Monte Carlo explicitly correlated second-order many-body perturbation theory

Johnson, Cole M.; Doran, Alexander E.; Zhang, Jinmei; Valeev, Edward F.; Hirata, So

doi:10.1063/1.4964854

Title: Monte Carlo explicitly correlated second-order many-body perturbation theory

Journal Article · Fri Oct 21 00:00:00 EDT 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4964854· OSTI ID:1473885

Johnson, Cole M. ^[1]; Doran, Alexander E. ^[1]; Zhang, Jinmei ^[2];

^[2];

^[1]

Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Chemistry

A stochastic algorithm is proposed and implemented that computes a basis-set-incompleteness (F12) correction to an ab initio second-order many-body perturbation energy as a short sum of 6- to 15-dimensional integrals of Gaussian-type orbitals, an explicit function of the electron-electron distance (geminal), and its associated excitation amplitudes held fixed at the values suggested by Ten-no. The integrals are directly evaluated (without a resolution-of-the-identity approximation or an auxiliary basis set) by the Metropolis Monte Carlo method. Applications of this method to 17 molecular correlation energies and 12 gas-phase reaction energies reveal that both the nonvariational and variational formulas for the correction give reliable correlation energies (98% or higher) and reaction energies (within 2 kJ mol^-1 with a smaller statistical uncertainty) near the complete-basis-set limits by using just the aug-cc-pVDZ basis set. The nonvariational formula is found to be 2–10 times less expensive to evaluate than the variational one, though the latter yields energies that are bounded from below and is, therefore, slightly but systematically more accurate for energy differences. Being capable of using virtually any geminal form, the method confirms the best overall performance of the Slater-type geminal among 6 forms satisfying the same cusp conditions. Lastly, not having to precompute lower-dimensional integrals analytically, to store them on disk, or to transform them in a nonscalable dense-matrix-multiplication algorithm, the method scales favorably with both system size and computer size; the cost increases only as O(n⁴) with the number of orbitals (n), and its parallel efficiency reaches 99.9% of the ideal case on going from 16 to 4096 computer processors.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-12ER46875; SC0008692; FG02-11ER16211; SC0006028

OSTI ID:: 1473885

Alternate ID(s):: OSTI ID: 1329495

Journal Information:: Journal of Chemical Physics, Vol. 145, Issue 15; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 14 works

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References (94)

Cusp Conditions for Molecular Wavefunctions Pack, Russell T.; Brown, W. Byers The Journal of Chemical Physics, Vol. 45, Issue 2 https://doi.org/10.1063/1.1727605	journal	July 1966
Møller-plesset calculations taking care of the correlation CUSP Klopper, Wim; Kutzelnigg, Werner Chemical Physics Letters, Vol. 134, Issue 1 https://doi.org/10.1016/0009-2614(87)80005-2	journal	February 1987
Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium Hylleraas, Egil A. Zeitschrift f�r Physik, Vol. 54, Issue 5-6 https://doi.org/10.1007/BF01375457	journal	May 1929
New correlation factors for explicitly correlated electronic wave functions Tew, David P.; Klopper, Wim The Journal of Chemical Physics, Vol. 123, Issue 7 https://doi.org/10.1063/1.1999632	journal	August 2005
Thermodynamic limit of the energy density in a crystal Hirata, So; Ohnishi, Yu-ya Physical Chemistry Chemical Physics, Vol. 14, Issue 21 https://doi.org/10.1039/c2cp23958b	journal	January 2012
Second-order Møller–Plesset theory with linear R12 terms (MP2-R12) revisited: Auxiliary basis set method and massively parallel implementation Valeev, Edward F.; Janssen, Curtis L. The Journal of Chemical Physics, Vol. 121, Issue 3 https://doi.org/10.1063/1.1759319	journal	July 2004
Brueckner-Goldstone quantum Monte Carlo for correlation energies and quasiparticle energy bands of one-dimensional solids Willow, Soohaeng Yoo; Kim, Kwang S.; Hirata, So Physical Review B, Vol. 90, Issue 20 https://doi.org/10.1103/PhysRevB.90.201110	journal	November 2014
Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 141, Issue 24 https://doi.org/10.1063/1.4904220	journal	December 2014
General orbital invariant MP2-F12 theory Werner, Hans-Joachim; Adler, Thomas B.; Manby, Frederick R. The Journal of Chemical Physics, Vol. 126, Issue 16 https://doi.org/10.1063/1.2712434	journal	April 2007
Semistochastic Projector Monte Carlo Method Petruzielo, F. R.; Holmes, A. A.; Changlani, Hitesh J. Physical Review Letters, Vol. 109, Issue 23 https://doi.org/10.1103/PhysRevLett.109.230201	journal	December 2012
The calculation of excited state properties with quantum Monte Carlo Ceperley, D. M.; Bernu, B. The Journal of Chemical Physics, Vol. 89, Issue 10 https://doi.org/10.1063/1.455398	journal	November 1988
Explicitly Correlated Electrons in Molecules Hättig, Christof; Klopper, Wim; Köhn, Andreas Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200168z	journal	December 2011
Computing molecular correlation energies with guaranteed precision Bischoff, Florian A.; Valeev, Edward F. The Journal of Chemical Physics, Vol. 139, Issue 11 https://doi.org/10.1063/1.4820404	journal	September 2013
Many-Body Problem with Strong Forces Jastrow, Robert Physical Review, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRev.98.1479	journal	June 1955
Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics Dahle, P?l; Helgaker, Trygve; Jonsson, Dan Physical Chemistry Chemical Physics, Vol. 9, Issue 24 https://doi.org/10.1039/b616488a	journal	January 2007
R12 methods in explicitly correlated molecular electronic structure theory Klopper, Wim; Manby, Frederick R.; Ten-No, Seiichiro International Reviews in Physical Chemistry, Vol. 25, Issue 3 https://doi.org/10.1080/01442350600799921	journal	July 2006
Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations Bak, Keld L.; Jørgensen, Poul; Olsen, Jeppe The Journal of Chemical Physics, Vol. 112, Issue 21 https://doi.org/10.1063/1.481544	journal	June 2000
A new functional for variational calculation of atomic and molecular second-order correlation energies Szalewicz, Krzystof; Jeziorski, Bogumil; Monkhorst, Hendrik J. Chemical Physics Letters, Vol. 91, Issue 3 https://doi.org/10.1016/0009-2614(82)83634-8	journal	September 1982
Stochastic evaluation of second-order Dyson self-energies Willow, Soohaeng Yoo; Kim, Kwang S.; Hirata, So The Journal of Chemical Physics, Vol. 138, Issue 16 https://doi.org/10.1063/1.4801862	journal	April 2013
