Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA

Abstract

We explore a separable resolution-of-the-identity formalism built on quadratures over limited sets of real-space points designed for all-electron calculations. Our implementation preserves in particular the use of common atomic orbitals and their related auxiliary basis sets. The set up of the present density fitting scheme, i.e. the calculation of the system specific quadrature weights, scales cubically with respect to the system size. Extensive accuracy tests are presented for the Fock exchange and MP2 correlation energies. We finally demonstrate random phase approximation (RPA) correlation energy calculations with a scaling that is cubic in terms of operations, quadratic in memory, with a small crossover with respect to our standard RI-RPA implementation.

References in corpus (6)

• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• Describing static correlation in bond dissociation by Kohn-Sham density functional theory
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
• Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange
• Decay properties of the one-particle Green function in real space and imaginary time

Cited by in corpus (33)

• Even more efficient quantum computations of chemistry through tensor hypercontraction
• The Bethe-Salpeter Equation Formalism: From Physics to Chemistry
• 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
• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets
• Connections and performances of Green's function methods for charged and neutral excitations
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation
• Reference Energies for Valence Ionizations and Satellite Transitions
• Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies
• Interpolative separable density fitting decomposition for accelerating Hartree-Fock exchange calculations within numerical atomic orbitals
• 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
• Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
• 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
• Towards Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies
• Can $GW$ Handle Multireference Systems?
• Bethe Salpeter Equation Spectra for Very Large Systems
• Optimized Attenuated Interaction: Enabling Stochastic Bethe-Salpeter Spectra for Large Systems
• 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
• Complex Absorbing Potential Green's Function Methods for Resonances
• 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
• Block Tensor Decomposition: A dual grid scheme with formal O(N3) for THC decomposition of molecular systems
• Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting
• Optical spectra of small silver clusters with the Bethe-Salpeter formalism: a Reassessment
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides