Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime.

Over the course of the past few decades, the field of computational chemistry has managed to manifest itself as a key complement to more traditional lab-oriented chemistry. This is particularly true in the wake of the recent renaissance of full configuration interaction (FCI)-level methodologies, albeit only if these can prove themselves sufficiently robust and versatile to be routinely applied to a variety of chemical problems of interest. In the present series of works, performance and feature enhancements of one such avenue toward FCI-level results for medium to large one-electron basis sets, the recently introduced many-body expanded full configuration interaction (MBE-FCI) formalism [ J. Phys. Chem. Lett. 2017 , 8 , 4633 ], will be presented. Specifically, in this opening part of the series, the capabilities of the MBE-FCI method in producing near-exact ground state energies for weakly correlated molecules of any spin multiplicity will be demonstrated.

[1]  P. S. Epstein,et al.  The Stark effect from the point of view of Schroedinger's quantum theory , 1926 .

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

[3]  R. Nesbet Configuration interaction in orbital theories , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  P. Löwdin Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction , 1955 .

[5]  Harrison Shull,et al.  NATURAL ORBITALS IN THE QUANTUM THEORY OF TWO-ELECTRON SYSTEMS , 1956 .

[6]  O. Sǐnanoğlu,et al.  MANY-ELECTRON THEORY OF ATOMS AND MOLECULES. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[7]  O. Sǐnanoğlu,et al.  MANY-ELECTRON THEORY OF ATOMS AND MOLECULES. I. SHELLS, ELECTRON PAIRS VS MANY-ELECTRON CORRELATIONS , 1962 .

[8]  J. Cizek On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[9]  R. Nesbet Atomic Bethe-Goldstone Equations. III. Correlation Energies of Ground States of Be, B, C, N, O, F, and Ne , 1968 .

[10]  Josef Paldus,et al.  Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the B H 3 Molecule , 1972 .

[11]  J. P. Malrieu,et al.  Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth‐order wavefunctions , 1973 .

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

[13]  Peter J. Knowles,et al.  A new determinant-based full configuration interaction method , 1984 .

[14]  Jeppe Olsen,et al.  Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces , 1988 .

[15]  P. Knowles,et al.  An efficient internally contracted multiconfiguration–reference configuration interaction method , 1988 .

[16]  P. Knowles,et al.  An efficient method for the evaluation of coupling coefficients in configuration interaction calculations , 1988 .

[17]  Rodney J. Bartlett,et al.  An open-shell spin-restricted coupled cluster method: application to ionization potentials in nitrogen , 1988 .

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

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

[20]  Peter J. Knowles,et al.  Unlimited full configuration interaction calculations , 1989 .

[21]  J. Olsen,et al.  Passing the one-billion limit in full configuration-interaction (FCI) calculations , 1990 .

[22]  B. Roos,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1990 .

[23]  Per-Olof Widmark,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1990 .

[24]  N. Oliphant,et al.  Coupled‐cluster method truncated at quadruples , 1991 .

[25]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[26]  G. Herzberg,et al.  Molecular Spectra and Molecular Structure , 1992 .

[27]  David L. Freeman,et al.  Algebraic and Diagrammatic Methods in Many-Fermion Theory , 1992 .

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

[29]  H. Stoll On the correlation energy of graphite , 1992 .

[30]  R. Bartlett,et al.  The coupled‐cluster single, double, triple, and quadruple excitation method , 1992 .

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

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

[33]  Jürgen Gauss,et al.  Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients , 1993 .

[34]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[35]  Sotiris S. Xantheas,et al.  Ab initio studies of cyclic water clusters (H2O)n, n=1–6. II. Analysis of many‐body interactions , 1994 .

[36]  J. Stanton Why CCSD(T) works: a different perspective , 1997 .

[37]  Jonathan Richard Shewchuk,et al.  Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates , 1997, Discret. Comput. Geom..

[38]  Richard L. Martin,et al.  Ab initio quantum chemistry using the density matrix renormalization group , 1998 .

[39]  Jeppe Olsen,et al.  Full configuration interaction benchmarking of coupled-cluster models for the lowest singlet energy surfaces of N2 , 2000 .

[40]  Klaus Ruedenberg,et al.  Identification of deadwood in configuration spaces through general direct configuration interaction , 2001 .

[41]  Mihály Kállay,et al.  Higher excitations in coupled-cluster theory , 2001 .

[42]  J. Olsen,et al.  A general coupled cluster study of the N2 molecule , 2001 .

[43]  Guido Fano,et al.  Quantum chemistry using the density matrix renormalization group , 2001 .

[44]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[45]  Garnet Kin-Lic Chan,et al.  Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrödinger equation for water , 2003 .

[46]  B. A. Hess,et al.  Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach , 2002, cond-mat/0204602.

[47]  Jürgen Gauss,et al.  State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. , 2004, The Journal of chemical physics.

[48]  K. Ruedenberg,et al.  Correlation energy extrapolation by intrinsic scaling. I. Method and application to the neon atom. , 2004, The Journal of chemical physics.

