We present a many-body GW formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential W, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.
We present a many-body GW formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential W, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.
The GW formalism, a Green’s function many-body perturbation theory, is growing in popularity for the description of the electronic properties of condensed matter systems in solid-state physics, and more recently chemistry. Unfortunately, its application to complex systems of interest in nanosciences, chemistry, or even biology, is hampered by the large associated computing cost, in particular in the case of disordered systems, or systems immersed in an opened environment (a solvent, a molecular medium, an electrode, etc.) The goal of the present PhD thesis is to focus on the development of multiscale techniques, merging high-level many-body treatments of the subsystem of interest, with a simplified but fully ab initio description of the electrostatic and dielectric environment. Such approaches aim to go beyond classical parametrized models, mainly developed in the quantum chemistry community, which are based on a continuum (“polarizable continuum model”) or discrete (QM/MM) description of the environment.To reach such a goal, we adopt a divide-and-conquer fragmentation scheme for the environment, particularly suited to molecular systems. This leads to a block-diagonal non- interacting electron susceptibility, decreasing the algorithmic complexity from quartic to cubic. To reduce the prefactor associated with the inversion of the Dyson equation for the screened Coulomb potential W, we have further developed a compression algorithm for the susceptibility operator. The automatic computation of an extremely compact polarization basis set allows a large reduction of the size of the susceptibility blocks, associated to the fragments in the environment. Such a method enables us to compute the dielectric response of systems made of several hundred thousand atoms, with an excellent accuracy when it comes to reproduce the effect of the environment as a response to an excitation in the immersed subsystem. This approach is presented through the study of fullerene bulk, surface and subsurface crystals.While the GW formalism is dynamical, with a frequency-dependent screened Coulomb potential W, a first study is done adopting a static approximation (low-frequency limit) for the screening properties of the environment. Such an approach follows the traditional semi-empirical models of a polarizable environment. This PhD thesis assesses the validity of such an approximation, which assumes an instantaneous response (adiabatic limit) of the environment to an electronic excitation, thanks to an explicit comparison with a fully dynamical dielectric response of the environment. The study of a surface of fullerenes, as well as a water molecule inside a metallic carbon nanotube, show that a static description of the environment leads to errors on the polarization energy below 10%, provided that the “folding” of the environment is treated in a proper way.The fragment approach is also applied to covalent insulator crystals, and more particularly to hexagonal boron nitride (h-BN). We explain how to compute the energy levels of point defects in h-BN, in the true dilute limit, and we give the asymptotic scaling laws for the renormalization of these energy levels, from the monolayer to a (n)-layer system. This study highlights thus the possibility to apply the fragment approach to covalent insulator systems, a possibility hinging probably on the short range behavior of the susceptibility in these systems.All of these developments, extending ab initio many-body methods to increasingly complex systems, have been implemented in the massively parallel code beDeft, dedicated to the study of the electronic properties of large scale systems.
We present a fragment-based many-body Green's function method suitable for treating large molecular systems in heterogeneous polarizable environments. The Green's function for a total system is approximated from fragment Green's functions and is expanded up to two-body terms. The screened Coulomb potential is approximated from the sum of intrafragment density-response functions, with interfragment polarization terms being neglected. The approximations for the Green's function and screened Coulomb potential lead to a many-body expansion of the self-energy. This expansion is essentially equivalent to the many-body expansion of the Fock matrix in the fragment molecular orbital method. To handle large molecular systems, the present implementation relies on the Coulomb hole plus screened exchange (COHSEX) approximation for the GW self-energy. The accuracy of the FMO-COHSEX method was demonstrated in comparison to conventional COHSEX results for organic molecular aggregates. We confirmed that the present fragmentation approximation can provide reasonably accurate results, and mean absolute errors for quasiparticle energies of less than 0.1 eV have been achieved for valence orbitals. We also assessed the accuracy of the COHSEX approximation to describe the effects of molecular aggregation of electronic states, by comparing them with the GW method. The COHSEX approximation has been shown to successfully describe the induced polarization and dispersion effects. As an illustrative application of the present method, we considered the electronic states of the pentacene thin film, which contains 1476 atoms. We investigated the impact of the induced polarization effect in the heterogeneous environment, highlighting the gap renormalization and the polarization-induced localization. This application shows that the present fragment-based method is useful for studying electronic structures of molecular aggregates in complex environments.
