Scalable implementations of accurate excited-state coupled cluster theories: Application of high-level methods to porphyrin-based systems

The development of reliable tools for excited-state simulations is very important for understanding complex processes in the broad class of light harvesting systems and optoelectronic devices. Over the last years we have been developing equation of motion coupled cluster (EOMCC) methods capable of tackling these problems. In this paper we discuss the parallel performance of EOMCC codes which provide accurate description of excited-state correlation effects. Two aspects are discussed in detail: (1) a new algorithm for the iterative EOMCC methods based on improved parallel task scheduling algorithms, and (2) parallel algorithms for the non-iterative methods describing the effect of triply excited configurations. We demonstrate that the most computationally intensive non-iterative part can take advantage of 210,000 cores of the Cray XT5 system at the Oak Ridge Leadership Computing Facility (OLCF), achieving over 80% parallel efficiency. In particular, we demonstrate the importance of the computationally demanding non-iterative many-body methods in matching experimental level of accuracy for several porphyrin-based systems.

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

[2]  Rodney J. Bartlett,et al.  The equation-of-motion coupled-cluster method: Excitation energies of Be and CO , 1989 .

[3]  Michael R. Wasielewski,et al.  Photoinduced electron transfer in supramolecular systems for artificial photosynthesis , 1992 .

[4]  Robert J. Harrison,et al.  Global Arrays: a portable "shared-memory" programming model for distributed memory computers , 1994, Proceedings of Supercomputing '94.

[5]  Marcel Nooijen,et al.  Many‐body similarity transformations generated by normal ordered exponential excitation operators , 1996 .

[6]  Jean-Luc Brédas.  Molecular understanding of organic solar cells: The challenges , 2013 .

[7]  H. Monkhorst,et al.  Calculation of properties with the coupled-cluster method , 2009 .

[8]  W. Schmidt,et al.  Diels-Alder reactivity of polycyclic aromatic hydrocarbons. 1. Acenes and benzologs , 1980 .

[9]  N. Nakatsuji,et al.  Cluster expansion of the wavefunction. Excited states , 1978 .

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

[11]  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.

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

[13]  M Hjorth-Jensen,et al.  Coupled cluster calculations of ground and excited states of nuclei. , 2004, Physical review letters.

[14]  So Hirata,et al.  Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis , 2001 .

[15]  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.

[16]  W. Schmidt,et al.  DIELS-ALDER REACTIVITY OF POLYCYCLIC AROMATIC HYDROCARBONS. 2. PHENES AND STARPHENES , 1980 .

[17]  Kirk A Peterson,et al.  Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn. , 2005, The Journal of chemical physics.

[18]  Akihiko Tsuda,et al.  Fully Conjugated Porphyrin Tapes with Electronic Absorption Bands That Reach into Infrared , 2001, Science.

[19]  Klaus Müllen,et al.  Nanographenes as active components of single-molecule electronics and how a scanning tunneling microscope puts them to work. , 2008, Accounts of chemical research.

[20]  Piotr Piecuch,et al.  Left‐eigenstate completely renormalized equation‐of‐motion coupled‐cluster methods: Review of key concepts, extension to excited states of open‐shell systems, and comparison with electron‐attached and ionized approaches , 2009 .

[21]  A. Osuka,et al.  Syntheses, structural characterizations, and optical and electrochemical properties of directly fused diporphyrins. , 2001, Journal of the American Chemical Society.

[22]  Karol Kowalski,et al.  New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states. , 2004, The Journal of chemical physics.

[23]  V. Tipparaju,et al.  Role of Many-Body Effects in Describing Low-Lying Excited States of π-Conjugated Chromophores: High-Level Equation-of-Motion Coupled-Cluster Studies of Fused Porphyrin Systems. , 2011, Journal of chemical theory and computation.

[24]  Harry L Anderson,et al.  Expanding the porphyrin pi-system by fusion with anthracene. , 2008, Organic letters.

[25]  Wojciech Pisula,et al.  Graphenes as potential material for electronics. , 2007, Chemical reviews.

[26]  John D. Watts,et al.  Economical triple excitation equation-of-motion coupled-cluster methods for excitation energies , 1995 .

[27]  D. J. Dean,et al.  Coupled-cluster approach to nuclear physics , 2004 .

[28]  Donald C. Comeau,et al.  The equation-of-motion coupled-cluster method. Applications to open- and closed-shell reference states , 1993 .

[29]  So Hirata,et al.  Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states. , 2007, The Journal of chemical physics.

[30]  J. B. Birks,et al.  Photophysics of aromatic molecules , 1970 .

[31]  John F. Stanton,et al.  The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties , 1993 .

[32]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[33]  Roland Lindh,et al.  Density fitting with auxiliary basis sets from Cholesky decompositions , 2009 .

[34]  Henrik Koch,et al.  Coupled cluster response functions , 1990 .

[35]  Karol Kowalski,et al.  The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt , 2001 .

[36]  Karol Kowalski,et al.  Coupled cluster calculations for static and dynamic polarizabilities of C60. , 2008, The Journal of chemical physics.

[37]  John R. Platt,et al.  Classification of Spectra of Cata-Condensed Hydrocarbons , 1949 .

[38]  Anna I Krylov,et al.  A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions. , 2008, The Journal of chemical physics.

[39]  Hans W. Horn,et al.  Fully optimized contracted Gaussian basis sets for atoms Li to Kr , 1992 .

[40]  So Hirata,et al.  Symbolic Algebra in Quantum Chemistry , 2006 .

[41]  V. Kellö,et al.  Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties , 1991 .

[42]  A. Penzkofer,et al.  CHEMICAL PHYSICS LETTERS , 1976 .

[43]  Kimihiko Hirao,et al.  Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory , 1978 .

[44]  Seigo Ito,et al.  Large pi-aromatic molecules as potential sensitizers for highly efficient dye-sensitized solar cells. , 2009, Accounts of chemical research.

[45]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

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

[47]  Thomas Bondo Pedersen,et al.  Reduced scaling in electronic structure calculations using Cholesky decompositions , 2003 .

[48]  Sriram Krishnamoorthy,et al.  Active-space completely-renormalized equation-of-motion coupled-cluster formalism: Excited-state studies of green fluorescent protein, free-base porphyrin, and oligoporphyrin dimer. , 2010, The Journal of chemical physics.

[49]  Arvi Freiberg,et al.  Demonstration and interpretation of significant asymmetry in the low-resolution and high-resolution Q(y) fluorescence and absorption spectra of bacteriochlorophyll a. , 2011, The Journal of chemical physics.

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

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

[52]  Kimihiko Hirao,et al.  Cluster expansion of the wavefunction , 1987 .

[53]  John D. Watts,et al.  Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods , 1996 .

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

[55]  Anna I. Krylov,et al.  Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model , 2001 .

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

[57]  Maxwell J. Crossley,et al.  Rigid Fused Oligoporphyrins as Potential Versatile Molecular Wires. 2. B3LYP and SCF Calculated Geometric and Electronic Properties of 98 Oligoporphyrin and Related Molecules , 1999 .

[58]  Poul Jørgensen,et al.  Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies , 1996 .

[59]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .