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.
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.
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 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.
In this lecture we present many-body perturbation theory as a method to determine quasiparticle excitations in solids, especially electronic band structures, accurately from first principles.The main ingredient is the electronic self-energy that, in principle, contains all many-body exchange and correlation effects beyond the Hartree potential.As its exact mathematical expression is unknown, approximations must be used in practical calculations.The approximation is obtained using a systematic algebraic approach on the basis of Green function techniques.It constitutes an expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the quasiparticles and includes dynamic screening through the creation of exchange-correlation holes around the bare particles.The implementation of the approximation relies on a perturbative treatment starting from density functional theory.Besides a detailed mathematical discussion we focus on the underlying physical concepts and show some illustrative applications.
The accuracy of the many-body perturbation theory GW formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. In the present study, we explore two less demanding alternatives for the calculation of electron-phonon coupling matrix elements on the many-body perturbation theory level. Namely, we test the accuracy of the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the constant screening approach, where variations of the screened Coulomb potential W upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We find this latter approximation to be the most reliable, whereas the static COHSEX ansatz leads to substantial errors. Our conclusions are validated in a few paradigmatic cases: diamond, graphene, and the C60 fullerene. These findings open the way for combining the present many-body perturbation approach with efficient linear-response theories.
Predicting the chemico-physical properties of large molecular systems is a formidable challenge in chemistry and materials science. Traditional quantum mechanical methods, while accurate, have impractical scaling for large molecules with thousands of atoms, which are crucial in the development of novel therapeutics, catalysts, and nanomaterials. To address this, molecular fragmentation algorithms have been proposed to improve scalability and enable extensive parallelism. In this article, we introduce a significant enhancement to the Fragment Molecular Orbital (FMO) method, termed the Coulomb-Perturbed Fragmentation (CPF) method. CPF incorporates algorithmic improvements and implementation enhancements to optimize performance on heterogeneous computing systems equipped with a large number of GPUs. Key developments include a significant simplification of iteratitve self-consistent field (SCF) algorithm, advanced data management through a one-sided communication model, topology-aware optimizations, and a hybrid communication strategy for intra-group exchanges. Moreover, CPF integrates a distributed dynamic multi-layer load balancing scheme to optimise fragment distribution and workload management across nodes and GPUs. Performance evaluations on a 420-atom benzene molecule system comprising 35 fragments reveal that CPF outperforms existing GPU/CPU-based FMO algorithms in both efficiency and accuracy. When deployed on the Gadi supercomputer, CPF achieves over 97% parallel efficiency on 20 nodes, with scalability maintaining above 98% and 90% efficiency in weak-scaling tests for smaller and larger systems, respectively. Notably, CPF matches or exceeds the computational accuracy of conventional FMO methods, marking a substantial progress in the field of computational chemistry for fragmentation-based large-scale molecular modelling.
In order to properly understand the utility of many-body perturbation theory as applied to finite systems, we use the configuration interaction approach to compute the electronic self-energy. The validity of the commonly used GW approximation from many-body perturbation theory is tested by comparing the self-energy explicitly computed according to the diagrammatic expansions to that from the inversion of the Dyson equation. It is constructed as a functional of the interacting Green function G and screened Coulomb interaction W. W is explicitly computed through the diagonalization of the many-body Hamiltonian and, thus, takes polarization effects into account beyond the random phase approximation. The Na9+ cluster and the dissociation of the C2 molecule are discussed as examples. We find that the GW approximation yields accurate results for weakly correlated systems with a predominantly single-determinant ground state such as Na9+ clusters. The C2 molecule is a pathological system with multideterminantal ground state where the GW approach ceases to be valid.