The divide–expand–consolidate MP2 scheme goes massively parallel

For large molecular systems conventional implementations of second order Møller–Plesset (MP2) theory encounter a scaling wall, both memory- and time-wise. We describe how this scaling wall can be removed. We present a massively parallel algorithm for calculating MP2 energies and densities using the divide–expand–consolidate scheme where a calculation on a large system is divided into many small fragment calculations employing local orbital spaces. The resulting algorithm is linear-scaling with system size, exhibits near perfect parallel scalability, removes memory bottlenecks and does not involve any I/O. The algorithm employs three levels of parallelisation combined via a dynamic job distribution scheme. Results on two molecular systems containing 528 and 1056 atoms (4278 and 8556 basis functions) using 47,120 and 94,240 cores are presented. The results demonstrate the scalability of the algorithm both with respect to the number of cores and with respect to system size. The presented algorithm is thus highly suited for large super computer architectures and allows MP2 calculations on large molecular systems to be carried out within a few hours – for example, the correlated calculation on the molecular system containing 1056 atoms took 2.37 hours using 94240 cores.

[1]  T. Daniel Crawford,et al.  Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules , 2002 .

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

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

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

[5]  R. Bartlett,et al.  The full CCSDT model for molecular electronic structure , 1987 .

[6]  Rodney J Bartlett,et al.  Parallel implementation of the equation-of-motion coupled-cluster singles and doubles method and application for radical adducts of cytosine. , 2009, The Journal of chemical physics.

[7]  Hermann Stoll,et al.  The correlation energy of crystalline silicon , 1992 .

[8]  Daniel Kats,et al.  Local CC2 response method for triplet states based on Laplace transform: excitation energies and first-order properties. , 2010, The Journal of chemical physics.

[9]  Philippe Y. Ayala,et al.  Linear scaling coupled cluster and perturbation theories in the atomic orbital basis , 1999 .

[10]  M. Urban,et al.  Optimized virtual orbitals for correlated calculations : Towards large scale CCSD(T) calculations of molecular dipole moments and polarizabilities , 2006 .

[11]  M. Head‐Gordon,et al.  An accurate local model for triple substitutions in fourth order Møller–Plesset theory and in perturbative corrections to singles and doubles coupled cluster methods , 2000 .

[12]  T. Crawford,et al.  Localized optimized orbitals, coupled cluster theory, and chiroptical response properties. , 2012, Physical chemistry chemical physics : PCCP.

[13]  Trygve Helgaker,et al.  Implementation of the incremental scheme for one-electron first-order properties in coupled-cluster theory. , 2009, The Journal of chemical physics.

[14]  J. Olsen,et al.  Coupled-cluster theory in a projected atomic orbital basis. , 2006, The Journal of chemical physics.

[15]  Kazuo Kitaura,et al.  Coupled-cluster theory based upon the fragment molecular-orbital method. , 2005, The Journal of chemical physics.

[16]  Kazuya Ishimura,et al.  New parallel algorithm for MP2 energy gradient calculations , 2007, J. Comput. Chem..

[17]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[18]  Kazuo Kitaura,et al.  Exploring chemistry with the fragment molecular orbital method. , 2012, Physical chemistry chemical physics : PCCP.

[19]  Christian Ochsenfeld,et al.  An atomic orbital-based reformulation of energy gradients in second-order Møller-Plesset perturbation theory. , 2008, The Journal of chemical physics.

[20]  M. Nooijen,et al.  Dynamically screened local correlation method using enveloping localized orbitals. , 2006, The Journal of chemical physics.

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

[22]  H. Werner,et al.  Local treatment of electron excitations in the EOM-CCSD method , 2003 .

[23]  Mark S. Gordon,et al.  A Novel Approach to Parallel Coupled Cluster Calculations: Combining Distributed and Shared Memory Techniques for Modern Cluster Based Systems , 2007 .

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

[25]  Tatiana Korona,et al.  Local CC2 electronic excitation energies for large molecules with density fitting. , 2006, The Journal of chemical physics.

[26]  H. Werner,et al.  The effect of local approximations in coupled-cluster wave functions on dipole moments and static dipole polarisabilitiesDedicated to Prof. W. Meyer on the occasion of his 65th birthday. , 2004 .

