Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction

Abstract

Here, we present a reduced scaling formulation of the state specific complete active space second-order perturbation method (CASPT2) requiring O(N4) operations and O(N2) memory for a fixed active space, where N is proportional to system size. Motivated by the properties of the Kronecker sum, we introduce the supporting subspace technique (SST), which decomposes the CASPT2 linear equations into two parts: a single-reference MP2 energy term using dressed orbitals, plus a reduced linear system with dimension scaling as O(N2). Together with Laplace quadrature, the SST allows us to reformulate CASPT2 using a MP2 energy computation and Fock builds. By further applying the tensor hyper-contraction (THC) approximation, the MP2-like term can be computed with O(N4) operations, and the remainder can be solved with O(N3) operations using the preconditioned conjugate gradient method. This is the first application of THC in the context of multi-reference methods. We also developed an efficient implementation of the method by utilizing graphical processing units and exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method against conventional CASPT2 for reactions in the gas phase. We apply the new method to Menshutkin SN2 reactions in carbon nanotubes, demonstrating the feasibility of CASPT2 calculations with O(100)more » atoms.« less

Authors:
 [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1468951
Grant/Contract Number:  
AC02-76SF00515; ACI-1429830; CHE-1565249
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Song, Chenchen, and Martínez, Todd J. Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction. United States: N. p., 2018. Web. doi:10.1063/1.5037283.
Copy to clipboard
Song, Chenchen, & Martínez, Todd J. Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction. United States. https://doi.org/10.1063/1.5037283
Copy to clipboard
Song, Chenchen, and Martínez, Todd J. Wed . "Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction". United States. https://doi.org/10.1063/1.5037283. https://www.osti.gov/servlets/purl/1468951.
Copy to clipboard
@article{osti_1468951,
title = {Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction},
author = {Song, Chenchen and Martínez, Todd J.},
abstractNote = {Here, we present a reduced scaling formulation of the state specific complete active space second-order perturbation method (CASPT2) requiring O(N4) operations and O(N2) memory for a fixed active space, where N is proportional to system size. Motivated by the properties of the Kronecker sum, we introduce the supporting subspace technique (SST), which decomposes the CASPT2 linear equations into two parts: a single-reference MP2 energy term using dressed orbitals, plus a reduced linear system with dimension scaling as O(N2). Together with Laplace quadrature, the SST allows us to reformulate CASPT2 using a MP2 energy computation and Fock builds. By further applying the tensor hyper-contraction (THC) approximation, the MP2-like term can be computed with O(N4) operations, and the remainder can be solved with O(N3) operations using the preconditioned conjugate gradient method. This is the first application of THC in the context of multi-reference methods. We also developed an efficient implementation of the method by utilizing graphical processing units and exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method against conventional CASPT2 for reactions in the gas phase. We apply the new method to Menshutkin SN2 reactions in carbon nanotubes, demonstrating the feasibility of CASPT2 calculations with O(100) atoms.},
doi = {10.1063/1.5037283},
journal = {Journal of Chemical Physics},
number = 4,
volume = 149,
place = {United States},
year = {Wed Jul 25 00:00:00 EDT 2018},
month = {Wed Jul 25 00:00:00 EDT 2018}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5037283
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 29 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Illustration of the (a) CASPT2 linear system and (b) the supported leading system. The two squares in the upper panel illustrate the sparsity pattern of the matrices, and the lower two graphs provide more details about the sparsity structure in the off-diagonal blocks (i.e., the gray blocks inmore » the squares). Each circle represents a subspace, denoted by the number of holes (H) and particles (P) as H(nH)P(nP), as well as the corresponding indices (i, j, holes; a, b, particles; K, L, hole-type active orbitals; C, G, particle-type active orbitals; D, active excitations). The circles are colored by the total number of holes and particles (purple, 0; blue, 1; green; 2; orange, 3; red, 4.). Lines connecting the circles represent coupling between subspaces. Blues lines represent coupling through hole indices, and red lines represent coupling through particle indices. The number of parallel lines indicate the form of the coupling (see the legend at top right). Dotted lines are for visual effect.« less
All figures and tables (7 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions
journal, May 2016

  • Roemelt, Michael; Guo, Sheng; Chan, Garnet K. -L.
  • The Journal of Chemical Physics, Vol. 144, Issue 20
  • DOI: 10.1063/1.4950757

Reduced scaling in electronic structure calculations using Cholesky decompositions
journal, June 2003

  • Koch, Henrik; Sánchez de Merás, Alfredo; Pedersen, Thomas Bondo
  • The Journal of Chemical Physics, Vol. 118, Issue 21
  • DOI: 10.1063/1.1578621

