Low-order Scaling $G_0{W}_0$ by Pair Atomic Density Fitting

Abstract

We derive a low-scaling $G_0{W}_0$ algorithm for molecules, using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO) based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-$\zeta$ (TZ) plus double polarization quality. Also owing to a very small prefactor, with these settings a $G_0{W}_0$ calculation for the largest of these clusters takes only 240 CPU hours. With errors of 0.24 eV for HOMO energies in the GW100 database on the quadruple-$\zeta$ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-tpye basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF-approach of accurately representing diffuse AO-products. We speculate, that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented DZ quality is decreasing with system size. On the augmented DZ level we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.

arXiv commentfinal version as accepted by JCTC https://pubs.acs.org/doi/10.1021/acs.jctc.0c00693

References in corpus (57)

• Array Programming with NumPy
• CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations
• The GW method
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Quasiparticle Self-Consistent GW Theory
• Modeling of graphite oxide
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• Many-body perturbation theory calculations using the yambo code
• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• 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
• Optical excitations in organic molecules, clusters and defects studied by first-principles Green's function methods
• A Benchmark of GW Methods for Azabenzenes: Is the GW Approximation Good Enough?
• GW quasi-particle spectra from occupied states only
• Predictive GW calculations using plane waves and pseudopotentials
• DFT: A Theory Full of Holes?
• First-principles GW calculations for DNA and RNA nucleobases
• The GW space-time method for the self-energy of large systems
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Levels of self-consistency in the GW approximation
• Self-consistent GW: All-electron implementation with localized basis functions
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Breaking the theoretical scaling limit for predicting quasi-particle energies: The stochastic GW approach
• Towards GW Calculations on Thousands of Atoms
• GW method with the self-consistent Sternheimer equation
• Benchmark of GW approaches for the GW100 testset
• Accurate absolute and relative core-level binding energies from $GW$
• Strong correlation in Kohn-Sham density functional theory
• Physical origin of satellite in photoemission of doped graphene: An ab-initio GW plus cumulant study
• Non-equilibrium GW approach to quantum transport in nano-scale contacts
• An O(N^3) implementation of Hedin's GW approximation for molecules
• Ab initio GW electron-electron interaction effects in Quantum Transport
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• Beyond the quasiparticle approximation: Fully self-consistent $GW$ calculations
• On The Relation Between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Oxidation States of Graphene: Insights from Computational Spectroscopy
• An overview of self-consistent field calculations within finite basis sets
• Enhancements to the GW space-time method
• Swift $GW$ beyond $10,000$ electrons using fractured stochastic orbitals
• Tensor-Structured Coupled Cluster Theory
• Many-body Green's function GW and Bethe-Salpeter study of the optical excitations in a paradigmatic model dipeptide
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Exploring approximations to the GW self-energy ionic gradients
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Dynamically screened vertex correction to $GW$
• Clustered Low-Rank Tensor Format: Introduction and Application to Fast Construction of Hartree-Fock Exchange
• Low Rank Approximation in $G_0{W}_0$ Approximation
• Decay properties of the one-particle Green function in real space and imaginary time
• Analytic continuation with Padé decomposition
• Plane wave basis set correction methods for RPA correlation energies
• Ab Initio Many-Body Perturbation Theory Calculations of the Electronic and Optical Properties of Cyclometalated Ir(III) Complexes
• A mathematical analysis of the GW0 method for computing electronic excited energies of molecules

Cited by in corpus (33)

• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets
• GPU Acceleration of Large-Scale Full-Frequency GW Calculations
• GW100: A Slater Type Orbital Perspective
• Implementation of relativistic coupled cluster theory for massively parallel GPU-accelerated computing architectures
• Scalable Molecular GW Calculations: Valence and Core Spectra
• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• 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
• Connections between many-body perturbation and coupled-cluster theories
• Towards Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy
• Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants
• Spin-orbit torque in single-molecule junctions from ab initio
• Low-scaling GW algorithm applied to twisted transition-metal dichalcogenide heterobilayers
• Assessment of the Ab Initio Bethe-Salpeter Equation Approach for the Low-Lying Excitation Energies of Bacteriochlorophylls and Chlorophylls
• Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies
• Can $GW$ Handle Multireference Systems?
• Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies
• Many-body $GW$ calculations with very large scale polarizable environments made affordable: a fully ab initio QM/QM approach
• Spatial Decay and Limits of Quantum Solute-Solvent Interactions
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework
• Complex Absorbing Potential Green's Function Methods for Resonances
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• Many-body perturbation theory with hybrid density functional theory starting points accelerated by adaptively compressed exchange
• Optical spectra of small silver clusters with the Bethe-Salpeter formalism: a Reassessment
• 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
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides
• All-electron Quasiparticle Self-consistent GW for Molecules and Periodic Systems within the Numerical Atomic Orbital Framework