Accurate quantum‐chemical calculations: The use of Gaussian‐type geminal functions in the treatment of electron correlation Persson, B. Joakim; Taylor, Peter R. The Journal of Chemical Physics, Vol. 105, Issue 14 https://doi.org/10.1063/1.472432	journal	October 1996
Evaluation of molecular integrals over Gaussian basis functions Dupuis, Michel; Rys, John; King, Harry F. The Journal of Chemical Physics, Vol. 65, Issue 1 https://doi.org/10.1063/1.432807	journal	July 1976
Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models Shepherd, James J.; Booth, George H.; Alavi, Ali The Journal of Chemical Physics, Vol. 136, Issue 24 https://doi.org/10.1063/1.4720076	journal	June 2012
Convergence Acceleration of Parallel Monte Carlo Second-Order Many-Body Perturbation Calculations Using Redundant Walkers Willow, Soohaeng Yoo; Hermes, Matthew R.; Kim, Kwang S. Journal of Chemical Theory and Computation, Vol. 9, Issue 10 https://doi.org/10.1021/ct400557z	journal	September 2013
Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory Kutzelnigg, Werner; Klopper, Wim The Journal of Chemical Physics, Vol. 94, Issue 3 https://doi.org/10.1063/1.459921	journal	February 1991
Rates of convergence of the partial‐wave expansions of atomic correlation energies Kutzelnigg, Werner; Morgan, John D. The Journal of Chemical Physics, Vol. 96, Issue 6 https://doi.org/10.1063/1.462811	journal	March 1992
Impact of electron–electron cusp on configuration interaction energies Prendergast, David; Nolan, M.; Filippi, Claudia The Journal of Chemical Physics, Vol. 115, Issue 4 https://doi.org/10.1063/1.1383585	journal	July 2001
Improving on the resolution of the identity in linear R12 ab initio theories Valeev, Edward F. Chemical Physics Letters, Vol. 395, Issue 4-6 https://doi.org/10.1016/j.cplett.2004.07.061	journal	September 2004
Symmetry-adapted integrals over many-electron basis functions and operators Dahle, P.; Taylor, P. R. Theoretical Chemistry Accounts, Vol. 105, Issue 6 https://doi.org/10.1007/PL00012384	journal	May 2001
Explicitly Correlated R12/F12 Methods for Electronic Structure Kong, Liguo; Bischoff, Florian A.; Valeev, Edward F. Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200204r	journal	December 2011
On the eigenfunctions of many-particle systems in quantum mechanics Kato, Tosio Communications on Pure and Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1002/cpa.3160100201	journal	January 1957
Erratum: “Stochastic many-body perturbation theory for anharmonic molecular vibrations” [J. Chem. Phys. 141, 084105 (2014)] Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 143, Issue 12 https://doi.org/10.1063/1.4932101	journal	September 2015
Erratum: “Stochastic algorithm for size-extensive vibrational self-consistent field methods on fully anharmonic potential energy surfaces” [J. Chem. Phys. 141, 244111 (2014)] Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 143, Issue 12 https://doi.org/10.1063/1.4932102	journal	September 2015
Variational formulation of perturbative explicitly-correlated coupled-cluster methods Torheyden, Martin; Valeev, Edward F. Physical Chemistry Chemical Physics, Vol. 10, Issue 23 https://doi.org/10.1039/b803620a	journal	January 2008
Monte Carlo MP2 on Many Graphical Processing Units Doran, Alexander E.; Hirata, So Journal of Chemical Theory and Computation, Vol. 12, Issue 10 https://doi.org/10.1021/acs.jctc.6b00588	journal	September 2016
The lowest wave function of the symmetrical many particles system Bijl, A. Physica, Vol. 7, Issue 9 https://doi.org/10.1016/0031-8914(40)90166-5	journal	November 1940
Publisher's Note: “A general formulation for the efficient evaluation of n -electron integrals over products of Gaussian charge distributions with Gaussian geminal functions” [J. Chem. Phys. 134, 244115 (2011)] Komornicki, Andrew; King, Harry F. The Journal of Chemical Physics, Vol. 135, Issue 12 https://doi.org/10.1063/1.3644335	journal	September 2011
Gaussian Geminals for Electron Pair Correlation Pan, Kee‐Chuan; King, Harry F. The Journal of Chemical Physics, Vol. 53, Issue 11 https://doi.org/10.1063/1.1673955	journal	December 1970
