Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So

doi:10.1080/00268976.2017.1288937

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Journal Article · Tue Mar 07 00:00:00 EST 2017 · Molecular Physics

DOI:https://doi.org/10.1080/00268976.2017.1288937· OSTI ID:1361645

Rai, Prashant ^[1]; Sargsyan, Khachik ^[1]; Najm, Habib ^[1]; Hermes, Matthew R. ^[2]; Hirata, So ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm^-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1361645

Report Number(s):: SAND--2017-0642J; 650599

Journal Information:: Molecular Physics, Journal Name: Molecular Physics Journal Issue: 17-18 Vol. 115; ISSN 0026-8976

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

References (85)

Monte Carlo Methods Kalos, Malvin H.; Whitlock, Paula A. https://doi.org/10.1002/9783527626212	book	September 2008
A literature survey of low-rank tensor approximation techniques Grasedyck, Lars; Kressner, Daniel; Tobler, Christine GAMM-Mitteilungen, Vol. 36, Issue 1 https://doi.org/10.1002/gamm.201310004	journal	August 2013
Computation of determinant expansion coefficients within the graphically contracted function method Gidofalvi, Gergely; Shepard, Ron Journal of Computational Chemistry, Vol. 30, Issue 15 https://doi.org/10.1002/jcc.21275	journal	November 2009
Principles for a direct SCF approach to LICAO - MO ab - initio calculations : Direct Almlöf, J.; Faegri, K.; Korsell, K. Journal of Computational Chemistry, Vol. 3, Issue 3 https://doi.org/10.1002/jcc.540030314	journal	September 1982
An efficient recursive algorithm to compute wave function optimization gradients for the graphically contracted function method Shepard, Ron; Gidofalvi, Gergely; Hovland, Paul D. International Journal of Quantum Chemistry, Vol. 110, Issue 15 https://doi.org/10.1002/qua.22867	journal	August 2010
Simplifications in the generation and transformation of two-electron integrals in molecular calculations Beebe, Nelson H. F.; Linderberg, Jan International Journal of Quantum Chemistry, Vol. 12, Issue 4 https://doi.org/10.1002/qua.560120408	journal	October 1977
Tensor Spaces and Numerical Tensor Calculus Hackbusch, Wolfgang Springer Series in Computational Mathematics https://doi.org/10.1007/978-3-642-28027-6	book	February 2012
Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition Carroll, J. Douglas; Chang, Jih-Jie Psychometrika, Vol. 35, Issue 3 https://doi.org/10.1007/BF02310791	journal	September 1970
A New Scheme for the Tensor Representation Hackbusch, W.; Kühn, S. Journal of Fourier Analysis and Applications, Vol. 15, Issue 5 https://doi.org/10.1007/s00041-009-9094-9	journal	October 2009
Multiresolution potential energy surfaces for vibrational state calculations Yagi, Kiyoshi; Hirata, So; Hirao, Kimihiko Theoretical Chemistry Accounts, Vol. 118, Issue 3 https://doi.org/10.1007/s00214-007-0363-x	journal	July 2007
Black Box Low Tensor-Rank Approximation Using Fiber-Crosses Espig, Mike; Grasedyck, Lars; Hackbusch, Wolfgang Constructive Approximation, Vol. 30, Issue 3 https://doi.org/10.1007/s00365-009-9076-9	journal	October 2009
Solution of self-consistent field electronic structure equations by a pseudospectral method Friesner, Richard A. Chemical Physics Letters, Vol. 116, Issue 1 https://doi.org/10.1016/0009-2614(85)80121-4	journal	April 1985
Use of approximate integrals in ab initio theory. An application in MP2 energy calculations Feyereisen, Martin; Fitzgerald, George; Komornicki, Andrew Chemical Physics Letters, Vol. 208, Issue 5-6 https://doi.org/10.1016/0009-2614(93)87156-W	journal	June 1993
Integral approximations for LCAO-SCF calculations Vahtras, O.; Almlöf, J.; Feyereisen, M. W. Chemical Physics Letters, Vol. 213, Issue 5-6 https://doi.org/10.1016/0009-2614(93)89151-7	journal	October 1993
