Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory
Abstract
We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter cISDF controls the trade-off between accuracy and cost. In particular, cISDF sets the number of interpolation points used in THC, NIP = cISDF × NX with NX being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., ωB97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 noncovalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on cISDF for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and C20. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wave function amplitudes as wellmore »
- Authors:
-
- Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Div.
- Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
- OSTI Identifier:
- 1779232
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Journal of Chemical Theory and Computation
- Additional Journal Information:
- Journal Volume: 16; Journal Issue: 1; Journal ID: ISSN 1549-9618
- Publisher:
- American Chemical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Lee, Joonho, Lin, Lin, and Head-Gordon, Martin. Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory. United States: N. p., 2019.
Web. doi:10.1021/acs.jctc.9b00820.
Lee, Joonho, Lin, Lin, & Head-Gordon, Martin. Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory. United States. https://doi.org/10.1021/acs.jctc.9b00820
Lee, Joonho, Lin, Lin, and Head-Gordon, Martin. 2019.
"Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory". United States. https://doi.org/10.1021/acs.jctc.9b00820. https://www.osti.gov/servlets/purl/1779232.
@article{osti_1779232,
title = {Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory},
author = {Lee, Joonho and Lin, Lin and Head-Gordon, Martin},
abstractNote = {We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter cISDF controls the trade-off between accuracy and cost. In particular, cISDF sets the number of interpolation points used in THC, NIP = cISDF × NX with NX being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., ωB97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 noncovalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on cISDF for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and C20. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wave function amplitudes as well as for the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.},
doi = {10.1021/acs.jctc.9b00820},
url = {https://www.osti.gov/biblio/1779232},
journal = {Journal of Chemical Theory and Computation},
issn = {1549-9618},
number = 1,
volume = 16,
place = {United States},
year = {Tue Dec 03 00:00:00 EST 2019},
month = {Tue Dec 03 00:00:00 EST 2019}
}
Works referenced in this record:
Semi-exact concentric atomic density fitting: Reduced cost and increased accuracy compared to standard density fitting
journal, February 2014
- Hollman, David S.; Schaefer, Henry F.; Valeev, Edward F.
- The Journal of Chemical Physics, Vol. 140, Issue 6
Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting
journal, November 2018
- Malone, Fionn D.; Zhang, Shuai; Morales, Miguel A.
- Journal of Chemical Theory and Computation, Vol. 15, Issue 1
An implementation of RI-SCF on parallel computers
journal, January 1997
- Fr�chtl, Herbert A.; Kendall, Rick A.; Harrison, Robert J.
- International Journal of Quantum Chemistry, Vol. 64, Issue 1
Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction Energies
journal, June 2015
- Kokkila Schumacher, Sara I. L.; Hohenstein, Edward G.; Parrish, Robert M.
- Journal of Chemical Theory and Computation, Vol. 11, Issue 7
Principles for a direct SCF approach to LICAO - MO ab - initio calculations : Direct
journal, September 1982
- Almlöf, J.; Faegri, K.; Korsell, K.
- Journal of Computational Chemistry, Vol. 3, Issue 3
Pseudospectral Hartree–Fock theory: Applications and algorithmic improvements
journal, September 1990
- Ringnalda, Murco N.; Belhadj, Mahfoud; Friesner, Richard A.
- The Journal of Chemical Physics, Vol. 93, Issue 5
Fitting the Coulomb potential variationally in Xα molecular calculations
journal, March 1983
- Dunlap, B. I.
- The Journal of Chemical Physics, Vol. 78, Issue 6
W4-11: A high-confidence benchmark dataset for computational thermochemistry derived from first-principles W4 data
journal, July 2011
- Karton, Amir; Daon, Shauli; Martin, Jan M. L.
- Chemical Physics Letters, Vol. 510, Issue 4-6
Auxiliary basis sets to approximate Coulomb potentials
journal, June 1995
- Eichkorn, Karin; Treutler, Oliver; Öhm, Holger
- Chemical Physics Letters, Vol. 240, Issue 4
Tensor decomposition in post-Hartree–Fock methods. II. CCD implementation
journal, December 2013
- Benedikt, Udo; Böhm, Karl-Heinz; Auer, Alexander A.
- The Journal of Chemical Physics, Vol. 139, Issue 22
The prism algorithm for two-electron integrals
journal, December 1991
- Gill, Peter M. W.; Pople, John A.
