A Density-Based Basis-Set Incompleteness Correction for GW Methods

Abstract

Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. This displeasing feature is due to lack of explicit electron-electron terms modeling the infamous Kato electron-electron cusp and the correlation Coulomb hole around it. Here, we propose a computationally efficient density-based basis set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics towards the complete basis set limit. The performance of this density-based correction is illustrated by computing the ionization potentials of the twenty smallest atoms and molecules of the GW100 test set at the perturbative $GW$ (or $G_0{W}_0$) level using increasingly large basis sets. We also compute the ionization potentials of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained.

11 pages, 2 figures (supporting information available)

References in corpus (33)

• The GW method
• Yambo: an \textit{ab initio} tool for excited state calculations
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• Long-range/short-range separation of the electron-electron interaction in density functional theory
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Understanding and reducing errors in density functional calculations
• Unified description of ground and excited states of finite systems: the self-consistent GW approach
• First-principles GW calculations for DNA and RNA nucleobases
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• Self-consistent GW: All-electron implementation with localized basis functions
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Local-spin-density functional for multideterminant density functional theory
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Second-order Green's function perturbation theory for periodic systems
• Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach
• Unphysical Discontinuities in GW Methods
• A Density-Based Basis-Set Correction For Wave Function Theory
• Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density
• Green functions and self-consistency: insights from the spherium model
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Fractional charge and spin errors in self-consistent Green's function theory
• Local Hamiltonians for quantitative Green's function embedding methods
• Chemically Accurate Excitation Energies With Small Basis Sets
• Three- and four-electron integrals involving Gaussian geminals: fundamental integrals, upper bounds and recurrence relations
• Helium atom excitations by the GW and Bethe-Salpeter many-body formalism
• Explicitly correlated formalism for second-order single-particle Green's function
• Many-electron integrals over gaussian basis functions. I. Recurrence relations for three-electron integrals
• A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules

Cited by in corpus (21)

• Reference Energies for Intramolecular Charge-Transfer Excitations
• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• Low-order Scaling $G_0{W}_0$ by Pair Atomic Density Fitting
• All-electron periodic $G_0{W}_0$ implementation with numerical atomic orbital basis functions: algorithm and benchmarks
• Connections and performances of Green's function methods for charged and neutral excitations
• GW100: A Slater Type Orbital Perspective
• A basis-set error correction based on density-functional theory for strongly correlated molecular systems
• On the basis set selection for molecular core-level $GW$ calculations
• Optical response and band structure of LiCoO2 including electron-hole interaction effects
• Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism
• The three channels of many-body perturbation theory: $GW$, particle-particle, and electron-hole $T$-matrix self-energies
• Extension of selected configuration interaction for transcorrelated methods
• Reference Vertical Excitation Energies for Transition Metal Compounds
• Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments?
• Basis-set correction for coupled-cluster estimation of dipole moments
• Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies
• Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model
• A density-fitting implementation of the density-based basis-set correction method
• Estimating complete basis set extrapolation error through random walk
• Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment