Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach

Abstract

We present an implementation of the $GW$ space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization nor sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a non-uniform distribution of real-space locations $\{{\mathbf{r}}_k\}$ optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained $\{{\mathbf{r}}_k\}$ distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.

References in corpus (42)

• The GW method
• Quasiparticle Self-Consistent GW Theory
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Fully selfconsistent GW calculations for molecules
• Coupling of excitons and defect states in boron-nitride nanostructures
• Efficient single photon emission from a high-purity hexagonal boron nitride crystal
• First-principles GW calculations for DNA and RNA nucleobases
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Optical absorption and emission mechanisms of single defects in hexagonal boron nitride
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Towards GW Calculations on Thousands of Atoms
• Ab-initio calculation of the electronic and optical excitations in polythiophene: effects of intra- and interchain screening
• Benchmark of GW approaches for the GW100 testset
• Fully self-consistent GW calculations for atoms and molecules
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• Short to long-range charge-transfer excitations in the zincbacteriochlorin-bacteriochlorin complex: a Bethe-Salpeter study
• An O(N^3) implementation of Hedin's GW approximation for molecules
• Electron-phonon coupling in the C60 fullerene within the many-body GW approach
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Low-order Scaling $G_0{W}_0$ by Pair Atomic Density Fitting
• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Optical spectra and exchange-correlation effects in molecular crystals
• First-principles Engineering of Charged Defects for Two-dimensional Quantum Technologies
• Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting
• Unphysical Discontinuities in GW Methods
• Electronic Excitations in Complex Molecular Environments: Many-Body Green's Functions Theory in VOTCA-XTP
• Correlated electron-hole mechanism for molecular doping in organic semiconductors
• Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Imaginary time, shredded propagator method for large-scale GW calculations
• Self-consistent GW method: O(N) algorithm for polarizability and self energy
• Complex time, shredded propagator method for large-scale GW calculations
• Effects of self-consistency and plasmon-pole models on GW calculations for closed-shell molecules
• Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
• Decay properties of the one-particle Green function in real space and imaginary time
• Robust analytic continuation approach to many-body GW calculations
• Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost

Cited by in corpus (41)

• Accurate computational prediction of core-electron binding energies in carbon-based materials: A machine-learning model combining density-functional theory and $\mathbf{GW}$
• GPU Acceleration of Large-Scale Full-Frequency GW Calculations
• Connections and performances of Green's function methods for charged and neutral excitations
• GW100: A Slater Type Orbital Perspective
• Photoluminescent properties of the carbon-dimer defect in hexagonal boron-nitride: a many-body finite-size cluster approach
• Accelerating core-level $GW$ calculations by combining the contour deformation approach with the analytic continuation of $W$
• Reference Energies for Valence Ionizations and Satellite Transitions
• A 'moment-conserving' reformulation of GW theory
• A similarity renormalization group approach to Green's function methods
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Connections between many-body perturbation and coupled-cluster theories
• Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/$GW$ and Wave Function Methods
• Low-Scaling Algorithm for the Random Phase Approximation using Tensor Hypercontraction with k-point Sampling
• Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation
• Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Low-scaling GW algorithm applied to twisted transition-metal dichalcogenide heterobilayers
• Spin-orbit torque in single-molecule junctions from ab initio
• Linear Scaling Calculations of Excitation Energies with Active-Space Particle-Particle Random Phase Approximation
• Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies
• Universal polarization energies for defects in monolayer, surface and bulk hexagonal boron nitride : A finite-size fragments GW approach
• Can $GW$ Handle Multireference Systems?
• Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies
• Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies
• Efficient Full-frequency GW Calculations using a Lanczos Method
• Renormalized Singles with Correlation in $GW$ Green's Function Theory for Accurate Quasiparticle Energies
• Many-body $GW$ calculations with very large scale polarizable environments made affordable: a fully ab initio QM/QM approach
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• Complex Absorbing Potential Green's Function Methods for Resonances
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting
• Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework
• Polarizable Continuum Models and Green's Function $\mathbf{GW}$ Formalism: On the Dynamics of the Solvent Electrons
• Optical spectra of small silver clusters with the Bethe-Salpeter formalism: a Reassessment
• Many-body perturbation theory with hybrid density functional theory starting points accelerated by adaptively compressed exchange
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides
• Electron correlation in semiconductors and insulators via symbolic regression
• Scalable and predictive spectra of correlated molecules with moment truncated iterated perturbation theory