Tensor rank is NP-complete Håstad, Johan Journal of Algorithms, Vol. 11, Issue 4 https://doi.org/10.1016/0196-6774(90)90014-6	journal	December 1990
PARAFAC. Tutorial and applications Bro, Rasmus Chemometrics and Intelligent Laboratory Systems, Vol. 38, Issue 2 https://doi.org/10.1016/S0169-7439(97)00032-4	journal	October 1997
Introduction to the Variational and Diffusion Monte Carlo Methods Toulouse, Julien; Assaraf, Roland; Umrigar, Cyrus J. Advances in Quantum Chemistry https://doi.org/10.1016/bs.aiq.2015.07.003	book	January 2016
Multiresolution separated representations of singular and weakly singular operators Beylkin, Gregory; Cramer, Robert; Fann, George Applied and Computational Harmonic Analysis, Vol. 23, Issue 2 https://doi.org/10.1016/j.acha.2007.01.001	journal	September 2007
The density-matrix renormalization group in the age of matrix product states Schollwöck, Ulrich Annals of Physics, Vol. 326, Issue 1 https://doi.org/10.1016/j.aop.2010.09.012	journal	January 2011
Tensors-structured numerical methods in scientific computing: Survey on recent advances Khoromskij, Boris N. Chemometrics and Intelligent Laboratory Systems, Vol. 110, Issue 1 https://doi.org/10.1016/j.chemolab.2011.09.001	journal	January 2012
Non-intrusive low-rank separated approximation of high-dimensional stochastic models Doostan, Alireza; Validi, AbdoulAhad; Iaccarino, Gianluca Computer Methods in Applied Mechanics and Engineering, Vol. 263 https://doi.org/10.1016/j.cma.2013.04.003	journal	August 2013
Fast and accurate 3D tensor calculation of the Fock operator in a general basis Khoromskaia, V.; Andrae, D.; Khoromskij, B. N. Computer Physics Communications, Vol. 183, Issue 11 https://doi.org/10.1016/j.cpc.2012.06.007	journal	November 2012
Møller–Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals Khoromskaia, V.; Khoromskij, B. N. Computer Physics Communications, Vol. 185, Issue 1 https://doi.org/10.1016/j.cpc.2013.08.004	journal	January 2014
Tensor decomposition in electronic structure calculations on 3D Cartesian grids Khoromskij, B. N.; Khoromskaia, V.; Chinnamsetty, S. R. Journal of Computational Physics, Vol. 228, Issue 16 https://doi.org/10.1016/j.jcp.2009.04.043	journal	September 2009
Adaptive sparse polynomial chaos expansion based on least angle regression Blatman, Géraud; Sudret, Bruno Journal of Computational Physics, Vol. 230, Issue 6 https://doi.org/10.1016/j.jcp.2010.12.021	journal	March 2011
High Dimensional Model Representations Li, Genyuan; Rosenthal, Carey; Rabitz, Herschel The Journal of Physical Chemistry A, Vol. 105, Issue 33 https://doi.org/10.1021/jp010450t	journal	August 2001
A Nested Molecule-Independent Neural Network Approach for High-Quality Potential Fits ^† Manzhos, Sergei; Wang, Xiaogang; Dawes, Richard The Journal of Physical Chemistry A, Vol. 110, Issue 16 https://doi.org/10.1021/jp055253z	journal	April 2006
Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies Khoromskaia, Venera; Khoromskij, Boris N. Physical Chemistry Chemical Physics, Vol. 17, Issue 47 https://doi.org/10.1039/C5CP01215E	journal	January 2015
Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties Christiansen, Ove Physical Chemistry Chemical Physics, Vol. 9, Issue 23 https://doi.org/10.1039/b618764a	journal	January 2007
Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs Chkifa, Abdellah; Cohen, Albert; Migliorati, Giovanni ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 49, Issue 3 https://doi.org/10.1051/m2an/2014050	journal	April 2015
