The divide–expand–consolidate coupled cluster scheme

The Divide‐Expand‐Consolidate (DEC) scheme is a linear‐scaling and massively parallel framework for high accuracy coupled cluster (CC) calculations on large molecular systems. It is designed as a black‐box method, which ensures error control in the correlation energy and molecular properties. DEC is combined with a massively parallel implementation to fully utilize modern manycore architectures providing a fast time to solution. The implementation ensures performance portability and will straightforwardly benefit from new hardware developments. The DEC scheme has been applied to several levels of CC theory and extended the range of application of those methods. WIREs Comput Mol Sci 2017, 7:e1319. doi: 10.1002/wcms.1319

[1]  Justus A. Calvin,et al.  Massively Parallel Implementation of Explicitly Correlated Coupled-Cluster Singles and Doubles Using TiledArray Framework. , 2016, The journal of physical chemistry. A.

[2]  Zoltán Rolik,et al.  An efficient linear-scaling CCSD(T) method based on local natural orbitals. , 2013, The Journal of chemical physics.

[3]  Stinne Høst,et al.  Local orbitals by minimizing powers of the orbital variance. , 2011, The Journal of chemical physics.

[4]  P. Jørgensen,et al.  Characterization and Generation of Local Occupied and Virtual Hartree-Fock Orbitals. , 2016, Chemical reviews.

[5]  Kaori Fukuzawa,et al.  Large scale FMO-MP2 calculations on a massively parallel-vector computer , 2008 .

[6]  Robert J. Harrison,et al.  Global arrays: A nonuniform memory access programming model for high-performance computers , 1996, The Journal of Supercomputing.

[7]  David P Tew,et al.  First UHF Implementation of the Incremental Scheme for Open-Shell Systems. , 2016, Journal of chemical theory and computation.

[8]  Y. Minenkov,et al.  Accuracy of DLPNO-CCSD(T) method for noncovalent bond dissociation enthalpies from coinage metal cation complexes. , 2015, Journal of chemical theory and computation.

[9]  Hans-Joachim Werner,et al.  Eliminating the domain error in local explicitly correlated second-order Møller-Plesset perturbation theory. , 2008, The Journal of chemical physics.

[10]  Isaiah Shavitt,et al.  Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory , 2009 .

[11]  F. Jensen,et al.  Electrostatic Potential of Insulin: Exploring the Limitations of Density Functional Theory and Force Field Methods. , 2013, Journal of chemical theory and computation.

[12]  Martin Schütz,et al.  Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T) , 2000 .

[13]  Thomas Kjærgaard,et al.  The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method. , 2017, The Journal of chemical physics.

[14]  John F. Ouyang,et al.  Combined Fragmentation Method: A Simple Method for Fragmentation of Large Molecules. , 2012, Journal of chemical theory and computation.

[15]  Marcin Ziółkowski,et al.  A Locality Analysis of the Divide-Expand-Consolidate Coupled Cluster Amplitude Equations. , 2011, Journal of chemical theory and computation.

[16]  Rodney J Bartlett,et al.  A natural linear scaling coupled-cluster method. , 2004, The Journal of chemical physics.

[17]  Guntram Rauhut,et al.  Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory , 1998 .

[18]  Thomas Kjærgaard,et al.  Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide-Expand-Consolidate CCSD(T) Model. , 2015, Journal of chemical theory and computation.

[19]  Luca Frediani,et al.  The Dalton quantum chemistry program system , 2013, Wiley interdisciplinary reviews. Computational molecular science.

[20]  Thomas Kjærgaard,et al.  The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient. , 2016, The Journal of chemical physics.

[21]  Marius S Frank,et al.  The PNO–MP2 gradient and its application to molecular geometry optimisations , 2017 .

[22]  Wei Li,et al.  Cluster-in-molecule local correlation method for post-Hartree–Fock calculations of large systems , 2016 .

[23]  P. Jørgensen,et al.  A perspective on the localizability of Hartree–Fock orbitals , 2013, Theoretical Chemistry Accounts.

[24]  Peter Pulay,et al.  Orbital-invariant formulation and second-order gradient evaluation in Møller-Plesset perturbation theory , 1986 .

[25]  Xiao He,et al.  The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy. , 2006, The Journal of chemical physics.