Revisiting the use of explicitly correlated geminals in coupled pair calculations: new perspectives and a proposal Monkhorst *, Hendrik J. Molecular Physics, Vol. 103, Issue 15-16 https://doi.org/10.1080/00268970500151494	journal	August 2005
Stochastic many-body perturbation theory for anharmonic molecular vibrations Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 141, Issue 8 https://doi.org/10.1063/1.4892614	journal	August 2014
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo Cleland, Deidre; Booth, George H.; Alavi, Ali The Journal of Chemical Physics, Vol. 132, Issue 4 https://doi.org/10.1063/1.3302277	journal	January 2010
Applications of quantum Monte Carlo methods in condensed systems Kolorenč, Jindřich; Mitas, Lubos Reports on Progress in Physics, Vol. 74, Issue 2 https://doi.org/10.1088/0034-4885/74/2/026502	journal	January 2011
Monte Carlo Methods in Ab Initio Quantum Chemistry Hammond, B. L.; Lester, W. A.; Reynolds, P. J. https://doi.org/10.1142/1170	book	March 1994
Note on an Approximation Treatment for Many-Electron Systems Møller, Chr.; Plesset, M. S. Physical Review, Vol. 46, Issue 7 https://doi.org/10.1103/PhysRev.46.618	journal	October 1934
Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor Manby, Frederick R.; Werner, Hans-Joachim; Adler, Thomas B. The Journal of Chemical Physics, Vol. 124, Issue 9 https://doi.org/10.1063/1.2173247	journal	March 2006
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions Grüneis, Andreas; Shepherd, James J.; Alavi, Ali The Journal of Chemical Physics, Vol. 139, Issue 8 https://doi.org/10.1063/1.4818753	journal	August 2013
Density functional theory for systems of very many atoms Kohn, W. International Journal of Quantum Chemistry, Vol. 56, Issue 4 https://doi.org/10.1002/qua.560560407	journal	November 1995
Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy Willow, Soohaeng Yoo; Zhang, Jinmei; Valeev, Edward F. The Journal of Chemical Physics, Vol. 140, Issue 3 https://doi.org/10.1063/1.4862255	journal	January 2014
Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams Willow, Soohaeng Yoo; Hirata, So The Journal of Chemical Physics, Vol. 140, Issue 2 https://doi.org/10.1063/1.4861561	journal	January 2014
Calculation of the molecular integrals with the range-separated correlation factor Silkowski, Michał; Lesiuk, Michał; Moszynski, Robert The Journal of Chemical Physics, Vol. 142, Issue 12 https://doi.org/10.1063/1.4915272	journal	March 2015
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001
Explicitly correlated second-order Møller–Plesset methods with auxiliary basis sets Klopper, Wim; Samson, Claire C. M. The Journal of Chemical Physics, Vol. 116, Issue 15 https://doi.org/10.1063/1.1461814	journal	April 2002
Molecular integrals over Gaussian-type geminal basis functions Persson, B. Joakim; Taylor, Peter R. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 97, Issue 1-4 https://doi.org/10.1007/s002140050258	journal	October 1997
Second-Order Many-Body Perturbation Theory: An Eternal Frontier Hirata, So; He, Xiao; Hermes, Matthew R. The Journal of Physical Chemistry A, Vol. 118, Issue 4 https://doi.org/10.1021/jp410587b	journal	December 2013
Communication: Excited states, dynamic correlation functions and spectral properties from full configuration interaction quantum Monte Carlo Booth, George H.; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 137, Issue 19 https://doi.org/10.1063/1.4766327	journal	November 2012
Error estimates on averages of correlated data Flyvbjerg, H.; Petersen, H. G. The Journal of Chemical Physics, Vol. 91, Issue 1 https://doi.org/10.1063/1.457480	journal	July 1989
Central Fields and Rydberg Formulas in Wave Mechanics Slater, J. C. Physical Review, Vol. 31, Issue 3 https://doi.org/10.1103/PhysRev.31.333	journal	March 1928
Projector Monte Carlo method based on configuration state functions. Test applications to the H4 system and dissociation of LiH Ohtsuka, Yuhki; Nagase, Shigeru Chemical Physics Letters, Vol. 463, Issue 4-6 https://doi.org/10.1016/j.cplett.2008.08.090	journal	October 2008
