Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon
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TL;DR: In this paper, an interpolative separable density fitting (ISDF) procedure was used to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis.
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Abstract: We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from O(Ne2) to O(Ne) when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn–Sham equations, where Ne is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in O(Ne3) operations, with a much smaller preconstant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the result...
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Even more efficient quantum computations of chemistry through tensor hypercontraction
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TL;DR: The key insight is to factorize the Hamiltonian using a method known as tensor hypercontraction (THC) and then to transform the Coulomb operator into an isospectral diagonal form with a non-orthogonal basis defined by the THC factors.
181
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo.
Paul R. C. Kent,Abdulgani Annaberdiyev,Anouar Benali,M. Chandler Bennett,Edgar Josué Landinez Borda,Peter Doak,Hongxia Hao,Kenneth D. Jordan,Jaron T. Krogel,Ilkka Kylänpää,Joonho Lee,Ye Luo,Fionn D. Malone,Cody A. Melton,Lubos Mitas,Miguel A. Morales,Eric Neuscamman,Fernando A. Reboredo,Brenda M. Rubenstein,Kayahan Saritas,Shiv Upadhyay,Guangming Wang,Shuai Zhang,Luning Zhao +23 more
TL;DR: In this paper, the authors review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility.
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
Paul R. C. Kent,Abdulgani Annaberdiyev,Anouar Benali,M. Chandler Bennett,Edgar Josué Landinez Borda,Peter Doak,Kenneth D. Jordan,Jaron T. Krogel,Ilkka Kylänpää,Joonho Lee,Ye Luo,Fionn D. Malone,Cody A. Melton,Lubos Mitas,Miguel A. Morales,Eric Neuscamman,Fernando A. Reboredo,Brenda M. Rubenstein,Kayahan Saritas,Shiv Upadhyay,Hongxia Hao,Guangming Wang,Shuai Zhang,Luning Zhao +23 more
TL;DR: In this article, the authors review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility.
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Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space-Time Approach.
Ivan Duchemin,Xavier Blase +1 more
TL;DR: In this article, an implementation of the GW space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization or sparsity cons...
74
Numerical methods for Kohn–Sham density functional theory
Lin Lin,Jianfeng Lu,Lexing Ying +2 more
TL;DR: The basics as well as state-of-the-art numerical methods are reviewed, and the unique numerical challenges of DFT are focused on.
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