[26]  Frederick R Manby,et al.  The orbital-specific-virtual local coupled cluster singles and doubles method. , 2012, The Journal of chemical physics.

[27]  Frank Neese,et al.  An efficient and near linear scaling pair natural orbital based local coupled cluster method. , 2013, The Journal of chemical physics.

[28]  Thomas Kjærgaard,et al.  MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme. , 2012, Physical chemistry chemical physics : PCCP.

[29]  Thomas Kjærgaard,et al.  Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme. , 2012, The Journal of chemical physics.

[30]  P. Jørgensen,et al.  Orbital spaces in the divide-expand-consolidate coupled cluster method. , 2016, The Journal of chemical physics.

[31]  Poul Jørgensen,et al.  The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[32]  Paul G. Mezey,et al.  A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions , 1989 .

[33]  P. Piecuch,et al.  Multilevel extension of the cluster-in-molecule local correlation methodology: merging coupled-cluster and Møller-Plesset perturbation theories. , 2010, The journal of physical chemistry. A.

[34]  Ryan P A Bettens,et al.  A new algorithm for molecular fragmentation in quantum chemical calculations. , 2006, The journal of physical chemistry. A.

[35]  D. Tew,et al.  Local explicitly correlated second-order Møller-Plesset perturbation theory with pair natural orbitals. , 2011, The Journal of chemical physics.

[36]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[37]  Frank Neese,et al.  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. , 2015, The Journal of chemical physics.

[38]  Edward F. Valeev,et al.  Explicitly correlated second-order Møller-Plesset perturbation theory in a Divide-Expand-Consolidate (DEC) context. , 2016, The Journal of chemical physics.

[39]  Wei Li,et al.  Generalized energy-based fragmentation approach for computing the ground-state energies and properties of large molecules. , 2007, The journal of physical chemistry. A.

[40]  Frederick R Manby,et al.  Local explicitly correlated second-order perturbation theory for the accurate treatment of large molecules. , 2009, The Journal of chemical physics.

[41]  Branislav Jansík,et al.  Maximum locality in occupied and virtual orbital spaces using a least-change strategy. , 2009, The Journal of chemical physics.

[42]  Aaron Vose,et al.  Massively parallel and linear-scaling algorithm for second-order Møller-Plesset perturbation theory applied to the study of supramolecular wires , 2017, Comput. Phys. Commun..

[43]  Hans-Joachim Werner,et al.  Scalable electron correlation methods I.: PNO-LMP2 with linear scaling in the molecular size and near-inverse-linear scaling in the number of processors. , 2015, Journal of chemical theory and computation.

[44]  Thomas Kjærgaard,et al.  The GPU‐enabled divide‐expand‐consolidate RI‐MP2 method (DEC‐RI‐MP2) , 2017, J. Comput. Chem..

[45]  Beverly A. Sanders,et al.  An infrastructure for scalable and portable parallel programs for computational chemistry , 2009, ICS '09.

[46]  Wei Li,et al.  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. , 2010, The journal of physical chemistry. A.

[47]  Mihály Kállay,et al.  An Integral-Direct Linear-Scaling Second-Order Møller-Plesset Approach. , 2016, Journal of chemical theory and computation.

[48]  Shridhar R. Gadre,et al.  Molecular tailoring approach in conjunction with MP2 and Ri‐MP2 codes: A comparison with fragment molecular orbital method , 2010, J. Comput. Chem..

[49]  Frederick R Manby,et al.  Tensor factorizations of local second-order Møller-Plesset theory. , 2010, The Journal of chemical physics.

[50]  Trygve Helgaker,et al.  An efficient density-functional-theory force evaluation for large molecular systems. , 2010, The Journal of chemical physics.

[51]  Hans-Joachim Werner,et al.  Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) , 2001 .

[52]  Jing Ma,et al.  Linear scaling local correlation approach for solving the coupled cluster equations of large systems , 2002, J. Comput. Chem..

[53]  Michael Dolg,et al.  Fully automated implementation of the incremental scheme: application to CCSD energies for hydrocarbons and transition metal compounds. , 2007, The Journal of chemical physics.

[54]  Joachim Friedrich,et al.  Incremental CCSD(T)(F12*)|MP2: A Black Box Method To Obtain Highly Accurate Reaction Energies. , 2013, Journal of chemical theory and computation.

