arXiv subjects

Fabien Bruneval

Publications and source records attributed to Fabien Bruneval.

At least 19 recordsLinked to original sources

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

$GW$+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↗

arXiv2024

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 methodologies for accounting for the so-called non-dynamic electronic correlation effects. Up to now, molecular calculations have been performed with real-valued orbitals. However, before extending the applicability of these methodologies to extended systems, where Bloch states are employed, the subtleties of working with complex-valued orbitals and the consequences of imposing time-reversal symmetry must be carefully addressed. In this work, we describe the theoretical and practical implications of adopting time-reversal symmetry in RDMFT and pCCD when allowing for complex-valued orbital coefficients. The theoretical considerations primarily affect the optimization algorithms, while the practical implications raise fundamental questions about the stability of solutions. Specifically, we find that complex solutions lower the energy when non-dynamic electronic correlation effects are pronounced. We present numerical examples to illustrate and discuss these instabilities and possible problems introduced by N-representability violations.

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

Capturing electronic correlations in electron-phonon interactions in molecular systems with the GW approximation

Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is however unclear how general this enhancement is, and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW and equation-of-motion coupled-cluster calculations. We find that GW can increase the magnitude of the electron-phonon coupling across this set of molecules by an average factor of 1.1-1.8 compared to DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as an accurate way of computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.

cond-mat.mtrl-sci↗

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

RPA, an accurate and fast method for the computation of static non-linear optical properties

The accurate computation of non-linear optical properties (NLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with the density-fitting techniques and the integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict NLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyper-polarizabilities. We show that RPA based on hybrid functional self-consistent field calculations yields as accurate NLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that RPA avoids any system-specific adjustment.

physics.chem-ph↗

arXiv2023

$GW$ density matrix to estimate self-consistent $GW$ total energy in solids

The $GW$ approximation is a well-established method for calculating ionization potentials and electron affinities in solids and molecules. For numerous years, obtaining self-consistent $GW$ total energies in solids has been a challenging objective that is not accomplished yet. However, it was shown recently that the linearized $GW$ density matrix permits a reliable prediction of the self-consistent $GW$ total energy for molecules [F. Bruneval et. al. J. Chem. Theory Comput. 17, 2126 (2021)] for which self-consistent $GW$ energies are available. Here we implement, test, and benchmark the linearized $GW$ density matrix for several solids. We focus on the total energy, lattice constant, and bulk modulus obtained from the $GW$ density matrix and compare our findings to more traditional results obtained within the random phase approximation (RPA). We conclude on the improved stability of the total energy obtained from the linearized $GW$ density matrix with respect to the mean-field starting point. We bring compelling clues that the RPA and the $GW$ density matrix total energies are certainly close to the self-consistent $GW$ total energy in solids if we use hybrid functionals with enriched exchange as a starting point.

physics.chem-ph↗

arXiv2019

Direct comparison of many-body methods for realistic electronic Hamiltonians

A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged methods, resulting in experiment-free reference values. These reference values are used to assess the accuracy of modern emerging and scalable approaches to the many-electron problem. The most accurate methods obtain energies indistinguishable from experimental results, with the agreement mainly limited by the experimental uncertainties. Comparison between methods enables a unique perspective on calculations of many-body systems of electrons.

cond-mat.mtrl-sci↗

arXiv2019

Reproducibility in $G_0W_0$ Calculations for Solids

Ab initio many-body perturbation theory within the $GW$ approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn-Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange correlation functional ``starting point'', are used to construct $G$ and $W$, and then perturbatively corrected by the resultant $GW$ self-energy. In practice, there are several ways to construct the $GW$ self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO$_2$, reported $GW$ fundamental gaps can vary by more than 1 eV. In this work, we address the convergence and key approximations in contemporary $G_0W_0$ calculations, including frequency-integration schemes and the treatment of the Coulomb divergence in the exact-exchange term. We study several systems,and compare three different $GW$ codes: BerkeleyGW, Abinit and Yambo. We demonstrate, for the first time, that the same quasiparticle energies for systems in the condensed phase can be obtained with different codes, and we provide a comprehensive assessment of implementations of the $GW$ approximation.

cond-mat.mtrl-sci↗

arXiv2017

An assessment of the low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach

The accurate prediction of singlet and triplet excitation energies is of significant fundamental interest and is critical for many applications. An area of intense research, most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel's set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relatively to higher level theories. Finally, we find that BSE-TDA calculations built on good DFT starting points, such as those utilizing optimally-tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.

