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Title: 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 · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4956454· OSTI ID:1565480

Here, we report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 method and to analyze the errors of the DEC approximation. The test set also contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Furthermore, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.

Research Organization:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
USDOE Office of Science (SC); European Research Council (ERC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1565480
Alternate ID(s):
OSTI ID: 1263691
Journal Information:
Journal of Chemical Physics, Vol. 145, Issue 2; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

References (83)

A near linear-scaling smooth local coupled cluster algorithm for electronic structure journal August 2006
Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method journal March 2009
Analytic gradients for coupled‐cluster energies that include noniterative connected triple excitations: Application to c i s ‐ and t r a n s ‐HONO journal May 1991
A direct MP2 gradient method journal February 1990
An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis journal April 2007
Low-order scaling local electron correlation methods. I. Linear scaling local MP2 journal October 1999
An improved semidirect MP2 gradient method journal February 1999
The ORCA program system: The ORCA program system journal June 2011
The elimination of singularities in derivative calculations journal October 1985
On some approximations in applications of X α theory journal October 1979
An efficient local coupled cluster method for accurate thermochemistry of large systems journal October 2011
Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations journal January 1982
Dynamically screened local correlation method using enveloping localized orbitals journal July 2006
Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory journal April 1998
Semidirect MP2 gradient evaluation on workstation computers: The MPGRAD program journal August 1993
Analytical energy gradients for local second-order Møller–Plesset perturbation theory using density fitting approximations journal July 2004
Auxiliary basis sets to approximate Coulomb potentials journal June 1995
MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme journal January 2012
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Orbital spaces in the divide-expand-consolidate coupled cluster method journal April 2016
General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory journal August 2007
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
An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory journal April 2008
Analytical differentiation of the energy contribution due to triple excitations in fourth-order Møller-Plesset perturbation theory journal December 1988
Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme journal September 2012
Rigorous integral screening for electron correlation methods journal November 2005
Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application journal November 1987
Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials
  • Eichkorn, Karin; Weigend, Florian; Treutler, Oliver
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 97, Issue 1-4 https://doi.org/10.1007/s002140050244
journal October 1997
On the efficient evaluation of analytic energy gradients journal December 1985
Linear scaling coupled cluster and perturbation theories in the atomic orbital basis journal November 1999
Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory journal January 2008
Tensor factorizations of local second-order Møller–Plesset theory journal January 2011
Analytical evaluation of energy gradients in quadratic configuration interaction theory journal September 1988
Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations journal July 2008
Linear scaling local correlation approach for solving the coupled cluster equations of large systems journal December 2001
Linear scaling coupled cluster method with correlation energy based error control journal July 2010
Mo/ller–Plesset energy derivatives journal August 1988
A derivation of the frozen-orbital unrestricted open-shell and restricted closed-shell second-order perturbation theory analytic gradient expressions
  • Aikens, Christine M.; Webb, Simon P.; Bell, Rob L.
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 110, Issue 4 https://doi.org/10.1007/s00214-003-0453-3
journal November 2003
Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model journal February 2016
A New dimension to quantum chemistry: Theoretical methods for the analytic evaluation of first, second, and third derivatives of the molecular electronic energy with respect to nuclear coordinates journal February 1986
Semi-direct algorithms for the MP2 energy and gradient journal February 1990
Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations journal March 2015
Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems journal February 1999
Analytic evaluation of energy gradients for the singles and doubles coupled cluster method including perturbative triple excitations: Theory and applications to FOOF and Cr 2 journal January 1991
Fully automated implementation of the incremental scheme: Application to CCSD energies for hydrocarbons and transition metal compounds journal April 2007
M�ller-Plesset (MP2) perturbation theory for large molecules journal November 1993
Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory journal July 2012
Analytical gradient of restricted second-order Møller–Plesset correlation energy with the resolution of the identity approximation, applied to the TCNE dimer anion complex journal July 2006
Nuclear second analytical derivative calculations using auxiliary basis set expansions journal January 2004
A new direct MP2 gradient algorithm with implementation on a massively parallel computer journal June 1996
A natural linear scaling coupled-cluster method journal January 2004
Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis journal January 2009
The analytic evaluation of second-order møller-plesset (MP2) dipole moment derivatives journal May 1987
Analytic energy gradient for second-order Møller-Plesset perturbation theory based on the fragment molecular orbital method journal July 2011
Localizability of dynamic electron correlation journal September 1983
Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) journal January 2001
Improved Design of Orbital Domains within the Cluster-in-Molecule Local Correlation Framework: Single-Environment Cluster-in-Molecule Ansatz and Its Application to Local Coupled-Cluster Approach with Singles and Doubles journal August 2010
Third‐order MBPT gradients journal May 1985
Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure journal September 1973
A parallel second-order Møller-Plesset gradient journal June 1997
Analytic first and second derivatives for the CCSDT-n (n = 1–3) models: a first step towards the efficient calculation of CCSDT properties journal January 2000
Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules : I. Theory journal January 1969
New parallel algorithm for MP2 energy gradient calculations journal January 2007
Derivative studies in hartree-fock and møller-plesset theories journal March 1979
Derivative studies in configuration–interaction theory journal April 1980
Analytic gradients from correlated wave functions via the two‐particle density matrix and the unitary group approach journal April 1980
Analytic Molecular Hessian Calculations for CC2 and MP2 Combined with the Resolution of Identity Approximation journal February 2013
A Locality Analysis of the Divide–Expand–Consolidate Coupled Cluster Amplitude Equations journal May 2011
A numerically stable procedure for calculating M�ller-Plesset energy derivatives, derived using the theory of Lagrangians journal January 1989
RI-MP2: first derivatives and global consistency journal October 1997
The structure of T 6 human insulin at 1.0 Å resolution journal February 2003
Local Treatment of Electron Correlation journal October 1993
Local treatment of electron correlation in coupled cluster theory journal April 1996
Analytical differentiation of the energy contribution due to triple excitations in quadratic configuration interaction theory journal November 1989
The divide-expand-consolidate family of coupled cluster methods: Numerical illustrations using second order Møller-Plesset perturbation theory journal January 2012
Some Recent Results concerning the Electronic Density and the Force Constants of Small Molecules journal April 1960
Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition journal March 2012
Coupled-cluster theory in a projected atomic orbital basis journal February 2006
Integral approximations for LCAO-SCF calculations journal October 1993
Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation journal May 2016
Coupled-cluster theory based upon the fragment molecular-orbital method journal October 2005
Efficient Structure Optimization with Second-Order Many-Body Perturbation Theory: The RIJCOSX-MP2 Method journal July 2010
Local correlation calculations using standard and renormalized coupled-cluster approaches journal September 2009

Cited By (4)

Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2) journal April 2019
Assessment of DFT for endohedral complexes' dipole moment: PNO-LCCSD-F12 as a reference method journal January 2018
Analytical energy gradients for local second-order Møller-Plesset perturbation theory using intrinsic bond orbitals journal October 2018
Explicitly correlated local coupled-cluster methods using pair natural orbitals journal July 2018