[55]  Yang,et al.  Direct calculation of electron density in density-functional theory: Implementation for benzene and a tetrapeptide. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[56]  Hans-Joachim Werner,et al.  Scalable Electron Correlation Methods. 2. Parallel PNO-LMP2-F12 with Near Linear Scaling in the Molecular Size. , 2015, Journal of chemical theory and computation.

[57]  Martin Head-Gordon,et al.  Non-iterative local second order Møller–Plesset theory , 1998 .

[58]  Stoll,et al.  Correlation energy of diamond. , 1992, Physical review. B, Condensed matter.

[59]  F. Neese,et al.  Mechanism of Olefin Asymmetric Hydrogenation Catalyzed by Iridium Phosphino-Oxazoline: A Pair Natural Orbital Coupled Cluster Study. , 2014, Journal of chemical theory and computation.

[60]  Gunnar Schmitz,et al.  Perturbative triples correction for local pair natural orbital based explicitly correlated CCSD(F12*) using Laplace transformation techniques. , 2016, The Journal of chemical physics.

[61]  Wei Li,et al.  Local correlation calculations using standard and renormalized coupled-cluster approaches. , 2009, The Journal of chemical physics.

[62]  Frank Neese,et al.  Sparse maps--A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory. , 2016, The Journal of chemical physics.

[63]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[64]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[65]  Frederick R Manby,et al.  Analytical energy gradients for local second-order Møller-Plesset perturbation theory using density fitting approximations. , 2004, The Journal of chemical physics.

[66]  Robert J. Harrison,et al.  Liquid water: obtaining the right answer for the right reasons , 2009, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis.

[67]  Hans-Joachim Werner,et al.  An efficient local coupled cluster method for accurate thermochemistry of large systems. , 2011, The Journal of chemical physics.

[68]  Hans-Joachim Werner,et al.  Local treatment of electron correlation in coupled cluster theory , 1996 .

[69]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

[70]  Dimitrios G Liakos,et al.  Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory. , 2015, Journal of chemical theory and computation.

[71]  M. Schütz,et al.  On the use of the Laplace transform in local correlation methods. , 2008, Physical chemistry chemical physics : PCCP.

[72]  M. Ratner.  Molecular electronic-structure theory , 2000 .

[73]  Branislav Jansík,et al.  Linear scaling coupled cluster method with correlation energy based error control. , 2010, The Journal of chemical physics.

[74]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[75]  Masato Kobayashi,et al.  Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations. , 2008, The Journal of chemical physics.

[76]  Hans-Joachim Werner,et al.  Comparison of explicitly correlated local coupled-cluster methods with various choices of virtual orbitals. , 2012, Physical chemistry chemical physics : PCCP.

[77]  Poul Jørgensen,et al.  Trust Region Minimization of Orbital Localization Functions. , 2012, Journal of chemical theory and computation.

[78]  Richard A. Friesner,et al.  Pseudospectral localized Mo/ller–Plesset methods: Theory and calculation of conformational energies , 1995 .

[79]  Martin Head-Gordon,et al.  A near linear-scaling smooth local coupled cluster algorithm for electronic structure. , 2006, The Journal of chemical physics.

[80]  John Z. H. Zhang,et al.  Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy , 2003 .

[81]  K. Kitaura,et al.  Fragment molecular orbital method: an approximate computational method for large molecules , 1999 .

[82]  Wei Li,et al.  A refined cluster-in-molecule local correlation approach for predicting the relative energies of large systems. , 2012, Physical chemistry chemical physics : PCCP.

[83]  Weitao Yang,et al.  A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules , 1995 .

[84]  Dieter Cremer,et al.  Møller–Plesset perturbation theory: from small molecule methods to methods for thousands of atoms , 2011 .

[85]  Frank Neese,et al.  Efficient Structure Optimization with Second-Order Many-Body Perturbation Theory: The RIJCOSX-MP2 Method. , 2010, Journal of chemical theory and computation.

[86]  Michael A Collins,et al.  Approximate ab initio energies by systematic molecular fragmentation. , 2005, The Journal of chemical physics.

[87]  Kasper Kristensen,et al.  The divide–expand–consolidate MP2 scheme goes massively parallel , 2013 .

