreement with previously published RPA@PBE studies, but, as expected, overestimates the experimentally available adsorption energies as well as recent CCSD(T) results.

cond-mat.mtrl-sci↗

arXiv2025

$GW$+2SOSEX self-energy made positive semi-definite

The formulation of vertex corrections beyond the $GW$ approximation within the framework of perturbation theory is a subtle and challenging task, which accounts for the wide variety of schemes proposed over the years. Exact self-energies are required to satisfy the mathematical condition of positive semi-definiteness. The $GW$ self-energy fulfills this property, but the vast majority of the vertex-corrected self-energy approximations do not. In this study, we devise a positive semi-definite extension to the $GW$+2SOSEX self-energy that we name $GW$+2SOSEX-psd. To reach this goal, we demonstrate the cancellation of the bare energy poles that are contained in the fully dynamic second-order in $W$ self-energy ($G3W2$). We then demonstrate on molecular examples the correct positive semi-definiteness of the proposed self-energy approximation and its good accuracy in predicting accurate quasiparticle energies for valence and core states.

physics.chem-ph↗

arXiv2025

Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections

We introduce the $Σ^{\text{BSE}}@L^{\text{BSE}}$ self-energy in the quasi-particle self-consistent $GW$ (qs$GW$) framework (qs$Σ^{\text{BSE}}@L^{\text{BSE}}$). Here, $L$ is the two-particle response function which we calculate by solving the Bethe-Salpeter equation with the static, first-order $GW$ kernel. The same kernel is added to $Σ$ directly. For a set of medium organic molecules, we show that including the vertex both in $L$ and $Σ$ is crucial. This approach retains the good performance of qs$GW$ for predicting first ionization potentials and fundamental gaps, while it greatly improves the description of electron affinities. Its good performance places qs$Σ^{\text{BSE}}@L^{\text{BSE}}$ among the best-performing electron propagator methods for charged excitations. Adding the vertex in $L$ only, as commonly done in the solid state community, leads to devastating results for electron affinities and fundamental gaps. We also test the performance of BSE@qs$GW$ and qs$Σ^{\text{BSE}}@L^{\text{BSE}}$ for neutral charge-transfer excitation and find both methods to perform similar. We conclude that $Σ^{\text{BSE}}@L^{\text{BSE}}$ is a promising approximation to the electronic self-energy beyond $GW$. We hope that future research on dynamical vertex effects, second-order vertex corrections, and full self-consistency will improve the accuracy of this method, both for charged and neutral excitation energies.

physics.chem-ph↗

arXiv2024

Why does the $GW$ approximation give accurate quasiparticle energies? The cancellation of vertex corrections quantified

Hedin's $GW$ approximation to the electronic self-energy has been impressively successful to calculate quasiparticle energies, such as ionization potentials, electron affinities, or electronic band structures. The success of this fairly simple approximation has been ascribed to the cancellation of the so-called vertex corrections that go beyond $GW$. This claim is mostly based on past calculations using vertex corrections within the crude local-density approximation. Here, we explore a wide variety of non-local vertex corrections in the polarizability and the self-energy, using first-order approximations or infinite summations to all orders. In particular, we use vertices based on statically screened interactions like in the Bethe-Salpeter equation. We demonstrate on realistic molecular systems that the two vertices in Hedin's equation essentially compensate. We further show that consistency between the two vertices is crucial to obtain realistic electronic properties. We finally consider increasingly large clusters and extrapolate that our conclusions would hold for extended systems.

physics.chem-ph↗

arXiv2024

Fully dynamic G3W2 self-energy for finite systems: Formulas and benchmark

Over the years, Hedin's $GW$ self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple $GW$ approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction $W$ for finite systems. This self-energy named $G3W2$ contains all the possible time orderings that combine 3 Green's functions $G$ and 2 dynamic $W$. We present the analytic formula and its imaginary frequency counterpart, the latter allowing us to treat larger molecules. The accuracy of the $G3W2$ self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24 and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the $G3W2$ self-energy nor any of the investigated approximations to it improve over one-shot $G_0W_0$ with a good starting point. Only quasi-particle self-consistent $GW$ HOMO energies are slightly improved by addition of the $G3W2$ self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