- International Journal of Quantum Chemistry, Vol. 40, Issue 6
A method for two‐electron Gaussian integral and integral derivative evaluation using recurrence relations
journal, November 1988
- Head‐Gordon, Martin; Pople, John A.
- The Journal of Chemical Physics, Vol. 89, Issue 9
Two-electron repulsion integrals over Gaussians functions
journal, December 1991
- Gill, Peter M. W.; Johnson, Benny G.; Pople, John A.
- International Journal of Quantum Chemistry, Vol. 40, Issue 6
Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range -Body Potentials in Many-Body Quantum Problems
journal, September 2013
- Parrish, Robert M.; Hohenstein, Edward G.; Schunck, Nicolas F.
- Physical Review Letters, Vol. 111, Issue 13
Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm
journal, July 2015
- Manzer, Samuel; Horn, Paul R.; Mardirossian, Narbe
- The Journal of Chemical Physics, Vol. 143, Issue 2
Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
journal, November 2018
- Lee, Joonho; Huggins, William J.; Head-Gordon, Martin
- Journal of Chemical Theory and Computation, Vol. 15, Issue 1
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon
journal, January 1993
- Woon, David E.; Dunning, Thom H.
- The Journal of Chemical Physics, Vol. 98, Issue 2
Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes
journal, January 2019
- Lee, Joonho; Head-Gordon, Martin
- Physical Chemistry Chemical Physics, Vol. 21, Issue 9
Linear scaling density fitting
journal, November 2006
- Sodt, Alex; Subotnik, Joseph E.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 125, Issue 19
General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks
journal, October 2013
- Epifanovsky, Evgeny; Zuev, Dmitry; Feng, Xintian
- The Journal of Chemical Physics, Vol. 139, Issue 13
Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules
journal, August 1986
- Friesner, Richard A.
- The Journal of Chemical Physics, Vol. 85, Issue 3
Laplace transform techniques in Mo/ller–Plesset perturbation theory
journal, January 1992
- Häser, Marco; Almlöf, Jan
- The Journal of Chemical Physics, Vol. 96, Issue 1
Pseudospectral full configuration interaction
journal, August 1992
- Martinez, Todd J.; Mehta, Aseem; Carter, Emily A.
- The Journal of Chemical Physics, Vol. 97, Issue 3
Self‐consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory
journal, April 1977
- Seeger, Rolf; Pople, John A.
- The Journal of Chemical Physics, Vol. 66, Issue 7
What Are the Ground State Structures of C 20 and C 24 ? An Explicitly Correlated Ab Initio Approach
journal, December 2015
- Manna, Debashree; Martin, Jan M. L.
- The Journal of Physical Chemistry A, Vol. 120, Issue 1
Improvements on the direct SCF method: Improved Direct SCF Method
journal, January 1989
- Häser, Marco; Ahlrichs, Reinhart
- Journal of Computational Chemistry, Vol. 10, Issue 1
Fast Hartree–Fock theory using local density fitting approximations
journal, November 2004
- Polly, Robert; Werner *, Hans-Joachim; Manby, Frederick R.
- Molecular Physics, Vol. 102, Issue 21-22
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
journal, September 2014
- Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny
- Molecular Physics, Vol. 113, Issue 2
A direct atomic orbital driven implementation of the coupled cluster singles and doubles (CCSD) model
journal, September 1994
- Koch, Henrik; Christiansen, Ove; Kobayashi, Rika
- Chemical Physics Letters, Vol. 228, Issue 1-3
Linear-scaling atomic orbital-based second-order Møller–Plesset perturbation theory by rigorous integral screening criteria
journal, February 2009
- Doser, Bernd; Lambrecht, Daniel S.; Kussmann, Jörg
- The Journal of Chemical Physics, Vol. 130, Issue 6
New pseudospectral algorithms for electronic structure calculations: Length scale separation and analytical two‐electron integral corrections
journal, September 1994
- Greeley, Burnham H.; Russo, Thomas V.; Mainz, Daniel T.
- The Journal of Chemical Physics, Vol. 101, Issue 5
Robust and variational fitting: Removing the four-center integrals from center stage in quantum chemistry
journal, September 2000
- Dunlap, B. I.
- Journal of Molecular Structure: THEOCHEM, Vol. 529, Issue 1-3
Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems
journal, February 1999
- Ayala, Philippe Y.; Scuseria, Gustavo E.