Classification of configurations and the determination of interacting and noninteracting spaces in configuration interaction
journal, February 1973

  • McLean, A. D.; Liu, B.
  • The Journal of Chemical Physics, Vol. 58, Issue 3
  • DOI: 10.1063/1.1679288

Influence of the choice of projection manifolds in the CASPT2 implementation
journal, December 2016

Multiconfigurational perturbation theory with level shift — the Cr2 potential revisited
journal, October 1995

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory
journal, July 2012

  • Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 137, Issue 4
  • DOI: 10.1063/1.4732310

A simple method for the evaluation of the second-order-perturbation energy from external double-excitations with a CASSCF reference wavefunction
journal, April 1982

An atomic orbital-based formulation of the complete active space self-consistent field method on graphical processing units
journal, June 2015

  • Hohenstein, Edward G.; Luehr, Nathan; Ufimtsev, Ivan S.
  • The Journal of Chemical Physics, Vol. 142, Issue 22
  • DOI: 10.1063/1.4921956

An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory
journal, May 2016

  • Hannon, Kevin P.; Li, Chenyang; Evangelista, Francesco A.
  • The Journal of Chemical Physics, Vol. 144, Issue 20
  • DOI: 10.1063/1.4951684

Consistent generalization of the Møller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory
journal, October 1987

Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction Energies
journal, June 2015

  • Kokkila Schumacher, Sara I. L.; Hohenstein, Edward G.; Parrish, Robert M.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 7
  • DOI: 10.1021/acs.jctc.5b00272

Tensor hypercontraction. II. Least-squares renormalization
journal, December 2012

  • Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4768233

Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation
journal, January 2008

  • Ufimtsev, Ivan S.; Martínez, Todd J.
  • Journal of Chemical Theory and Computation, Vol. 4, Issue 2
  • DOI: 10.1021/ct700268q

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction
journal, May 2014

  • Parrish, Robert M.; Sherrill, C. David; Hohenstein, Edward G.
  • The Journal of Chemical Physics, Vol. 140, Issue 18
  • DOI: 10.1063/1.4876016

Direct configuration interaction with a reference state composed of many reference configurations
journal, November 1980

  • Siegbahn, Per E. M.
  • International Journal of Quantum Chemistry, Vol. 18, Issue 5
  • DOI: 10.1002/qua.560180510

Analytical Derivative Coupling for Multistate CASPT2 Theory
journal, May 2017

  • Park, Jae Woo; Shiozaki, Toru
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 6
  • DOI: 10.1021/acs.jctc.7b00018

A perspective on the CASPT2 method
journal, April 2011

  • Pulay, Peter
  • International Journal of Quantum Chemistry, Vol. 111, Issue 13
  • DOI: 10.1002/qua.23052

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

A spin-adapted size-extensive state-specific multi-reference perturbation theory. I. Formal developments
journal, January 2012

  • Mao, Shuneng; Cheng, Lan; Liu, Wenjian
  • The Journal of Chemical Physics, Vol. 136, Issue 2
  • DOI: 10.1063/1.3672083

Chemistry Inside Carbon Nanotubes:  the Menshutkin S N 2 Reaction
journal, February 2002

  • Halls, Mathew D.; Schlegel, H. Bernhard
  • The Journal of Physical Chemistry B, Vol. 106, Issue 8
  • DOI: 10.1021/jp0137165

Second‐order perturbation theory with a complete active space self‐consistent field reference function
journal, January 1992

  • Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O.
  • The Journal of Chemical Physics, Vol. 96, Issue 2
  • DOI: 10.1063/1.462209

Introduction of n -electron valence states for multireference perturbation theory
journal, June 2001

  • Angeli, C.; Cimiraglia, R.; Evangelisti, S.
  • The Journal of Chemical Physics, Vol. 114, Issue 23
  • DOI: 10.1063/1.1361246

An efficient internally contracted multiconfiguration–reference configuration interaction method
journal, November 1988

  • Werner, Hans‐Joachim; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 89, Issue 9
  • DOI: 10.1063/1.455556

Coulombic potential energy integrals and approximations
journal, May 1973

  • Whitten, J. L.
  • The Journal of Chemical Physics, Vol. 58, Issue 10
  • DOI: 10.1063/1.1679012

Calibration of Cholesky Auxiliary Basis Sets for Multiconfigurational Perturbation Theory Calculations of Excitation Energies
journal, February 2010

  • Boström, Jonas; Delcey, Mickaël G.; Aquilante, Francesco
  • Journal of Chemical Theory and Computation, Vol. 6, Issue 3
  • DOI: 10.1021/ct900612k