Electronic structure of materials from first principles is essential for one-to-one comparisons between theories and experiments. However, the many-body effects resulting from electron correlation and their interplay with other degrees of freedom pose a great challenge to design an ab initio approximate method with good accuracy and efficiency at the same time. In this thesis, we present our recent developments of ab initio many-body theory for solids based on the finite-temperature Green’s function formalism. We begin by reviewing the basic concepts and definitions of realistic electronic Hamiltonians (Ch. 2) as well as Green’s functions at finite temperature (Ch. 3). Overviews of self-consistent many-body perturbation theories and quantum embedding theories are then presented in Chs. 4 and 5 as complementary materials for the following chapters. In Ch. 6, we present algorithms and implementation details for the finite-temperature self-consistent GW (scGW) method in Gaussian-type orbitals for solids. Our implementation is based on the finite-temperature Green’s function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of self-energies are explicitly evaluated. We show agreement with other, differently formulated finite-temperature scGW implementations. By migrating computationally intensive calculations to GPUs, we obtain scalable results on large supercomputers with nearly optimal performance. Inclusion of relativistic effects in scGW is discussed in Ch. 7. Our formulation of relativistic scGW is based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and their interplay with electron correlation without adjustable parameters. We examine the effect of the X2C1e by comparison to the established four-component formalism and reach excellent agreement. The simplicity of X2C1e enables construction of higher order theories, such as embedding theories, on top of perturbative calculations. In Ch. 8, we use self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO3 and SrMnO3. In the strongly correlated metallic SrVO3, we find that the usual attribution of the satellite peaks at -1.8 eV to Hund or Hubbard physics in the t2g orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO3 we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter-free study of correlated perovskites. Lastly, in Ch. 9, we apply the Green’s function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems in strongly correlated solids within the framework of SEET. We describe the implementation details of our Green’s function coupled cluster (GFCC) solver, investigate its performance, and highlight potential advantages and problems on examples of impurities created for antiferromagnetic MnO and paramagnetic SrMnO3. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization. However, when correlations become strong, the singles and doubles approximation used in GFCC could lead to instabilities in searching for the particle number present in impurity problems.
Within the framework of many-body perturbation theory based on Green's functions, the GW approximation has emerged as a pivotal method for computing quasiparticle energies and excitation spectra. However, its high computational cost and steep scaling present significant challenges for applications to large molecular systems. In this work, we extend the block tensor decomposition (BTD) algorithm, recently developed in our previous work [Zhang et al., J. Chem. Phys. 163, 174109 (2025)] for low-rank tensor compression, to enable a formally O(N3)-scaling GW algorithm. By integrating BTD with an imaginary-time GW formalism and introducing a real space screening strategy for the polarizability, we achieve an observed scaling of approximately O(N2) in test systems. Key parameters of the algorithm are optimized on the S66 dataset using the JADE algorithm, ensuring a balanced compromise between accuracy and efficiency. Our BTD-based random phase approximation also exhibits O(N2) scaling, and eigenvalue-self-consistent GW calculations become feasible for systems with over 3000 basis functions. This work establishes BTD as an efficient and scalable approach for large-scale GW calculations in molecular systems.
Within the framework of many-body perturbation theory based on Green's functions, the GW approximation has emerged as a pivotal method for computing quasiparticle energies and excitation spectra. However, its high computational cost and steep scaling present significant challenges for applications to large molecular systems. In this work, we extend the block tensor decomposition (BTD) algorithm, recently developed in our previous work [J. Chem. Phys. 163, 174109 (2025)] for low-rank tensor compression, to enable a formally O(N3)-scaling GW algorithm. By integrating BTD with an imaginary-time GW formalism and introducing a real space screening strategy for the polarizability, we achieve an observed scaling of approximately O(N2) in test systems. Key parameters of the algorithm are optimized on the S66 dataset using the JADE algorithm, ensuring a balanced compromise between accuracy and efficiency. Our BTD-based random phase approximation also exhibits O(N2) scaling, and eigenvalue-self-consistent GW calculations become feasible for systems with over 3000 basis functions. This work establishes BTD as an efficient and scalable approach for large-scale GW calculations in molecular systems.
We present a molecular extension of our recently proposed Green’s function embedding method, interacting-bath dynamical embedding theory (ibDET), for computing charged excitation energies at the GW and EOM-CCSD levels. Starting from atom-centered impurities, we construct bath representations that capture the frequency-dependent entanglement between the impurity and its environment and can be systematically improved via the construction of cluster-specific natural orbitals. Utilizing a GW or coupled-cluster Green’s function solver, the self-energy of the full system is assembled from all embedding problems to obtain the interacting Green’s function. We show that ibDET provides accurate spectral properties with much reduced cost for a broad range of systems, including conjugated molecules and nanoclusters. Compared with full-system results, the errors in the predicted ionization potentials and electron affinities are around 0.1 eV or smaller, while each embedding problem includes only a small fraction of the total orbital space. This work provides an efficient and scalable framework for computing spectral properties of molecular systems.