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

[28]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[29]  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.

[30]  Takeshi Ishikawa,et al.  Fragment molecular orbital calculation using the RI-MP2 method , 2009 .

[31]  T. Daniel Crawford,et al.  Local correlation in coupled cluster calculations of molecular response properties , 2004 .

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

[33]  S. Hirata.  Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories , 2003 .

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

[35]  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.

[36]  Klaus Ruedenberg,et al.  Localized Atomic and Molecular Orbitals , 1963 .

[37]  Tatiana Korona,et al.  Transition strengths and first-order properties of excited states from local coupled cluster CC2 response theory with density fitting. , 2007, The Journal of chemical physics.

[38]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..

[39]  Christian Ochsenfeld,et al.  A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme , 1997 .

[40]  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.

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

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

[43]  S. Hirata,et al.  Fragment and localized orbital methods in electronic structure theory. , 2012, Physical chemistry chemical physics : PCCP.

[44]  P. Kam,et al.  : 4 , 1898, You Can Cross the Massacre on Foot.

[45]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

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

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

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

[49]  Masato Kobayashi,et al.  Two‐level hierarchical parallelization of second‐order Møller–plesset perturbation calculations in divide‐and‐conquer method , 2011, J. Comput. Chem..

[50]  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.

[51]  Christian Ochsenfeld,et al.  Rigorous integral screening for electron correlation methods. , 2005, The Journal of chemical physics.

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

[53]  Marcus D. Hanwell,et al.  Avogadro: an advanced semantic chemical editor, visualization, and analysis platform , 2012, Journal of Cheminformatics.

[54]  Christian Ochsenfeld,et al.  Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO-MP2 theory. , 2008, Physical chemistry chemical physics : PCCP.

[55]  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.

[56]  Hiromi Nakai.  Themed issue: Fragment and localized orbital methods in electronic structure theory , 2012 .

[57]  Paweł Sałek,et al.  Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory. , 2007, The Journal of chemical physics.

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

[59]  Michio Katouda,et al.  Efficient parallel algorithm of second‐order Møller–Plesset perturbation theory with resolution‐of‐identity approximation (RI‐MP2) , 2009 .

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

[61]  R J Bartlett,et al.  Parallel implementation of electronic structure energy, gradient, and Hessian calculations. , 2008, The Journal of chemical physics.

[62]  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.

[63]  K. Kitaura,et al.  Analytic energy gradient for second-order Møller-Plesset perturbation theory based on the fragment molecular orbital method. , 2011, The Journal of chemical physics.

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

[65]  Mark S. Gordon,et al.  Coupled cluster algorithms for networks of shared memory parallel processors , 2007, Comput. Phys. Commun..

[66]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

[67]  T. Crawford,et al.  Local correlation domains for coupled cluster theory: optical rotation and magnetic-field perturbations. , 2008, Physical chemistry chemical physics : PCCP.

[68]  Roland Lindh,et al.  Utilizing high performance computing for chemistry: parallel computational chemistry. , 2010, Physical chemistry chemical physics : PCCP.

[69]  T. Korona.  The effect of local approximations on first-order properties from expectation-value coupled cluster theory , 2011 .

[70]  R. Bartlett,et al.  Transferability in the natural linear-scaled coupled-cluster effective Hamiltonian approach: Applications to dynamic polarizabilities and dispersion coefficients. , 2008, The Journal of chemical physics.

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

[72]  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.

[73]  P. Čárský,et al.  Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition. , 2012, The Journal of chemical physics.

[74]  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.

[75]  Christian Ochsenfeld,et al.  Linear and sublinear scaling formation of Hartree-Fock-type exchange matrices , 1998 .

[76]  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.

[77]  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.

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

[79]  Benny G. Johnson,et al.  THE CONTINUOUS FAST MULTIPOLE METHOD , 1994 .

[80]  Edward F. Valeev,et al.  Second-order Møller-Plesset theory with linear R12 terms (MP2-R12) revisited: auxiliary basis set method and massively parallel implementation. , 2004, The Journal of chemical physics.

[81]  Guntram Rauhut,et al.  Analytical energy gradients for local coupled-cluster methods , 2001 .