Extensivity of Energy and Electronic and Vibrational Structure Methods for Crystals Hirata, So; Keçeli, Murat; Ohnishi, Yu-ya Annual Review of Physical Chemistry, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-physchem-032511-143718	journal	May 2012
Numerical solution of the Sinanoǧlu equation using a multicentre radial-angular grid Hirata, So; Shiozaki, Toru; Johnson, Cole M. Molecular Physics, Vol. 115, Issue 5 https://doi.org/10.1080/00268976.2016.1199822	journal	June 2016
Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories Hirata, So The Journal of Physical Chemistry A, Vol. 107, Issue 46 https://doi.org/10.1021/jp034596z	journal	November 2003
Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems Neuhauser, Daniel; Rabani, Eran; Baer, Roi Journal of Chemical Theory and Computation, Vol. 9, Issue 1 https://doi.org/10.1021/ct300946j	journal	December 2012
Initiation of explicitly correlated Slater-type geminal theory Ten-no, Seiichiro Chemical Physics Letters, Vol. 398, Issue 1-3 https://doi.org/10.1016/j.cplett.2004.09.041	journal	November 2004
Analysis of the errors in explicitly correlated electronic structure theory May, Andrew J.; Valeev, Edward; Polly, Robert Physical Chemistry Chemical Physics, Vol. 7, Issue 14 https://doi.org/10.1039/b507781h	journal	January 2005
Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions Ceperley, D. Physical Review B, Vol. 18, Issue 7 https://doi.org/10.1103/PhysRevB.18.3126	journal	October 1978
Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations Huang, Chien-Jung; Umrigar, C. J.; Nightingale, M. P. The Journal of Chemical Physics, Vol. 107, Issue 8 https://doi.org/10.1063/1.474658	journal	August 1997
Combining explicitly correlated R12 and Gaussian geminal electronic structure theories Valeev, Edward F. The Journal of Chemical Physics, Vol. 125, Issue 24 https://doi.org/10.1063/1.2403852	journal	December 2006
NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations Valiev, M.; Bylaska, E. J.; Govind, N. Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489 https://doi.org/10.1016/j.cpc.2010.04.018	journal	September 2010
New implementation of second-order Møller-Plesset perturbation theory with an analytic Slater-type geminal Ten-no, Seiichiro The Journal of Chemical Physics, Vol. 126, Issue 1 https://doi.org/10.1063/1.2403853	journal	January 2007
Stochastic evaluation of second-order many-body perturbation energies Willow, Soohaeng Yoo; Kim, Kwang S.; Hirata, So The Journal of Chemical Physics, Vol. 137, Issue 20 https://doi.org/10.1063/1.4768697	journal	November 2012
Efficient recursive computation of molecular integrals over Cartesian Gaussian functions Obara, S.; Saika, A. The Journal of Chemical Physics, Vol. 84, Issue 7 https://doi.org/10.1063/1.450106	journal	April 1986
Computing many-body wave functions with guaranteed precision: The first-order Møller-Plesset wave function for the ground state of helium atom Bischoff, Florian A.; Harrison, Robert J.; Valeev, Edward F. The Journal of Chemical Physics, Vol. 137, Issue 10 https://doi.org/10.1063/1.4747538	journal	September 2012
LI. The zero-point energy of a system of particles Dingle, R. B. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 304 https://doi.org/10.1080/14786444908521743	journal	May 1949
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
Elimination of Coulombic infinities through transformation of the Hamiltonian Nooijen, Marcel; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 109, Issue 19 https://doi.org/10.1063/1.477485	journal	November 1998
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space Booth, George H.; Thom, Alex J. W.; Alavi, Ali The Journal of Chemical Physics, Vol. 131, Issue 5 https://doi.org/10.1063/1.3193710	journal	January 2009
Local configuration interaction: An efficient approach for larger molecules Sæbø, Svein; Pulay, Peter Chemical Physics Letters, Vol. 113, Issue 1 https://doi.org/10.1016/0009-2614(85)85003-X	journal	January 1985