- The Journal of Chemical Physics, Vol. 110, Issue 8
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations
journal, February 2002
- Weigend, Florian; Köhn, Andreas; Hättig, Christof
- The Journal of Chemical Physics, Vol. 116, Issue 8
Open-shell coupled-cluster valence-bond theory augmented with an independent amplitude approximation for three-pair correlations: Application to a model oxygen-evolving complex and single molecular magnet
journal, December 2018
- Lee, Joonho; Small, David W.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 149, Issue 24
Linear scaling density functional calculations via the continuous fast multipole method
journal, May 1996
- White, Christopher A.; Johnson, Benny G.; Gill, Peter M. W.
- Chemical Physics Letters, Vol. 253, Issue 3-4
M�ller-Plesset (MP2) perturbation theory for large molecules
journal, November 1993
- H�ser, Marco
- Theoretica Chimica Acta, Vol. 87, Issue 1-2
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
journal, December 2017
- Lu, Jianfeng; Thicke, Kyle
- Journal of Computational Physics, Vol. 351
Linear Scaling Density Functional Calculations with Gaussian Orbitals
journal, June 1999
- Scuseria, Gustavo E.
- The Journal of Physical Chemistry A, Vol. 103, Issue 25
Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers
journal, March 1996
- Bernholdt, David E.; Harrison, Robert J.
- Chemical Physics Letters, Vol. 250, Issue 5-6
Adaptively Compressed Polarizability Operator for Accelerating Large Scale Ab Initio Phonon Calculations
journal, January 2017
- Lin, Lin; Xu, Ze; Ying, Lexing
- Multiscale Modeling & Simulation, Vol. 15, Issue 1
The continuous fast multipole method
journal, November 1994
- White, Christopher A.; Johnson, Benny G.; Gill, Peter M. W.
- Chemical Physics Letters, Vol. 230, Issue 1-2
Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers
journal, August 2018
- Lee, Joonho; Head-Gordon, Martin
- Journal of Chemical Theory and Computation, Vol. 14, Issue 10
Robust variational fitting: Gáspár's variational exchange can accurately be treated analytically
journal, April 2000
- Dunlap, B. I.
- Journal of Molecular Structure: THEOCHEM, Vol. 501-502
Tensor-structured coupled cluster theory
journal, November 2017
- Schutski, Roman; Zhao, Jinmo; Henderson, Thomas M.
- The Journal of Chemical Physics, Vol. 147, Issue 18
Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange
journal, February 2009
- Neese, Frank; Wennmohs, Frank; Hansen, Andreas
- Chemical Physics, Vol. 356, Issue 1-3
Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2
journal, March 2013
- Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.
- The Journal of Chemical Physics, Vol. 138, Issue 12
The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
journal, October 1970
- Boys, S.F.; Bernardi, F.
- Molecular Physics, Vol. 19, Issue 4, p. 553-566
Computation of electron repulsion integrals involving contracted Gaussian basis functions
journal, May 1978
- Pople, John A.; Hehre, Warren J.
- Journal of Computational Physics, Vol. 27, Issue 2
Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method
journal, November 2004
- Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D.
- The Journal of Chemical Physics, Vol. 121, Issue 20
Making the random phase approximation to electronic correlation accurate
journal, October 2009
- Grüneis, Andreas; Marsman, Martijn; Harl, Judith
- The Journal of Chemical Physics, Vol. 131, Issue 15
Efficient Implementation of the Pair Atomic Resolution of the Identity Approximation for Exact Exchange for Hybrid and Range-Separated Density Functionals
journal, January 2015
- Manzer, Samuel F.; Epifanovsky, Evgeny; Head-Gordon, Martin
- Journal of Chemical Theory and Computation, Vol. 11, Issue 2
An efficient algorithm for the generation of two-electron repulsion integrals over gaussian basis functions
journal, April 1989
- Gill, Peter M. W.; Head-Gordon, Martin; Pople, John A.
