The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

Bykov, Dmytro; Kristensen, Kasper; Kjærgaard, Thomas

doi:10.1063/1.4956454

Title: The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

Abstract

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.

Authors:

Bykov, Dmytro ^[1]; Kristensen, Kasper ^[1]; Kjærgaard, Thomas ^[1]

Aarhus Univ. (Denmark)

Publication Date:: Thu Jul 14 00:00:00 EDT 2016

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:: USDOE Office of Science (SC); European Research Council (ERC)

OSTI Identifier:: 1565480

Alternate Identifier(s):: OSTI ID: 1263691

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 145; Journal Issue: 2; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY

Citation Formats


                    Bykov, Dmytro, Kristensen, Kasper, and Kjærgaard, Thomas. The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4956454.

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                    Bykov, Dmytro, Kristensen, Kasper, & Kjærgaard, Thomas. The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient.  United States.  https://doi.org/10.1063/1.4956454

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                    Bykov, Dmytro, Kristensen, Kasper, and Kjærgaard, Thomas. Thu .  
"The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient".  United States.  https://doi.org/10.1063/1.4956454.  https://www.osti.gov/servlets/purl/1565480.

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@article{osti_1565480,

  title        = {The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient},

  author       = {Bykov, Dmytro and Kristensen, Kasper and Kjærgaard, Thomas},

  abstractNote = {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.},

  doi          = {10.1063/1.4956454},

  journal      = {Journal of Chemical Physics},

  number       = 2,

  volume       = 145,

  place        = {United States},

  year         = {Thu Jul 14 00:00:00 EDT 2016},

  month        = {Thu Jul 14 00:00:00 EDT 2016}

}

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Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2)
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Explicitly correlated local coupled-cluster methods using pair natural orbitals
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Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 6
DOI: 10.1002/wcms.1371

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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 Bykov, Dmytro ; Kristensen, Kasper ; Kjærgaard, Thomas - Journal of Chemical Physics

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 methodmore »« less
https://doi.org/10.1063/1.4956454
The GPU-enabled divide-expand-consolidate RI-MP2 method (DEC-RI-MP2)

Journal Article Bykov, Dmytro ; Kjaergaard, Thomas - Journal of Computational Chemistry

We report porting of the Divide-Expand-Consolidate Resolution of the Identity second-order Møller–Plesset perturbation (DEC-RI-MP2) method to the graphic processing units (GPUs) using OpenACC compiler directives. It is shown that the OpenACC compiler directives implementation efficiently accelerates the rate-determining step of the DEC-RI-MP2 method with minor implementation effort. Moreover, the GPU acceleration results in a better load balance and thus in an overall scaling improvement of the DEC algorithm. The resulting cross-platform hybrid MPI/OpenMP/OpenACC implementation has scalable and portable performance on heterogeneous HPC architectures. The GPU-enabled code was benchmarked using a reduced version of the S12L test set of Stefan Grimmemore »« less
https://doi.org/10.1002/jcc.24678
Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model

Journal Article Baudin, Pablo ; Ettenhuber, Patrick ; Reine, Simen ; ... - Journal of Chemical Physics

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 fragmentmore »« less
Cited by 43
https://doi.org/10.1063/1.4940732

Full Text Available
The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method

Journal Article Kjærgaard, Thomas - Journal of Chemical Physics

The divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-RI-MP2) theory method introduced in Baudin et al. [J. Chem. Phys. 144, 054102 (2016)] is greatly improved by introducing the Laplace transform of the orbital energy denominator in order to construct the double amplitudes directly in the local basis. Moreover, our paper introduces the auxiliary reduction procedure, which reduces the set of the auxiliary functions employed in the individual fragments. The resulting Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation method is applied to the insulin molecule where we obtain a factor 9.5 speedup compared to the DEC-RI-MP2 method.
Cited by 21
https://doi.org/10.1063/1.4973710

Full Text Available
Explicitly correlated second-order Møller-Plesset perturbation theory in a Divide-Expand-Consolidate (DEC) context

Journal Article Wang, Yang Min ; Hättig, Christof ; Reine, Simen ; ... - Journal of Chemical Physics

We present the DEC-RIMP2-F12 method where we have augmented the Divide Expand-Consolidate resolution-of-the-identity second-order Møller-Plesset perturbation theory method (DEC-RIMP2) [P. Baudin et al., J. Chem. Phys. 144, 054102 (2016)] with an explicitly correlated (F12) correction. Here, the new method is linear-scaling, massively parallel, and it corrects for the basis set incompleteness error in an efficient manner. In addition, we observe that the F12 contribution decreases the domain error of the DEC-RIMP2 correlation energy by roughly an order of magnitude. An important feature of the DEC scheme is the inherent error control defined by a single parameter, and this feature ismore »« less
Cited by 10
https://doi.org/10.1063/1.4951696

Full Text Available

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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

Abstract

Citation Formats

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 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 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 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

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
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
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
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