Shared memory multiprocessing implementation of resolution-of-the-identity second-order Møller–Plesset perturbation theory with attenuated and unattenuated results for intermolecular interactions between large molecules

We examine the second-order Møller–Plesset perturbation theory energy under the resolution-of-the-identity approximation (RI-MP2) and present an improved algorithm for single-node, multi-threaded computation. This algorithm is based on shared memory parallelisation of the rate-limiting steps and an overall reduction in the number of disk reads. The requisite fifth-order computation in RI-MP2 calculations is efficiently parallelised within this algorithm, with improvements in overall parallel efficiency as the system size increases. Fourth-order steps are also parallelised. As an application, we present energies and timings for several large, noncovalently interacting systems with this algorithm, and demonstrate that the RI-MP2 cost is still typically less than 40% of the underlying self consistent field (SCF) calculation. The attenuated RI-MP2 energy is also implemented with this algorithm, and some new large-scale tests of this method are reported. The attenuated RI-MP2(terfc, aug-cc-pVDZ) method yields excellent agreement with benchmark values for the L7 database (R. Sedlak et al., J. Chem. Theory Comput. 2013, 9, 3364) and 10 tetrapeptide conformers (L. Goerigk et al., Phys. Chem. Chem. Phys. 2013, 15, 7028), with at least a 90% reduction in the root-mean-squared (RMS) error versus RI-MP2/aug-cc-pVDZ.

[1]  M. Head‐Gordon,et al.  Attenuated second-order Møller-Plesset perturbation theory: performance within the aug-cc-pVTZ basis. , 2013, Physical chemistry chemical physics : PCCP.

[2]  P. Pulay,et al.  The accuracy of quantum chemical methods for large noncovalent complexes. , 2013, Journal of chemical theory and computation.

[3]  Y. Shao,et al.  Accelerating MP2C dispersion corrections for dimers and molecular crystals. , 2013, The Journal of chemical physics.

[4]  Anna I. Krylov,et al.  Q‐Chem: an engine for innovation , 2013 .

[5]  L. Radom,et al.  Accurate quantum chemical energies for tetrapeptide conformations: why MP2 data with an insufficient basis set should be handled with caution. , 2013, Physical chemistry chemical physics : PCCP.

[6]  Martin Head-Gordon,et al.  Attenuating Away the Errors in Inter- and Intramolecular Interactions from Second-Order Møller-Plesset Calculations in the Small Aug-cc-pVDZ Basis Set. , 2012, The journal of physical chemistry letters.

[7]  Kazuya Ishimura,et al.  MPI/OpenMP hybrid parallel implementation of second-order Møller–Plesset perturbation theory using numerical quadratures , 2011 .

[8]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[9]  Andreas Heßelmann,et al.  Accurate Intermolecular Interaction Energies from a Combination of MP2 and TDDFT Response Theory. , 2010, Journal of chemical theory and computation.

[10]  M. Head‐Gordon,et al.  Long-range corrected double-hybrid density functionals. , 2009, The Journal of chemical physics.

[11]  Alexandre Tkatchenko,et al.  Dispersion-corrected Møller-Plesset second-order perturbation theory. , 2009, The Journal of chemical physics.

[12]  W. Goddard,et al.  Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics , 2009, Proceedings of the National Academy of Sciences.

[13]  A. Tkatchenko,et al.  Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. , 2009, Physical review letters.

[14]  A. Hesselmann.  Improved supermolecular second order Møller-Plesset intermolecular interaction energies using time-dependent density functional response theory. , 2008, The Journal of chemical physics.

[15]  Martin Head-Gordon,et al.  A study of the effect of attenuation curvature on molecular correlation energies by introducing an explicit cutoff radius into two-electron integrals. , 2008, The journal of physical chemistry. A.

[16]  Barbara Chapman,et al.  Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation) , 2007 .

[17]  A. Becke,et al.  Exchange-hole dipole moment and the dispersion interaction revisited. , 2007, The Journal of chemical physics.

[18]  Slawomir M Cybulski,et al.  The origin of deficiency of the supermolecule second-order Moller-Plesset approach for evaluating interaction energies. , 2007, The Journal of chemical physics.

[19]  Yihan Shao,et al.  An improved algorithm for analytical gradient evaluation in resolution‐of‐the‐identity second‐order Møller‐Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis , 2007, J. Comput. Chem..

[20]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[21]  Martin Head-Gordon,et al.  Analytical gradient of restricted second-order Møller-Plesset correlation energy with the resolution of the identity approximation, applied to the TCNE dimer anion complex , 2006 .

[22]  Shawn T. Brown,et al.  Advances in methods and algorithms in a modern quantum chemistry program package. , 2006, Physical chemistry chemical physics : PCCP.

[23]  Jirí Cerný,et al.  Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. , 2006, Physical chemistry chemical physics : PCCP.

[24]  Arnim Hellweg,et al.  Distributed memory parallel implementation of energies and gradients for second-order Møller-Plesset perturbation theory with the resolution-of-the-identity approximation. , 2006, Physical chemistry chemical physics : PCCP.

[25]  Christof Hättig,et al.  Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr , 2005 .

[26]  Stefan Grimme,et al.  Accurate description of van der Waals complexes by density functional theory including empirical corrections , 2004, J. Comput. Chem..

[27]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[28]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[29]  F. Weigend,et al.  RI-MP2: first derivatives and global consistency , 1997 .

[30]  Ida M. B. Nielsen,et al.  A new direct MP2 gradient algorithm with implementation on a massively parallel computer , 1996 .

[31]  D. Bernholdt,et al.  Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers , 1996 .

[32]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[33]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

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

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

[36]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

[37]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

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