physics.comp-ph↗

arXiv2023

Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants

We report an all-electron, atomic orbital (AO) based, two-component (2C) implementation of the $GW$ approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the $GW$ self-energy at a quasi-one-component level, our 2C $GW$ algorithm is only about a factor of two to three slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened $G3W2$ correction. Comparison of first ionization potentials of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations of around 70 meV for $G_0W_0$@PBE and $G_0W_0$@PBE0. These are most likely due to technical differences in both implementations, most notably the use of different basis sets, pseudopotential approximations, different treatment of the frequency dependency of the self-energy and the choice of the 2C-Hamiltonian. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. $G_0W_0$PBE0 (25 \% exact exchange) and $G_0W_0$BHLYP (50 \% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Eigenvalue-only self-consistent $GW$ (ev$GW$) and quasi-particle self-consistent $GW$ (qs$GW$) significantly overestimate the IPs. Perturbative $G3W2$ corrections improve the agreement with experiment in cases where $G_0W_0$ alone underestimates the IPs. With a MAD of only 140 meV, 2C-$G_0W_0$PBE0 + $G3W2$ is in best agreement with the experimental reference values.

physics.chem-ph↗

arXiv2022

Towards Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy

Pair atomic density fitting (PADF) is a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random phase approximation (RPA) or second-order Møller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. In this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favourable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. We then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater Type Orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-$ζ$ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.

physics.chem-ph↗

arXiv2022

Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies

With increasing inter-electronic distance, the screening of the electron-electron interaction by the presence of other electrons becomes the dominant source of electron correlation. This effect is described by the random phase approximation (RPA) which is therefore a promising method for the calculation of weak interactions. The success of the RPA relies on the cancellation of errors, which can be traced back to the violation of the crossing symmetry of the 4-point vertex, leading to strongly overestimated total correlation energies. By addition of second-order screened exchange (SOSEX) to the correlation energy, this issue is substantially reduced. In the adiabatic connection (AC) SOSEX formalism, one of the two electron-electron interaction lines in the second-order exchange term is dynamically screened (SOSEX($W$,$v_c$)). A related SOSEX expression in which both electron-electron interaction lines are statically screened (SOSEX($W(0)$,$W(0)$)) is obtained from the $G3W2$ contribution to the electronic self-energy. In contrast to SOSEX($W$,$v_c$), the evaluation of this correlation energy expression does not require an expensive numerical frequency integration and is therefore advantageous from a computational perspective. We compare the accuracy of the statically screened variant to RPA and RPA+SOSEX($W$,$v_c$) for a wide range of chemical reactions. While both methods fail for barrier heights, SOSEX($W(0)$,$W(0)$) agrees very well with SOSEX($W$,$v_c$) for charged excitations and non-covalent interactions where they lead to major improvements over RPA.

physics.chem-ph↗

arXiv2022

Quasiparticle Self-Consistent $GW$-Bethe-Salpeter equation calculations for large chromophoric systems

The $GW$-Bethe-Salpeter Equation (BSE) method is promising for calculating the low-lying excited states of molecular systems. So far, it has only been applied to rather small molecules, and in the commonly implemented diagonal approximations to the electronic self-energy it depends on a mean-field starting point. We describe here an implementation of the self-consistent and starting-point independent quasiparticle self-consistent (qs$GW$)-BSE approach which is suitable for calculations on large molecules. We herein show that eigenvalue-only self-consistency leads to an unfaithful description of certain excitonic states for Chlorophyll dimers while the qs$GW$-BSE vertical excitation energies (VEE) are in excellent agreement with spectroscopic experiments for Chlorophyll monomers and dimers measured in the gas phase. On the other hand, VEEs from time-dependent density functional theory calculations tend to disagree with experimental values and using different range-separated hybrid (RSH) kernels changes the VEEs by up to 0.5 eV. We use the new qs$GW$-BSE implementation to calculate the lowest excitation energies of the six chromophores of the photosystem II (PSII) reaction center (RC) with nearly 2000 correlated electrons. Using more than 11000 (6000) basis functions, the calculation could be completed in less than 5 (2) days one a single modern compute node. In agreement with previous TD-DFT calculations using RSH kernels on models that do also not include environment effects, our qs$GW$-BSE calculations only yield states with local character in the low-energy spectrum of the hexameric complex. Earlier work with RSH kernels has demonstrated that the protein environment facilitates the experimentally observed interchromophoric charge transfer. Therefore, future research will need to combine correlation effects beyond TD-DFT with an explicit treatment of environment electrostatics.

physics.chem-ph↗