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants Zhang, Shiwei; Krakauer, Henry Physical Review Letters, Vol. 90, Issue 13 https://doi.org/10.1103/PhysRevLett.90.136401	journal	April 2003
Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states Ten-no, Seiichiro The Journal of Chemical Physics, Vol. 138, Issue 16 https://doi.org/10.1063/1.4802766	journal	April 2013
Introduction to the Variational and Diffusion Monte Carlo Methods Toulouse, Julien; Assaraf, Roland; Umrigar, Cyrus J. Advances in Quantum Chemistry https://doi.org/10.1016/bs.aiq.2015.07.003	book	January 2016
Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures Ten-no, Seiichiro The Journal of Chemical Physics, Vol. 121, Issue 1 https://doi.org/10.1063/1.1757439	journal	January 2004
Explicitly correlated electronic structure theory from R12/F12 ansätze: Explicitly correlated electronic structure theory Ten-no, Seiichiro; Noga, Jozef Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 1 https://doi.org/10.1002/wcms.68	journal	May 2011
Diagrammatic Monte Carlo for correlated fermions Kozik, E.; Van Houcke, K.; Gull, E. EPL (Europhysics Letters), Vol. 90, Issue 1 https://doi.org/10.1209/0295-5075/90/10004	journal	April 2010
M ONTE C ARLO M ETHODS IN E LECTRONIC S TRUCTURES FOR L ARGE S YSTEMS Lüchow, Arne; Anderson, James B. Annual Review of Physical Chemistry, Vol. 51, Issue 1 https://doi.org/10.1146/annurev.physchem.51.1.501	journal	October 2000
Direct calculation of electron density in density-functional theory Yang, Weitao Physical Review Letters, Vol. 66, Issue 11 https://doi.org/10.1103/PhysRevLett.66.1438	journal	March 1991
Ground State of the Electron Gas by a Stochastic Method Ceperley, D. M.; Alder, B. J. Physical Review Letters, Vol. 45, Issue 7, p. 566-569 https://doi.org/10.1103/PhysRevLett.45.566	journal	August 1980
Computation of two-electron Gaussian integrals for wave functions including the correlation factor r12exp(−γr122) Samson, Claire C. M.; Klopper, Wim; Helgaker, Trygve Computer Physics Communications, Vol. 149, Issue 1 https://doi.org/10.1016/S0010-4655(02)00590-8	journal	November 2002
r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l Kutzelnigg, Werner Theoretica Chimica Acta, Vol. 68, Issue 6 https://doi.org/10.1007/BF00527669	journal	December 1985
The Normal State of Helium Slater, J. C. Physical Review, Vol. 32, Issue 3 https://doi.org/10.1103/PhysRev.32.349	journal	September 1928
Basis-set convergence of correlated calculations on water Helgaker, Trygve; Klopper, Wim; Koch, Henrik The Journal of Chemical Physics, Vol. 106, Issue 23 https://doi.org/10.1063/1.473863	journal	June 1997
Prediction of Reaction Barriers and Thermochemical Properties with Explicitly Correlated Coupled-Cluster Methods: A Basis Set Assessment Zhang, Jinmei; Valeev, Edward F. Journal of Chemical Theory and Computation, Vol. 8, Issue 9 https://doi.org/10.1021/ct3005547	journal	August 2012
Local Treatment of Electron Correlation Saebo, S.; Pulay, P. Annual Review of Physical Chemistry, Vol. 44, Issue 1 https://doi.org/10.1146/annurev.pc.44.100193.001241	journal	October 1993
Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. I. Second‐order perturbation treatment for He, Be, H ₂ , and LiH Szalewicz, Krzysztof; Jeziorski, Bogumil; Monkhorst, Hendrik J. The Journal of Chemical Physics, Vol. 78, Issue 3 https://doi.org/10.1063/1.444884	journal	February 1983
A general formulation for the efficient evaluation of n -electron integrals over products of Gaussian charge distributions with Gaussian geminal functions Komornicki, Andrew; King, Harry F. The Journal of Chemical Physics, Vol. 134, Issue 24 https://doi.org/10.1063/1.3600745	journal	June 2011
Second-order Møller-Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals Wind, Peter; Klopper, Wim; Helgaker, Trygve Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 107, Issue 3 https://doi.org/10.1007/s00214-001-0318-6	journal	March 2002

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