[88]  Frank Neese,et al.  Chemical applications carried out by local pair natural orbital based coupled-cluster methods. , 2014, Chemical Society reviews.

[89]  S. F. Boys.  Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another , 1960 .

[90]  Yuto Komeiji,et al.  Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems. , 2014, Physical chemistry chemical physics : PCCP.

[91]  Masato Kobayashi,et al.  Divide-and-conquer-based linear-scaling approach for traditional and renormalized coupled cluster methods with single, double, and noniterative triple excitations. , 2009, The Journal of chemical physics.

[92]  P. Jørgensen,et al.  Orbital localization using fourth central moment minimization. , 2012, The Journal of chemical physics.

[93]  Masato Kobayashi,et al.  Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method. , 2007, The Journal of chemical physics.

[94]  Wei Li,et al.  A fragment energy assembler method for Hartree-Fock calculations of large molecules. , 2006, The Journal of chemical physics.

[95]  Dimitrios G Liakos,et al.  Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis. , 2009, The Journal of chemical physics.

[96]  Thomas Kjærgaard,et al.  Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide-expand-consolidate RI-MP2 model. , 2016, The Journal of chemical physics.

[97]  Shuhua Li,et al.  Improved cluster-in-molecule local correlation approach for electron correlation calculation of large systems. , 2014, The journal of physical chemistry. A.

[98]  Takahito Nakajima,et al.  Massively parallel algorithm and implementation of RI‐MP2 energy calculation for peta‐scale many‐core supercomputers , 2016, J. Comput. Chem..

[99]  F. Manby,et al.  Explicitly correlated second-order perturbation theory using density fitting and local approximations. , 2006, The Journal of chemical physics.

[100]  Michael Dolg,et al.  Fully Automated Incremental Evaluation of MP2 and CCSD(T) Energies: Application to Water Clusters. , 2009, Journal of chemical theory and computation.

[101]  Jógvan Magnus Haugaard Olsen,et al.  Accuracy of Protein Embedding Potentials: An Analysis in Terms of Electrostatic Potentials. , 2015, Journal of chemical theory and computation.

[102]  Hans-Joachim Werner,et al.  Local explicitly correlated coupled-cluster methods: efficient removal of the basis set incompleteness and domain errors. , 2009, The Journal of chemical physics.

[103]  Frank Neese,et al.  Geminal-spanning orbitals make explicitly correlated reduced-scaling coupled-cluster methods robust, yet simple. , 2014, The Journal of chemical physics.

[104]  Hans-Joachim Werner,et al.  An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit. , 2011, The Journal of chemical physics.

[105]  Zoltán Rolik,et al.  A general-order local coupled-cluster method based on the cluster-in-molecule approach. , 2011, The Journal of chemical physics.

[106]  D. Tew,et al.  Automated incremental scheme for explicitly correlated methods. , 2010, The Journal of chemical physics.

[107]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[108]  Georg Hetzer,et al.  Multipole approximation of distant pair energies in local MP2 calculations , 1998 .

[109]  F. Neese,et al.  Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method. , 2009, The Journal of chemical physics.

[110]  D. Tew,et al.  Explicitly correlated PNO-MP2 and PNO-CCSD and their application to the S66 set and large molecular systems. , 2014, Physical chemistry chemical physics : PCCP.

[111]  John F. Stanton,et al.  A massively parallel tensor contraction framework for coupled-cluster computations , 2014, J. Parallel Distributed Comput..

[112]  M. Gordon,et al.  Combined fragment molecular orbital cluster in molecule approach to massively parallel electron correlation calculations for large systems. , 2015, The journal of physical chemistry. A.

[113]  Wei Li,et al.  An efficient implementation of the "cluster-in-molecule" approach for local electron correlation calculations. , 2006, The Journal of chemical physics.

[114]  Takahito Nakajima,et al.  MPI/OpenMP Hybrid Parallel Algorithm of Resolution of Identity Second-Order Møller-Plesset Perturbation Calculation for Massively Parallel Multicore Supercomputers. , 2013, Journal of chemical theory and computation.

[115]  C. Kozmutza,et al.  Application of the many‐body perturbation theory by using localized orbitals , 1983 .

[116]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[117]  Gunnar Schmitz,et al.  A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs† , 2013 .

[118]  M. Krauss,et al.  Configuration‐Interaction Calculation of H3 and H2 , 1965 .