- International Journal of Quantum Chemistry, Vol. 36, Issue S23
Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O ( r 6 ) to O ( r 4 )
journal, July 2014
- Shenvi, Neil; van Aggelen, Helen; Yang, Yang
- The Journal of Chemical Physics, Vol. 141, Issue 2
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory
journal, July 2012
- Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 137, Issue 4
Simplifications in the generation and transformation of two-electron integrals in molecular calculations
journal, October 1977
- Beebe, Nelson H. F.; Linderberg, Jan
- International Journal of Quantum Chemistry, Vol. 12, Issue 4
Low rank factorization of the Coulomb integrals for periodic coupled cluster theory
journal, March 2017
- Hummel, Felix; Tsatsoulis, Theodoros; Grüneis, Andreas
- The Journal of Chemical Physics, Vol. 146, Issue 12
Pseudospectral Hartree–Fock gradient calculations
journal, June 1991
- Won, Youngdo; Lee, Jung‐Goo; Ringnalda, Murco N.
- The Journal of Chemical Physics, Vol. 94, Issue 12
Tensor hypercontraction. II. Least-squares renormalization
journal, December 2012
- Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 137, Issue 22
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon
journal, October 2017
- Hu, Wei; Lin, Lin; Yang, Chao
- Journal of Chemical Theory and Computation, Vol. 13, Issue 11
On some approximations in applications of X α theory
journal, October 1979
- Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R.
- The Journal of Chemical Physics, Vol. 71, Issue 8
Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes
journal, January 2017
- Lee, Joonho; Small, David W.; Epifanovsky, Evgeny
- Journal of Chemical Theory and Computation, Vol. 13, Issue 2
Attractive electron-electron interactions within robust local fitting approximations
journal, April 2013
- Merlot, Patrick; Kjaergaard, Thomas; Helgaker, Trygve
- Journal of Computational Chemistry, Vol. 34, Issue 17
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction
journal, May 2014
- Parrish, Robert M.; Sherrill, C. David; Hohenstein, Edward G.
- The Journal of Chemical Physics, Vol. 140, Issue 18
Coupled‐cluster theory employing approximate integrals: An approach to avoid the input/output and storage bottlenecks
journal, July 1994
- Rendell, Alistair P.; Lee, Timothy J.
- The Journal of Chemical Physics, Vol. 101, Issue 1
Separable resolution-of-the-identity with all-electron Gaussian bases: Application to cubic-scaling RPA
journal, May 2019
- Duchemin, Ivan; Blase, Xavier
- The Journal of Chemical Physics, Vol. 150, Issue 17
A geometric approach to direct minimization
journal, June 2002
- Van Voorhis, Troy; Head-Gordon, Martin
- Molecular Physics, Vol. 100, Issue 11
Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction
journal, July 2018
- Song, Chenchen; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 149, Issue 4
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989
- Dunning, Thom H.
- The Journal of Chemical Physics, Vol. 90, Issue 2
Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations
journal, May 2003
- Werner, Hans-Joachim; Manby, Frederick R.; Knowles, Peter J.
- The Journal of Chemical Physics, Vol. 118, Issue 18
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions
journal, May 1992
- Kendall, Rick A.; Dunning, Thom H.; Harrison, Robert J.
- The Journal of Chemical Physics, Vol. 96, Issue 9
Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis
journal, March 2017
- Schäfer, Tobias; Ramberger, Benjamin; Kresse, Georg
- The Journal of Chemical Physics, Vol. 146, Issue 10
Coulombic potential energy integrals and approximations
journal, May 1973
- Whitten, J. L.
- The Journal of Chemical Physics, Vol. 58, Issue 10
Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials
journal, October 1997
- Eichkorn, Karin; Weigend, Florian; Treutler, Oliver
- Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 97, Issue 1-4
Solution of the Hartree–Fock equations for polyatomic molecules by a pseudospectral method
journal, March 1987
- Friesner, Richard A.
- The Journal of Chemical Physics, Vol. 86, Issue 6
Pseudospectral Mo/ller–Plesset perturbation theory through third order
journal, March 1994
- Martinez, Todd J.; Carter, Emily A.
- The Journal of Chemical Physics, Vol. 100, Issue 5
Third-Order Møller–Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions
journal, July 2019
- Bertels, Luke W.; Lee, Joonho; Head-Gordon, Martin
- The Journal of Physical Chemistry Letters, Vol. 10, Issue 15
Efficient recursive computation of molecular integrals over Cartesian Gaussian functions
journal, April 1986
- Obara, S.; Saika, A.
