skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4940732· OSTI ID:1565468
ORCiD logo [1];  [1];  [2];  [1]; ORCiD logo [1]
  1. Aarhus Univ. (Denmark). qLEAP Center for Theoretical Chemistry, Dept. of Chemistry
  2. Univ. of Oslo (Norway). Centre for Theoretical and Computational Chemistry, Dept. of Chemistry
+ Show Author Affiliations

The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DEC-RI-MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1565468
Alternate ID(s):
OSTI ID: 1421154
Journal Information:
Journal of Chemical Physics, Vol. 144, Issue 5; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 43 works
Citation information provided by
Web of Science

References (75)

Reduced scaling in electronic structure calculations using Cholesky decompositions journal June 2003
A perspective on the localizability of Hartree–Fock orbitals journal November 2013
The role of databases in support of computational chemistry calculations journal October 1996
Maximum locality in occupied and virtual orbital spaces using a least-change strategy journal September 2009
Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory journal March 2012
Fully Automated Incremental Evaluation of MP2 and CCSD(T) Energies: Application to Water Clusters journal January 2009
The divide–expand–consolidate MP2 scheme goes massively parallel journal April 2013
Molecular tailoring approach in conjunction with MP2 and Ri-MP2 codes: A comparison with fragment molecular orbital method journal January 2010
Molecular Electronic-Structure Theory book August 2000
On some approximations in applications of X α theory journal October 1979
Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory journal January 2013
Local CC2 electronic excitation energies for large molecules with density fitting journal September 2006
Pipek-Mezey localization of occupied and virtual orbitals journal April 2013
Analytical energy gradients for local second-order Møller–Plesset perturbation theory using density fitting approximations journal July 2004
MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme journal January 2012
Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations journal May 2003
Basis Set Exchange:  A Community Database for Computational Sciences journal March 2007
Electrostatic Potential of Insulin: Exploring the Limitations of Density Functional Theory and Force Field Methods journal August 2013
Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals journal July 2015
The Dalton quantum chemistry program system: The Dalton program
  • Aidas, Kestutis; Angeli, Celestino; Bak, Keld L.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3 https://doi.org/10.1002/wcms.1172
journal September 2013
Coulombic potential energy integrals and approximations journal May 1973
Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme journal September 2012
Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency journal April 2009
Resolution of the identity atomic orbital Laplace transformed second order Møller–Plesset theory for nonconducting periodic systems journal January 2008
On first-row diatomic molecules and local density models journal January 1979
Trust Region Minimization of Orbital Localization Functions journal August 2012
RI-MP2 Gradient Calculation of Large Molecules Using the Fragment Molecular Orbital Method journal January 2012
Fragment molecular orbital calculation using the RI-MP2 method journal May 2009
Unbiased auxiliary basis sets for accurate two-electron integral approximations journal September 2007
Linear-scaling atomic orbital-based second-order Møller–Plesset perturbation theory by rigorous integral screening criteria journal February 2009
The impact of the resolution of the identity approximate integral method on modern ab initio algorithm development
  • Kendall, Rick A.; Früchtl, Herbert A.
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 97, Issue 1-4 https://doi.org/10.1007/s002140050249
journal October 1997
Orbital localization using fourth central moment minimization journal December 2012
Møller-Plesset perturbation theory: from small molecule methods to methods for thousands of atoms: Møller-Plesset perturbation theory journal May 2011
Accelerating Resolution-of-the-Identity Second-Order Møller−Plesset Quantum Chemistry Calculations with Graphical Processing Units † journal March 2008
A systematic way for the cost reduction of density fitting methods journal December 2014
Linear scaling coupled cluster method with correlation energy based error control journal July 2010
Approximate ab initio energies by systematic molecular fragmentation journal April 2005
Improved Cluster-in-Molecule Local Correlation Approach for Electron Correlation Calculation of Large Systems journal June 2014
MPI/OpenMP Hybrid Parallel Algorithm of Resolution of Identity Second-Order Møller–Plesset Perturbation Calculation for Massively Parallel Multicore Supercomputers journal November 2013
Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems journal February 1999
Application of resolution of identity approximation of second-order Møller–Plesset perturbation theory to three-body fragment molecular orbital method journal August 2011
Explicitly correlated second-order perturbation theory using density fitting and local approximations journal February 2006
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations journal February 2002
Efficient parallel algorithm of second-order Møller-Plesset perturbation theory with resolution-of-identity approximation (RI-MP2) journal January 2009
Localized Atomic and Molecular Orbitals journal July 1963
Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units journal August 2014
M�ller-Plesset (MP2) perturbation theory for large molecules journal November 1993
Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method journal August 2007
Large scale FMO-MP2 calculations on a massively parallel-vector computer journal May 2008
An approximate second-order Møller–Plesset perturbation approach for large molecular calculations journal August 2006
Local and density fitting approximations within the short-range/long-range hybrid scheme: application to large non-bonded complexes journal January 2008
Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers journal March 1996
Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr journal January 2005
Development of new auxiliary basis functions of the Karlsruhe segmented contracted basis sets including diffuse basis functions (def2-SVPD, def2-TZVPPD, and def2-QVPPD) for RI-MP2 and RI-CC calculations journal January 2015
Localized Atomic and Molecular Orbitals. II journal November 1965
Distributed memory parallel implementation of energies and gradients for second-order Møller–Plesset perturbation theory with the resolution-of-the-identity approximation journal January 2006
On the use of the Laplace transform in local correlation methods journal January 2008
A fast intrinsic localization procedure applicable for a b i n i t i o and semiempirical linear combination of atomic orbital wave functions journal May 1989
A Linear-Scaling MP2 Method for Large Molecules by Rigorous Integral-Screening Criteria journal April 2010
Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide–Expand–Consolidate CCSD(T) Model journal June 2015
Ab initio calculations on large molecules: The multiplicative integral approximation journal September 1988
Local orbitals by minimizing powers of the orbital variance journal May 2011
A tight distance-dependent estimator for screening three-center Coulomb integrals over Gaussian basis functions journal April 2015
An efficient localization procedure for large systems using a sequential transformation strategy journal December 2014
Density fitting in second-order linear-r12 Møller–Plesset perturbation theory journal September 2003
A Locality Analysis of the Divide–Expand–Consolidate Coupled Cluster Amplitude Equations journal May 2011
Note on an Approximation Treatment for Many-Electron Systems journal October 1934
RI-MP2: first derivatives and global consistency journal October 1997
Local MP2 with Density Fitting for Periodic Systems: A Parallel Implementation journal August 2011
The divide-expand-consolidate family of coupled cluster methods: Numerical illustrations using second order Møller-Plesset perturbation theory journal January 2012
Fitting basis sets for the RI-MP2 approximate second-order many-body perturbation theory method journal August 1998
Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton journal April 1999
Integral approximations for LCAO-SCF calculations journal October 1993
The relative energies of polypeptide conformers predicted by linear scaling second-order Møller-Plesset perturbation theory journal September 2014
Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another journal April 1960

Cited By (4)

A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals journal January 2020
Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2) journal April 2019
Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems journal October 2017
Explicitly correlated local coupled-cluster methods using pair natural orbitals journal July 2018

Similar Records

The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient
Journal Article · Thu Jul 14 00:00:00 EDT 2016 · Journal of Chemical Physics · OSTI ID:1565468
The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient
Journal Article · Thu Jul 14 00:00:00 EDT 2016 · Journal of Chemical Physics · OSTI ID:1565468
MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme
Journal Article · Sun Jan 01 00:00:00 EST 2012 · Physical Chemistry Chemical Physics. PCCP (Print) · OSTI ID:1565468
+4 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Chemistry
Physics