[49]  Beate Paulus,et al.  Convergence of the ab initio many-body expansion for the cohesive energy of solid mercury , 2004 .

[50]  K. Ruedenberg,et al.  Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine. , 2005, The Journal of chemical physics.

[51]  Mario A. Storti,et al.  MPI for Python , 2005, J. Parallel Distributed Comput..

[52]  Beate Paulus,et al.  On the accuracy of correlation-energy expansions in terms of local increments. , 2005, The Journal of chemical physics.

[53]  C. David Sherrill,et al.  The XΣg+1, BΔg1, and B′Σg+1 states of C2: A comparison of renormalized coupled-cluster and multireference methods with full configuration interaction benchmarks , 2005 .

[54]  Garnet Kin-Lic Chan,et al.  Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group. , 2006, The Journal of chemical physics.

[55]  Henry Krakauer,et al.  Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis. , 2006, The Journal of chemical physics.

[56]  Donald G Truhlar,et al.  Electrostatically Embedded Many-Body Expansion for Large Systems, with Applications to Water Clusters. , 2007, Journal of chemical theory and computation.

[57]  Jiří Čížek,et al.  On the Use of the Cluster Expansion and the Technique of Diagrams in Calculations of Correlation Effects in Atoms and Molecules , 2007 .

[58]  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.

[59]  R. Nesbet Atomic Bethe‐Goldstone Equations , 2007 .

[60]  B. Roos The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[61]  Mario A. Storti,et al.  MPI for Python: Performance improvements and MPI-2 extensions , 2008, J. Parallel Distributed Comput..

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

[63]  K. Ruedenberg,et al.  A priori Identification of Configurational Deadwood , 2009 .

[64]  Michael Hanrath,et al.  Dissociating N2: a multi-reference coupled cluster study on the potential energy surfaces of ground and excited states , 2009 .

[65]  Ali Alavi,et al.  Fermion Monte Carlo without fixed nodes: a game of life, death, and annihilation in Slater determinant space. , 2009, The Journal of chemical physics.

[66]  Ali Alavi,et al.  Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo. , 2010, The Journal of chemical physics.

[67]  The range of electron correlation between localized molecular orbitals. A full configuration interaction analysis for the NCCN molecule. , 2010, The journal of physical chemistry. A.

[68]  Ali Alavi,et al.  Approaching chemical accuracy using full configuration-interaction quantum Monte Carlo: a study of ionization potentials. , 2010, The Journal of chemical physics.

[69]  Anton V. Sinitskiy,et al.  Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method. , 2010, The Journal of chemical physics.

[70]  Sandeep Sharma,et al.  The density matrix renormalization group in quantum chemistry. , 2011, Annual review of physical chemistry.

[71]  Lisandro Dalcin,et al.  Parallel distributed computing using Python , 2011 .

[72]  Ali Alavi,et al.  Breaking the carbon dimer: the challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods. , 2011, The Journal of chemical physics.

[73]  Nan Lin,et al.  Dynamical mean-field theory for quantum chemistry. , 2010, Physical review letters.

[74]  L. Stella,et al.  Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study , 2011, 1110.1746.

[75]  Gaël Varoquaux,et al.  The NumPy Array: A Structure for Efficient Numerical Computation , 2011, Computing in Science & Engineering.

[76]  Spencer R Pruitt,et al.  Fragmentation methods: a route to accurate calculations on large systems. , 2012, Chemical reviews.

[77]  Ali Alavi,et al.  Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study. , 2012, Journal of chemical theory and computation.

[78]  Quantum chemistry: Quadruply bonded carbon. , 2012, Nature chemistry.

[79]  C J Umrigar,et al.  Semistochastic projector Monte Carlo method. , 2012, Physical review letters.

[80]  Ali Alavi,et al.  Full Configuration Interaction Excitations of Ethene and Butadiene: Resolution of an Ancient Question. , 2012, Journal of chemical theory and computation.

[81]  Donald G Truhlar,et al.  Electrostatically embedded many-body method for dipole moments, partial atomic charges, and charge transfer. , 2012, Physical chemistry chemical physics : PCCP.

[82]  P. Hiberty,et al.  Quadruple bonding in C2 and analogous eight-valence electron species. , 2012, Nature chemistry.

[83]  Henry S Rzepa,et al.  One molecule, two atoms, three views, four bonds? , 2013, Angewandte Chemie.

[84]  Ali Alavi,et al.  Towards an exact description of electronic wavefunctions in real solids , 2012, Nature.

[85]  G. Frenking,et al.  Critical comments on "One molecule, two atoms, three views, four bonds?". , 2013, Angewandte Chemie.

[86]  Dimitri Van Neck,et al.  The density matrix renormalization group for ab initio quantum chemistry , 2014, The European Physical Journal D.

[87]  John M Herbert,et al.  Aiming for benchmark accuracy with the many-body expansion. , 2014, Accounts of chemical research.