- The Journal of Chemical Physics, Vol. 84, Issue 7
On Resolution-of-the-Identity Electron Repulsion Integral Approximations and Variational Stability
journal, September 2017
- Wirz, Lukas N.; Reine, Simen S.; Pedersen, Thomas Bondo
- Journal of Chemical Theory and Computation, Vol. 13, Issue 10
Use of approximate integrals in ab initio theory. An application in MP2 energy calculations
journal, June 1993
- Feyereisen, Martin; Fitzgerald, George; Komornicki, Andrew
- Chemical Physics Letters, Vol. 208, Issue 5-6
Computation of electron repulsion integrals using the rys quadrature method
journal, July 1983
- Rys, J.; Dupuis, M.; King, H. F.
- Journal of Computational Chemistry, Vol. 4, Issue 2
A multicenter numerical integration scheme for polyatomic molecules
journal, February 1988
- Becke, A. D.
- The Journal of Chemical Physics, Vol. 88, Issue 4
Convergence acceleration of iterative sequences. the case of scf iteration
journal, July 1980
- Pulay, Péter
- Chemical Physics Letters, Vol. 73, Issue 2
Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory
journal, June 2019
- Lee, Joonho; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 150, Issue 24
Pseudospectral double excitation configuration interaction
journal, May 1993
- Martinez, Todd J.; Carter, Emily A.
- The Journal of Chemical Physics, Vol. 98, Issue 9
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
- Mardirossian, Narbe; Head-Gordon, Martin
- Physical Chemistry Chemical Physics, Vol. 16, Issue 21
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost
journal, December 2015
- Lu, Jianfeng; Ying, Lexing
- Journal of Computational Physics, Vol. 302
ImprovedSCF convergence acceleration
journal, January 1982
- Pulay, P.
- Journal of Computational Chemistry, Vol. 3, Issue 4
Discrete variable representation in electronic structure theory: Quadrature grids for least-squares tensor hypercontraction
journal, May 2013
- Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 138, Issue 19
Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) Time
journal, July 2013
- Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.
- The Journal of Physical Chemistry B, Vol. 117, Issue 42
Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure
journal, September 1973
- Baerends, E. J.; Ellis, D. E.; Ros, P.
- Chemical Physics, Vol. 2, Issue 1
An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions
journal, August 2019
- Lee, Joonho; Malone, Fionn D.; Morales, Miguel A.
- The Journal of Chemical Physics, Vol. 151, Issue 6
Linear and sublinear scaling formation of Hartree–Fock-type exchange matrices
journal, August 1998
- Ochsenfeld, Christian; White, Christopher A.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 109, Issue 5
Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit?
journal, April 2013
- Řezáč, Jan; Hobza, Pavel
- Journal of Chemical Theory and Computation, Vol. 9, Issue 5
Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction
journal, January 2017
- Song, Chenchen; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 146, Issue 3
Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units
journal, October 2017
- Song, Chenchen; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 147, Issue 16
Electron repulsion integral approximations and error bounds: Molecular applications
journal, September 1974
- Jafri, J. A.; Whitten, J. L.
- The Journal of Chemical Physics, Vol. 61, Issue 5
Solution of self-consistent field electronic structure equations by a pseudospectral method
journal, April 1985
- Friesner, Richard A.
- Chemical Physics Letters, Vol. 116, Issue 1
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions
journal, December 2012
- Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David
- The Journal of Chemical Physics, Vol. 137, Issue 22
A standard grid for density functional calculations
journal, July 1993
- Gill, Peter M. W.; Johnson, Benny G.; Pople, John A.
- Chemical Physics Letters, Vol. 209, Issue 5-6
Integral approximations for LCAO-SCF calculations
journal, October 1993
- Vahtras, O.; Almlöf, J.; Feyereisen, M. W.
- Chemical Physics Letters, Vol. 213, Issue 5-6
Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity
journal, May 2016
- Song, Chenchen; Martínez, Todd J.
- The Journal of Chemical Physics, Vol. 144, Issue 17
Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation with Applications to Hybrid Functional Electronic Structure Calculations
journal, January 2018
- Dong, Kun; Hu, Wei; Lin, Lin
- Journal of Chemical Theory and Computation, Vol. 14, Issue 3
Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) Time
journal, July 2013
- Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.
- The Journal of Physical Chemistry B, Vol. 117, Issue 42
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction
journal, May 2014
- Parrish, Robert M.; Sherrill, C. David; Hohenstein, Edward G.
- The Journal of Chemical Physics, Vol. 140, Issue 18
Tensor-Structured Coupled Cluster Theory
text, January 2017
- Schutski, Roman; Zhao, Jinmo; Henderson, Thomas M.
- arXiv