Ab initio potential energy surface for vibrational state calculations of H2CO Yagi, Kiyoshi; Oyanagi, Chikako; Taketsugu, Tetsuya The Journal of Chemical Physics, Vol. 118, Issue 4 https://doi.org/10.1063/1.1531105	journal	January 2003
Coulombic potential energy integrals and approximations Whitten, J. L. The Journal of Chemical Physics, Vol. 58, Issue 10 https://doi.org/10.1063/1.1679012	journal	May 1973
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree–Fock and density functional theory Yanai, Takeshi; Fann, George I.; Gan, Zhengting The Journal of Chemical Physics, Vol. 121, Issue 7 https://doi.org/10.1063/1.1768161	journal	August 2004
Multiresolution quantum chemistry in multiwavelet bases: Hartree–Fock exchange Yanai, Takeshi; Fann, George I.; Gan, Zhenting The Journal of Chemical Physics, Vol. 121, Issue 14 https://doi.org/10.1063/1.1790931	journal	October 2004
Multiresolution quantum chemistry: Basic theory and initial applications Harrison, Robert J.; Fann, George I.; Yanai, Takeshi The Journal of Chemical Physics, Vol. 121, Issue 23 https://doi.org/10.1063/1.1791051	journal	December 2004
Using neural networks to represent potential surfaces as sums of products Manzhos, Sergei; Carrington, Tucker The Journal of Chemical Physics, Vol. 125, Issue 19 https://doi.org/10.1063/1.2387950	journal	November 2006
Interpolating moving least-squares methods for fitting potential energy surfaces: Computing high-density potential energy surface data from low-density ab initio data points Dawes, Richard; Thompson, Donald L.; Guo, Yin The Journal of Chemical Physics, Vol. 126, Issue 18 https://doi.org/10.1063/1.2730798	journal	May 2007
Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals Aquilante, Francesco; Pedersen, Thomas Bondo; Lindh, Roland The Journal of Chemical Physics, Vol. 126, Issue 19 https://doi.org/10.1063/1.2736701	journal	May 2007
Interpolating moving least-squares methods for fitting potential energy surfaces: A strategy for efficient automatic data point placement in high dimensions Dawes, Richard; Thompson, Donald L.; Wagner, Albert F. The Journal of Chemical Physics, Vol. 128, Issue 8 https://doi.org/10.1063/1.2831790	journal	February 2008
Size-extensive vibrational self-consistent field method Keçeli, Murat; Hirata, So The Journal of Chemical Physics, Vol. 135, Issue 13 https://doi.org/10.1063/1.3644895	journal	October 2011
On first-row diatomic molecules and local density models Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. The Journal of Chemical Physics, Vol. 71, Issue 12 https://doi.org/10.1063/1.438313	journal	January 1979
On some approximations in applications of X α theory Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. The Journal of Chemical Physics, Vol. 71, Issue 8 https://doi.org/10.1063/1.438728	journal	October 1979
Solution of the Hartree–Fock equations for polyatomic molecules by a pseudospectral method Friesner, Richard A. The Journal of Chemical Physics, Vol. 86, Issue 6 https://doi.org/10.1063/1.451955	journal	March 1987
Product representation of potential energy surfaces Jäckle, A.; Meyer, H. ‐D. The Journal of Chemical Physics, Vol. 104, Issue 20 https://doi.org/10.1063/1.471513	journal	May 1996
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 4 https://doi.org/10.1063/1.4732310	journal	July 2012
Vibrational self-consistent field method for many-mode systems: A new approach and application to the vibrations of CO adsorbed on Cu(100) Carter, Stuart; Culik, Susan J.; Bowman, Joel M. The Journal of Chemical Physics, Vol. 107, Issue 24 https://doi.org/10.1063/1.474210	journal	December 1997
Optimized coordinates for anharmonic vibrational structure theories Yagi, Kiyoshi; Keçeli, Murat; Hirata, So The Journal of Chemical Physics, Vol. 137, Issue 20 https://doi.org/10.1063/1.4767776	journal	November 2012