[88]  T. Crawford,et al.  Computing optical rotation via an N-body approach , 2014, Theoretical Chemistry Accounts.

[89]  John M Herbert,et al.  Understanding the many-body expansion for large systems. I. Precision considerations. , 2014, The Journal of chemical physics.

[90]  E. Davidson,et al.  Singlet-triplet energy gaps for diradicals from particle-particle random phase approximation. , 2015, The journal of physical chemistry. A.

[91]  Sandeep Sharma A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer. , 2015, The Journal of chemical physics.

[92]  Garnet Kin-Lic Chan,et al.  The ab-initio density matrix renormalization group in practice. , 2015, The Journal of chemical physics.

[93]  John F. Stanton,et al.  Non-orthogonal spin-adaptation of coupled cluster methods: A new implementation of methods including quadruple excitations. , 2015, The Journal of chemical physics.

[94]  P. Jørgensen,et al.  On the convergence of perturbative coupled cluster triples expansions: error cancellations in the CCSD(T) model and the importance of amplitude relaxation. , 2015, The Journal of chemical physics.

[95]  Ryan M. Richard,et al.  Understanding the many-body expansion for large systems. II. Accuracy considerations. , 2016, The Journal of chemical physics.

[96]  Martin Head-Gordon,et al.  A deterministic alternative to the full configuration interaction quantum Monte Carlo method. , 2016, The Journal of chemical physics.

[97]  P. Jørgensen,et al.  Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. I. Triples expansions. , 2015, The Journal of chemical physics.

[98]  Markus Reiher,et al.  New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation. , 2015, Chimia.

[99]  Francesco A Evangelista,et al.  A Deterministic Projector Configuration Interaction Approach for the Ground State of Quantum Many-Body Systems. , 2016, Journal of chemical theory and computation.

[100]  P. Jørgensen,et al.  Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. II. Quadruples expansions. , 2015, The Journal of chemical physics.

[101]  Wenjian Liu,et al.  iCI: Iterative CI toward full CI. , 2016, Journal of chemical theory and computation.

[102]  C J Umrigar,et al.  Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling. , 2016, Journal of chemical theory and computation.

[103]  C J Umrigar,et al.  Efficient Heat-Bath Sampling in Fock Space. , 2015, Journal of chemical theory and computation.

[104]  Jeffrey B Schriber,et al.  Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy. , 2016, The Journal of chemical physics.

[105]  Francesco A. Evangelista,et al.  Adaptive Configuration Interaction for Computing Challenging Electronic Excited States with Tunable Accuracy. , 2017, Journal of chemical theory and computation.

[106]  Sandeep Sharma,et al.  Excited states using semistochastic heat-bath configuration interaction. , 2017, The Journal of chemical physics.

[107]  P. Zimmerman Strong correlation in incremental full configuration interaction. , 2017, The Journal of chemical physics.

[108]  David M. Ceperley,et al.  Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods , 2017, 1705.01608.

[109]  Adam A Holmes,et al.  Cheap and Near Exact CASSCF with Large Active Spaces. , 2017, Journal of chemical theory and computation.

[110]  P. Zimmerman Incremental full configuration interaction. , 2017, The Journal of chemical physics.

[111]  J. J. Eriksen,et al.  Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit. , 2017, The journal of physical chemistry letters.

[112]  John E Herr,et al.  The many-body expansion combined with neural networks. , 2016, The Journal of chemical physics.

[113]  Dominika Zgid,et al.  Generalized Self-Energy Embedding Theory. , 2017, The journal of physical chemistry letters.

[114]  P. Zimmerman Singlet-Triplet Gaps through Incremental Full Configuration Interaction. , 2017, The journal of physical chemistry. A.

[115]  Ali Alavi,et al.  Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory. , 2016, Journal of chemical theory and computation.

[116]  George H. Booth,et al.  Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments, and parallel distribution. , 2017, The Journal of chemical physics.

[117]  Jeffery S. Boschen,et al.  Correlation Energy Extrapolation by Many-Body Expansion. , 2017, The journal of physical chemistry. A.

[118]  G. Chan,et al.  A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces. , 2018, Journal of chemical theory and computation.

[119]  Yann Garniron,et al.  A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks. , 2018, Journal of chemical theory and computation.

[120]  Benjamin G. Levine,et al.  Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction. , 2018, Journal of chemical theory and computation.

[121]  J P Coe,et al.  Machine Learning Configuration Interaction. , 2018, Journal of chemical theory and computation.

[122]  Yann Garniron,et al.  Selected configuration interaction dressed by perturbation. , 2018, The Journal of chemical physics.

[123]  N. S. Blunt,et al.  Communication: An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo. , 2018, The Journal of chemical physics.

[124]  Sandeep Sharma,et al.  PySCF: the Python‐based simulations of chemistry framework , 2018 .

[125]  Paul M Zimmerman,et al.  Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction. , 2018, The journal of physical chemistry. A.