physics.comp-ph↗

arXiv2016

Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes

Charged excitations of the oligoacene family of molecules, relevant for astrophysics and technological applications, are widely studied and therefore provide an excellent system for benchmarking theoretical methods. In this work, we evaluate the performance of many-body perturbation theory within the GW approximation relative to new high-quality CCSD(T) reference data for charged excitations of the acenes. We compare GW calculations with a number of hybrid density functional theory starting points and with eigenvalue self-consistency. Special focus is given to elucidating the trend of GW-predicted excitations with molecule length increasing from benzene to hexacene. We find that GW calculations with starting points based on an optimally tuned range-separated hybrid (OTRSH) density functional and eigenvalue self-consistency can yield quantitative ionization potentials for the acenes. However, for larger acenes, the predicted electron affinities can deviate considerably from reference values. Our work paves the way for predictive and cost-effective GW calculations of charged excitations of molecules and identifies certain limitations of current GW methods used in practice for larger molecules.

physics.chem-ph↗

arXiv2016

Effects of quantum confinement on excited state properties of SrTiO$_3$ from ab initio many-body perturbation theory

The Ruddlesden-Popper (RP) homologous series Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ provides a useful template for the study and control of the effects of dimensionality and quantum confinement on the excited state properties of the complex oxide SrTiO$_3$. We use ab initio many-body perturbation theory within the $GW$ approximation and the Bethe-Salpeter equation approach to calculate quasiparticle energies and absorption spectrum of Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ for $n=1-5$ and $\infty$. Our computed direct and indirect optical gaps are in excellent agreement with spectroscopic measurements. The calculated optical spectra reproduce the main experimental features and reveal excitonic structure near the gap edge. We find that electron-hole interactions are important across the series, leading to significant exciton binding energies that increase for small $n$ and reach a value of 330~meV for $n=1$, a trend attributed to increased quantum confinement. We find that the lowest-energy singlet exciton of Sr$_2$TiO$_4$ ($n=1$) localizes in the 2D plane defined by the TiO$_2$ layer, and explain the origin of its localization.

cond-mat.mtrl-sci↗

arXiv2015

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules

The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased, and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel's widely-used time-dependent density functional theory benchmark set [M. Schreiber et al. J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step, and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory.

cond-mat.mtrl-sci↗

arXiv2014

Comprehensive ab initio study of doping in bulk ZnO with group-V elements

Despite the lack of reproducible experimental confirmation, group-V elements have been considered as possible sources of p-type doping in ZnO in the form of simple and complex defects. Using ab initio calculations, based on state-of-the-art hybrid exchange-correlation functional, we study a wide range of defects and defect complexes related with N, P, As, and Sb impurities. We show that none of the candidates for p-type doping can be considered a good source of holes in the valence band due to deep acceptor levels and low formation energies of compensating donor defects. In addition, we discuss the stability of complexes in different regimes.

cond-mat.mtrl-sci↗

arXiv2014

Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium

We report an implementation of the constrained random phase approximation (cRPA) method within the projector augmented-wave framework. It allows for the calculation of the screened interaction in the same Wannier orbitals as our recent DFT+U and DFT+DMFT implementations. We present calculations of the dynamical Coulomb screened interaction in uranium dioxide and alpha and gamma cerium on Wannier functions. We show that a self-consistent calculation of the static screened interaction in DFT+U together with a consistent Wannier basis is mandatory for gamma cerium and uranium dioxide. We emphasize that a static approximation for the screened interaction in alpha cerium is too drastic.

cond-mat.str-el↗

arXiv2013

Point defect modeling in materials: coupling ab initio and elasticity approaches

Modeling point defects at an atomic scale requires careful treatment of the long-range atomic relaxations. This elastic field can strongly affect point defect properties calculated in atomistic simulations because of the finite size of the system under study. This is an important restriction for ab initio methods which are limited to a few hundred atoms. We propose an original approach coupling ab initio calculations and linear elasticity theory to obtain the properties of an isolated point defect for reduced supercell sizes. The reliability and benefit of our approach are demonstrated for three problematic cases: the self-interstitial in zirconium, clusters of self-interstitials in iron, and the neutral vacancy in silicon.

cond-mat.mtrl-sci↗