Tensor hypercontraction. II. Least-squares renormalization Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768233	journal	December 2012
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768241	journal	December 2012
Product representation of potential energy surfaces. II Jäckle, A.; Meyer, H. -D. The Journal of Chemical Physics, Vol. 109, Issue 10 https://doi.org/10.1063/1.476977	journal	September 1998
Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2 Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M. The Journal of Chemical Physics, Vol. 138, Issue 12 https://doi.org/10.1063/1.4795514	journal	March 2013
Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm Nakatani, Naoki; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 138, Issue 13 https://doi.org/10.1063/1.4798639	journal	April 2013
Second-order many-body perturbation expansions of vibrational Dyson self-energies Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 139, Issue 3 https://doi.org/10.1063/1.4813123	journal	July 2013
Multi-layer Potfit: An accurate potential representation for efficient high-dimensional quantum dynamics Otto, Frank The Journal of Chemical Physics, Vol. 140, Issue 1 https://doi.org/10.1063/1.4856135	journal	January 2014
Optimized coordinates in vibrational coupled cluster calculations Thomsen, Bo; Yagi, Kiyoshi; Christiansen, Ove The Journal of Chemical Physics, Vol. 140, Issue 15 https://doi.org/10.1063/1.4870775	journal	April 2014
The multifacet graphically contracted function method. I. Formulation and implementation Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R. The Journal of Chemical Physics, Vol. 141, Issue 6 https://doi.org/10.1063/1.4890734	journal	August 2014
The multifacet graphically contracted function method. II. A general procedure for the parameterization of orthogonal matrices and its application to arc factors Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R. The Journal of Chemical Physics, Vol. 141, Issue 6 https://doi.org/10.1063/1.4890735	journal	August 2014
Stochastic many-body perturbation theory for anharmonic molecular vibrations Hermes, Matthew R.; Hirata, So The Journal of Chemical Physics, Vol. 141, Issue 8 https://doi.org/10.1063/1.4892614	journal	August 2014
Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates Cheng, Xiaolu; Steele, Ryan P. The Journal of Chemical Physics, Vol. 141, Issue 10 https://doi.org/10.1063/1.4894507	journal	September 2014
Using multi-dimensional Smolyak interpolation to make a sum-of-products potential Avila, Gustavo; Carrington, Tucker The Journal of Chemical Physics, Vol. 143, Issue 4 https://doi.org/10.1063/1.4926651	journal	July 2015
Higher-order diagrammatic vibrational coupled-cluster theory Faucheaux, Jacob A.; Hirata, So The Journal of Chemical Physics, Vol. 143, Issue 13 https://doi.org/10.1063/1.4931472	journal	October 2015
Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions Ziegler, Benjamin; Rauhut, Guntram The Journal of Chemical Physics, Vol. 144, Issue 11 https://doi.org/10.1063/1.4943985	journal	March 2016
Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format Böhm, Karl-Heinz; Auer, Alexander A.; Espig, Mike The Journal of Chemical Physics, Vol. 144, Issue 24 https://doi.org/10.1063/1.4953665	journal	June 2016
Tensor decomposition in potential energy surface representations Ostrowski, Lukas; Ziegler, Benjamin; Rauhut, Guntram The Journal of Chemical Physics, Vol. 145, Issue 10 https://doi.org/10.1063/1.4962368	journal	September 2016
Variational quantum approaches for computing vibrational energies of polyatomic molecules Bowman, Joel M.; Carrington, Tucker; Meyer, Hans-Dieter Molecular Physics, Vol. 106, Issue 16-18 https://doi.org/10.1080/00268970802258609	journal	August 2008
