Parallel Implementation of Multireference Coupled-Cluster Theories Based on the Reference-Level Parallelism.

A novel algorithm for implementing a general type of multireference coupled-cluster (MRCC) theory based on the Jeziorski-Monkhorst exponential ansatz [Jeziorski, B.; Monkhorst, H. J. Phys. Rev. A1981, 24, 1668] is introduced. The proposed algorithm utilizes processor groups to calculate the equations for the MRCC amplitudes. In the basic formulation, each processor group constructs the equations related to a specific subset of references. By flexible choice of processor groups and subset of reference-specific sufficiency conditions designated to a given group, one can ensure optimum utilization of available computing resources. The performance of this algorithm is illustrated on the examples of the Brillouin-Wigner and Mukherjee MRCC methods with singles and doubles (BW-MRCCSD and Mk-MRCCSD). A significant improvement in scalability and in reduction of time to solution is reported with respect to recently reported parallel implementation of the BW-MRCCSD formalism [Brabec, J.; van Dam, H. J. J.; Kowalski, K.; Pittner, J. Chem. Phys. Lett.2011, 514, 347].

[1]  Josef Paldus,et al.  Energetics of naphthynes — Performance of reduced multi-reference coupled-cluster methods for diradicals , 2009 .

[2]  Sanghamitra Das,et al.  Full implementation and benchmark studies of Mukherjee's state-specific multireference coupled-cluster ansatz. , 2010, The Journal of chemical physics.

[3]  Karol Kowalski,et al.  Complete set of solutions of multireference coupled-cluster equations: The state-universal formalism , 2000 .

[4]  Francesco A Evangelista,et al.  Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. , 2007, The Journal of chemical physics.

[5]  Uttam Sinha Mahapatra,et al.  A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications , 1999 .

[6]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[7]  Piecuch,et al.  Application of Hilbert-space coupled-cluster theory to simple (H2)2 model systems: Planar models. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[8]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[9]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[10]  Josef Paldus,et al.  The general-model-space state-universal coupled-cluster method exemplified by the LiH molecule , 2003 .

[11]  Joseph I. Landman,et al.  Parallelization of multi-reference coupled-cluster method , 2000, Parallel Comput..

[12]  Tjerk P. Straatsma,et al.  NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations , 2010, Comput. Phys. Commun..

[13]  Rodney J. Bartlett,et al.  Hilbert space multireference coupled-cluster methods. I: The single and double excitation model , 1991 .

[14]  Jiří Pittner,et al.  Continuous transition between Brillouin-Wigner and Rayleigh-Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster , 2003 .

[15]  Francesco A Evangelista,et al.  High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems. , 2006, The Journal of chemical physics.

[16]  H. Weidenmüller,et al.  The effective interaction in nuclei and its perturbation expansion: An algebraic approach , 1972 .

[17]  Josef Paldus,et al.  N-reference, M-state coupled-cluster method: Merging the state-universal and reduced multireference coupled-cluster theories , 2003 .

[18]  Rodney J. Bartlett,et al.  A Hilbert space multi-reference coupled-cluster study of the H4 model system , 1991 .

[19]  Nicholas Petraco,et al.  General-Model-Space State–Universal Coupled-Cluster Method: Diagrammatic Approach , 2004 .

[20]  Kiran Bhaskaran-Nair,et al.  Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations. , 2008, The Journal of chemical physics.

[21]  P. Durand,et al.  Direct determination of effective Hamiltonians by wave-operator methods. I. General formalism , 1983 .

[22]  Petr Nachtigall,et al.  Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene , 1999 .

[23]  Jürgen Gauss,et al.  Parallel Calculation of CCSDT and Mk-MRCCSDT Energies. , 2010, Journal of chemical theory and computation.

[24]  Uttam Sinha Mahapatra,et al.  Potential energy surface studies via a single root multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[25]  Ivan Hubač,et al.  Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory , 2000 .

[26]  Kiran Bhaskaran-Nair,et al.  Multireference Mukherjee's coupled cluster method with triexcitations in the linked formulation: Efficient implementation and applications. , 2010, The Journal of chemical physics.

[27]  Stefan Grimme,et al.  Parallel multireference configuration interaction calculations on mini-beta-carotenes and beta-carotene. , 2009, The Journal of chemical physics.

[28]  H. Weidenmüller,et al.  Perturbation theory for the effective interaction in nuclei , 1973 .

[29]  Michael Hanrath,et al.  An exponential multireference wave-function Ansatz. , 2005, The Journal of chemical physics.

[30]  Sriram Krishnamoorthy,et al.  Massively parallel implementation of the multireference Brillouin–Wigner CCSD method , 2011 .

[31]  Jarek Nieplocha,et al.  Advances, Applications and Performance of the Global Arrays Shared Memory Programming Toolkit , 2006, Int. J. High Perform. Comput. Appl..

[32]  Jack Dongarra,et al.  Preface: Basic Linear Algebra Subprograms Technical (Blast) Forum Standard , 2002 .

[33]  Rodney J. Bartlett,et al.  The multireference coupled‐cluster method in Hilbert space: An incomplete model space application to the LiH molecule , 1991 .

[34]  Jiří Pittner,et al.  Uncoupled multireference state-specific Mukherjee's coupled cluster method with triexcitations. , 2010, The Journal of chemical physics.

[35]  Jack J. Dongarra,et al.  Basic Linear Algebra Subprograms Technical (Blast) Forum Standard (1) , 2002, Int. J. High Perform. Comput. Appl..

[36]  Alberto Requena,et al.  Theoretical study of the low-lying excited states of β-carotene isomers by a multireference configuration interaction method , 2010 .

[37]  Josef Paldus,et al.  Spin‐adapted multireference coupled‐cluster approach: Linear approximation for two closed‐shell‐type reference configurations , 1988 .

[38]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[39]  H. Monkhorst,et al.  Coupled-cluster method for multideterminantal reference states , 1981 .

[40]  Kiran Bhaskaran-Nair,et al.  Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation. , 2011, The Journal of chemical physics.

[41]  Ivan Hubač,et al.  Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach. , 1998 .

[42]  P. Pulay.  Improved SCF convergence acceleration , 1982 .

[43]  Josef Paldus,et al.  Orthogonally spin‐adapted state‐universal coupled‐cluster formalism: Implementation of the complete two‐reference theory including cubic and quartic coupling terms , 1994 .

[44]  Karol Kowalski,et al.  New classes of non-iterative energy corrections to multi-reference coupled-cluster energies , 2004 .

[45]  A. Curioni,et al.  Car-Parrinello molecular dynamics on massively parallel computers. , 2005, Chemphyschem : a European journal of chemical physics and physical chemistry.

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

[47]  C. Bloch,et al.  Sur la théorie des perturbations des états liés , 1958 .

[48]  Carlos E. Soliverez,et al.  General theory of effective Hamiltonians , 1981 .

[49]  Jiří Pittner,et al.  Method of moments for the continuous transition between the Brillouin–Wigner-type and Rayleigh–Schrödinger-type multireference coupled cluster theories , 2009 .

[50]  Piecuch,et al.  Application of Hilbert-space coupled-cluster theory to simple (H2)2 model systems. II. Nonplanar models. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[51]  Josef Paldus,et al.  General-model-space state-universal coupled-cluster theory: Connectivity conditions and explicit equations , 2003 .

[52]  Uttam Sinha Mahapatra,et al.  Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients , 1999 .