Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Journal Article · · Journal of Chemical Theory and Computation
 [1];  [2];  [1]
  1. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
  2. Columbia University, New York, NY (United States)
+ Show Author Affiliations
Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. In conclusion, we perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division (CSGB)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
2281832
Journal Information:
Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 17 Vol. 19; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (77)

First Principles Computation of Lattice Energies of Organic Solids: The Benzene Crystal journal March 2008
Accurate treatment of solids with the HSE screened hybrid journal October 2010
Simplifications in the generation and transformation of two-electron integrals in molecular calculations journal October 1977
Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals journal May 2005
The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals journal July 2007
Solution of self-consistent field electronic structure equations by a pseudospectral method journal April 1985
On the Beebe-Linderberg two-electron integral approximation journal December 1986
Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure journal September 1973
Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange journal February 2009
Seeking widely applicable dispersion-corrected GGA functionals: The performances of TCA+D3 and RevTCA+D3 on solid-state systems journal January 2023
Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach journal April 2005
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting journal December 2017
On the prediction of band gaps from hybrid functional theory journal July 2001
Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction journal March 2021
Low-Rank Approximations Accelerated Plane-Wave Hybrid Functional Calculations with k-Point Sampling journal December 2021
Integral-Direct Hartree–Fock and Møller–Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal journal August 2022
Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method journal November 2022
Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids with Pseudopotentials Near the Basis Set Limit journal December 2022
Interpolative Separable Density Fitting for Accelerating Two-Electron Integrals: A Theoretical Perspective journal January 2023
Adaptively Compressed Exchange Operator journal April 2016
Assessment of Different Quantum Mechanical Methods for the Prediction of Structure and Cohesive Energy of Molecular Crystals journal June 2016
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon journal October 2017
Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation with Applications to Hybrid Functional Electronic Structure Calculations journal January 2018
Electronic Exchange and Correlation in van der Waals Systems: Balancing Semilocal and Nonlocal Energy Contributions journal February 2018
Comprehensive Thermochemical Benchmark Set of Realistic Closed-Shell Metal Organic Reactions journal March 2018
Robust Periodic Fock Exchange with Atom-Centered Gaussian Basis Sets journal August 2018
Assessment of DFT Methods for Transition Metals with the TMC151 Compilation of Data Sets and Comparison with Accuracies for Main-Group Chemistry journal April 2019
Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory journal November 2019
Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction journal January 2020
Interpolative Separable Density Fitting Decomposition for Accelerating Hartree–Fock Exchange Calculations within Numerical Atomic Orbitals journal June 2020
Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals journal December 2016
Energy Ranking of Molecular Crystals Using Density Functional Theory Calculations and an Empirical van der Waals Correction journal August 2005
Ab Initio Investigation of Structure and Cohesive Energy of Crystalline Urea journal December 2006
DFT-D3 Study of Some Molecular Crystals journal March 2014
B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to molecular crystals journal January 2008
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
MN15: A Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions journal January 2016
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions journal January 2017
Theory and practice of modeling van der Waals interactions in electronic-structure calculations journal January 2019
XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy journal January 2023
Coulombic potential energy integrals and approximations journal May 1973
Electron repulsion integral approximations and error bounds: Molecular applications journal September 1974
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu journal April 2010
An overlap fitted chain of spheres exchange method journal October 2011
Linear scaling computation of the Hartree–Fock exchange matrix journal August 1996
A linear scaling method for Hartree–Fock exchange calculations of large molecules journal November 1996
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory journal July 2012
Linear scaling computation of the Fock matrix journal April 1997
Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build journal June 1997
Linear and sublinear scaling formation of Hartree–Fock-type exchange matrices journal August 1998
Tensor hypercontraction. II. Least-squares renormalization journal December 2012
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions journal December 2012
Toward reliable density functional methods without adjustable parameters: The PBE0 model journal April 1999
Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory journal March 2014
Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O ( r   6 ) to O ( r   4 ) journal July 2014
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V journal February 2015
Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm journal July 2015
SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters journal January 2016
ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation journal June 2016
Gaussian and plane-wave mixed density fitting for periodic systems journal October 2017
Towards hybrid density functional calculations of molecular crystals via fragment-based methods journal September 2018
Fast periodic Gaussian density fitting by range separation journal April 2021
Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package journal August 2021
Approaching the basis set limit in Gaussian-orbital-based periodic calculations with transferability: Performance of pure density functionals for simple semiconductors journal October 2021
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals journal April 2017
A hybrid Gaussian and plane wave density functional scheme journal October 1997
Self-consistent Hartree-Fock and screened-exchange calculations in solids: Application to silicon journal September 1986
Projector augmented-wave method journal December 1994
Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions journal January 1996
Separable dual-space Gaussian pseudopotentials journal July 1996
Comparison of screened hybrid density functional theory to diffusion Monte Carlo in calculations of total energies of silicon phases and defects journal September 2006
Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential journal May 2008
Accurate defect levels obtained from the HSE06 range-separated hybrid functional journal April 2010
Assessing the accuracy of hybrid functionals in the determination of defect levels: Application to the As antisite in GaAs journal August 2011
Regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: Towards chemical accuracy in nontrivial systems journal April 2013
Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy journal August 2014
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals [Supplemental Data] fileset June 2017

Similar Records

Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory
Journal Article · Mon Dec 02 19:00:00 EST 2019 · Journal of Chemical Theory and Computation · OSTI ID:1779232
Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity
Journal Article · Sat May 07 00:00:00 EDT 2016 · Journal of Chemical Physics · OSTI ID:22657956
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon
Journal Article · Thu Sep 28 20:00:00 EDT 2017 · Journal of Chemical Theory and Computation · OSTI ID:1480242

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
97 MATHEMATICS AND COMPUTING