MULTIMODE: A code to calculate rovibrational energies of polyatomic molecules Bowman, Joel M.; Carter, Stuart; Huang, Xinchuan International Reviews in Physical Chemistry, Vol. 22, Issue 3 https://doi.org/10.1080/0144235031000124163	journal	July 2003
Permutationally invariant potential energy surfaces in high dimensionality Braams, Bastiaan J.; Bowman, Joel M. International Reviews in Physical Chemistry, Vol. 28, Issue 4 https://doi.org/10.1080/01442350903234923	journal	October 2009
Diagrammatic theories of anharmonic molecular vibrations Hermes, Matthew R.; Hirata, So International Reviews in Physical Chemistry, Vol. 34, Issue 1 https://doi.org/10.1080/0144235X.2014.1001220	journal	December 2014
Complete-graph tensor network states: a new fermionic wave function ansatz for molecules Marti, Konrad H.; Bauer, Bela; Reiher, Markus New Journal of Physics, Vol. 12, Issue 10 https://doi.org/10.1088/1367-2630/12/10/103008	journal	October 2010
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001
The density-matrix renormalization group Schollwöck, U. Reviews of Modern Physics, Vol. 77, Issue 1 https://doi.org/10.1103/RevModPhys.77.259	journal	April 2005
Dynamical Theory of Crystal Lattices Born, Max; Huang, Kun; Lax, M. American Journal of Physics, Vol. 23, Issue 7 https://doi.org/10.1119/1.1934059	journal	October 1955
Algorithms for Numerical Analysis in High Dimensions Beylkin, Gregory; Mohlenkamp, Martin J. SIAM Journal on Scientific Computing, Vol. 26, Issue 6 https://doi.org/10.1137/040604959	journal	January 2005
Tensor Decompositions and Applications Kolda, Tamara G.; Bader, Brett W. SIAM Review, Vol. 51, Issue 3 https://doi.org/10.1137/07070111X	journal	August 2009
Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays Khoromskij, B. N.; Khoromskaia, V. SIAM Journal on Scientific Computing, Vol. 31, Issue 4 https://doi.org/10.1137/080730408	journal	January 2009
Tensor-Train Decomposition Oseledets, I. V. SIAM Journal on Scientific Computing, Vol. 33, Issue 5 https://doi.org/10.1137/090752286	journal	January 2011
Hierarchical Singular Value Decomposition of Tensors Grasedyck, Lars SIAM Journal on Matrix Analysis and Applications, Vol. 31, Issue 4 https://doi.org/10.1137/090764189	journal	January 2010
Numerical Solution of the Hartree–Fock Equation in Multilevel Tensor-Structured Format Khoromskij, B. N.; Khoromskaia, V.; Flad, H. -J. SIAM Journal on Scientific Computing, Vol. 33, Issue 1 https://doi.org/10.1137/090777372	journal	January 2011
Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis Khoromskaia, V.; Khoromskij, B. N.; Schneider, R. SIAM Journal on Scientific Computing, Vol. 35, Issue 2 https://doi.org/10.1137/120884067	journal	January 2013
A Least-Squares Method for Sparse Low Rank Approximation of Multivariate Functions Chevreuil, M.; Lebrun, R.; Nouy, A. SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, Issue 1 https://doi.org/10.1137/13091899X	journal	January 2015
A Multilinear Singular Value Decomposition De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos SIAM Journal on Matrix Analysis and Applications, Vol. 21, Issue 4 https://doi.org/10.1137/S0895479896305696	journal	January 2000
The Density Matrix Renormalization Group in Quantum Chemistry Chan, Garnet Kin-Lic; Sharma, Sandeep Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103338	journal	May 2011
The Density Matrix Renormalization Group Algorithm in Quantum Chemistry Marti, Konrad Heinrich; Reiher, Markus Zeitschrift für Physikalische Chemie, Vol. 224, Issue 3-4 https://doi.org/10.1524/zpch.2010.6125	journal	April 2010

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