Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction.

We present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix-vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 1016 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2-5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.

[1]  F. Grein,et al.  Multiconfiguration wavefunctions obtained by application of the generalized Brillouin theorem , 1971 .

[2]  B. Roos,et al.  A new method for large-scale Cl calculations , 1972 .

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

[4]  Robert J. Buenker,et al.  Individualized configuration selection in CI calculations with subsequent energy extrapolation , 1974 .

[5]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

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

[7]  R. R. Alfano,et al.  Heterofission in pentacene-doped tetracene single crystals , 1977 .

[8]  B. Roos,et al.  A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach , 1980 .

[9]  B. Roos,et al.  A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method , 1980 .

[10]  Nicholas C. Handy,et al.  Multi-root configuration interaction calculations , 1980 .

[11]  Vincenzo Balzani,et al.  Quenching of singlet and triplet excited states of aromatic molecules by europium ions , 1982 .

[12]  Michael W. Schmidt,et al.  Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model , 1982 .

[13]  QUENCHING OF SINGLET AND TRIPLET EXCITED STATES OF AROMATIC MOLECULES BY EUROPIUM IONS , 1982 .

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

[15]  Per E. M. Siegbahn,et al.  A new direct CI method for large CI expansions in a small orbital space , 1984 .

[16]  I. Røeggen,et al.  On the Beebe-Linderberg two-electron integral approximation , 1986 .

[17]  Włodzisław Duch,et al.  GRMS or Graphical Representation of Model Spaces , 1986 .

[18]  J. Olsen,et al.  A non-linear approach to configuration interaction: The low-rank CI method (LR CI) , 1987 .

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

[20]  Low-rank configuration interaction with orbital optimization - the LR SCF approach , 1988 .

[21]  Peter J. Knowles,et al.  Very large full configuration interaction calculations , 1989 .

[22]  Peter J. Knowles,et al.  A determinant based full configuration interaction program , 1989 .

[23]  Robert J. Harrison,et al.  An efficient implementation of the full-CI method using an (n–2)-electron projection space , 1989 .

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

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

[26]  Emily A. Carter,et al.  Pseudospectral full configuration interaction , 1992 .

[27]  H. Koch,et al.  A variational matrix decomposition applied to full configuration-interaction calculations , 1992 .

[28]  Stefano Evangelisti,et al.  A vector and parallel full configuration interaction algorithm , 1993 .

[29]  A. Mitrushenkov.  Passing the several billions limit in FCI calculations on a mini-computer , 1994 .

[30]  A. Mitrushenkov,et al.  Passing the several billion limit in FCI calculations on a mini-computer. A norm-consistent zero CI threshold estimate within the dynamic CI approach , 1995 .

[31]  R. Weinkauf,et al.  Photodetachment photoelectron spectroscopy of mass selected anions: anthracene and the anthracene-H2O cluster , 1997 .

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

[33]  Yixiang Cao,et al.  Correlated ab Initio Electronic Structure Calculations for Large Molecules , 1999 .

[34]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

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

[36]  Robert J. Harrison,et al.  Calibrating quantum chemistry: A multi-teraflop, parallel-vector, full-configuration interaction program for the Cray-X1 , 2005, ACM/IEEE SC 2005 Conference (SC'05).

[37]  R. Lindh,et al.  Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals. , 2007, The Journal of chemical physics.

[38]  Garnet Kin-Lic Chan,et al.  The radical character of the acenes: a density matrix renormalization group study. , 2007, The Journal of chemical physics.

[39]  Zoltán Rolik,et al.  A sparse matrix based full-configuration interaction algorithm. , 2008, The Journal of chemical physics.

[40]  Roland Lindh,et al.  Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. , 2009, The Journal of chemical physics.

[41]  Björn O. Roos,et al.  The complete active space SCF method in a fock‐matrix‐based super‐CI formulation , 2009 .

[42]  F. Grein,et al.  A multiconfiguration method for excited states of atoms and molecules , 2009 .

[43]  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.

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

[45]  Robert M Parrish,et al.  Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[46]  Robert M Parrish,et al.  Tensor hypercontraction. II. Least-squares renormalization. , 2012, The Journal of chemical physics.

[47]  P. Taylor.  Lossless compression of wave function information using matrix factorization: A "gzip" for quantum chemistry. , 2013, The Journal of chemical physics.

[48]  Robert M Parrish,et al.  Exact tensor hypercontraction: a universal technique for the resolution of matrix elements of local finite-range N-body potentials in many-body quantum problems. , 2013, Physical review letters.

[49]  Seiichiro Ten-no,et al.  Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states. , 2013, The Journal of chemical physics.

[50]  T. Martínez,et al.  Tensor hypercontraction equation-of-motion second-order approximate coupled cluster: electronic excitation energies in O(N4) time. , 2013, The journal of physical chemistry. B.

[51]  Garnet Kin-Lic Chan,et al.  Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm. , 2013, The Journal of chemical physics.

[52]  Gustavo E. Scuseria,et al.  Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function , 2014, 1407.4800.

[53]  T. Martínez,et al.  Tensor Hypercontraction Second-Order Møller-Plesset Perturbation Theory: Grid Optimization and Reaction Energies. , 2015, Journal of chemical theory and computation.

[54]  Benjamin G. Levine,et al.  Nanoscale multireference quantum chemistry: full configuration interaction on graphical processing units. , 2015, Journal of chemical theory and computation.

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

[56]  Todd J Martínez,et al.  Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity. , 2016, The Journal of chemical physics.

[57]  Robert M Parrish,et al.  "Balancing" the Block Davidson-Liu Algorithm. , 2016, Journal of chemical theory and computation.

[58]  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.

[59]  Filipp Furche,et al.  Accelerating molecular property calculations with nonorthonormal Krylov space methods. , 2016, The Journal of chemical physics.

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

[61]  Benjamin G. Levine,et al.  Complete active space configuration interaction from state-averaged configuration interaction singles natural orbitals: Analytic first derivatives and derivative coupling vectors. , 2017, The Journal of chemical physics.

[62]  T. Martínez,et al.  Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction. , 2017, The Journal of chemical physics.

[63]  Benjamin G. Levine,et al.  A direct-compatible formulation of the coupled perturbed complete active space self-consistent field equations on graphical processing units. , 2017, The Journal of chemical physics.