A modified definition of the zeroth-order Hamiltonian in multiconfigurational perturbation theory (CASPT2)
journal, September 2004

MCSCF Study of the S N 2 Menshutkin Reaction in Aqueous Solution within the Polarizable Continuum Model
journal, April 1998

  • Amovilli, Claudio; Mennucci, Benedetta; Floris, Franca Maria
  • The Journal of Physical Chemistry B, Vol. 102, Issue 16
  • DOI: 10.1021/jp9803945

Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co III (diiminato)(NPh)
journal, April 2008

  • Aquilante, Francesco; Malmqvist, Per-Åke; Pedersen, Thomas Bondo
  • Journal of Chemical Theory and Computation, Vol. 4, Issue 5
  • DOI: 10.1021/ct700263h

Laplace transform techniques in Mo/ller–Plesset perturbation theory
journal, January 1992

  • Häser, Marco; Almlöf, Jan
  • The Journal of Chemical Physics, Vol. 96, Issue 1
  • DOI: 10.1063/1.462485

Construction of open shell perturbation theory invariant with respect to orbital degeneracy
journal, August 1994

Parallelization of a multiconfigurational perturbation theory
journal, June 2013

  • Vancoillie, Steven; Delcey, Mickaël G.; Lindh, Roland
  • Journal of Computational Chemistry, Vol. 34, Issue 22
  • DOI: 10.1002/jcc.23342

Multireference Møller—Plesset perturbation theory for high-spin open-shell systems
journal, August 1992

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory
journal, January 2017

  • Sharma, Sandeep; Knizia, Gerald; Guo, Sheng
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 2
  • DOI: 10.1021/acs.jctc.6b00898

Considerations in constructing a multireference second‐order perturbation theory
journal, March 1994

  • Kozlowski, Pawel M.; Davidson, Ernest R.
  • The Journal of Chemical Physics, Vol. 100, Issue 5
  • DOI: 10.1063/1.466355

Predictive theory for the combination kinetics of two alkyl radicals
journal, January 2006

  • Klippenstein, Stephen J.; Georgievskii, Yuri; Harding, Lawrence B.
  • Physical Chemistry Chemical Physics, Vol. 8, Issue 10
  • DOI: 10.1039/b515914h

Generalized Møller—Plesset perturbation theory applied to general MCSCF reference wave functions
journal, September 1991

BAGEL: Brilliantly Advanced General Electronic-structure Library: BAGEL
journal, August 2017

  • Shiozaki, Toru
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1
  • DOI: 10.1002/wcms.1331

Comparison of Multireference Møller−Plesset Theory and Time-Dependent Methods for the Calculation of Vertical Excitation Energies of Molecules †
journal, July 2002

  • Parac, Maja; Grimme, Stefan
  • The Journal of Physical Chemistry A, Vol. 106, Issue 29
  • DOI: 10.1021/jp020550e

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model
journal, September 1982

An efficient method for the evaluation of coupling coefficients in configuration interaction calculations
journal, April 1988

Generalized Mo/ller–Plesset perturbation theory: Second order results for two‐configuration, open‐shell excited singlet, and doublet wave functions
journal, April 1989

  • Wolinski, Krzysztof; Pulay, Peter
  • The Journal of Chemical Physics, Vol. 90, Issue 7
  • DOI: 10.1063/1.456696

Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory
journal, June 2011

  • Granovsky, Alexander A.
  • The Journal of Chemical Physics, Vol. 134, Issue 21
  • DOI: 10.1063/1.3596699

Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients
journal, August 2011

  • Shiozaki, Toru; Győrffy, Werner; Celani, Paolo
  • The Journal of Chemical Physics, Vol. 135, Issue 8
  • DOI: 10.1063/1.3633329

A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach
journal, May 1980

Complete active space second-order perturbation theory with cumulant approximation for extended active-space wavefunction from density matrix renormalization group
journal, November 2014

  • Kurashige, Yuki; Chalupský, Jakub; Lan, Tran Nguyen
  • The Journal of Chemical Physics, Vol. 141, Issue 17
  • DOI: 10.1063/1.4900878

A thorough understanding of the Diels-Alder reaction of 1,3-butadiene and ethylene: DIELS-ALDER REACTION OF 1,3-BUTADIENE AND ETHYLENE
journal, May 2014

  • Cui, Cheng-Xing; Liu, Ya-Jun
  • Journal of Physical Organic Chemistry, Vol. 27, Issue 8
  • DOI: 10.1002/poc.3313

Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis
journal, June 2017

  • Helmich-Paris, Benjamin; Knecht, Stefan
  • The Journal of Chemical Physics, Vol. 146, Issue 22
  • DOI: 10.1063/1.4984591

Predictive Theory for Hydrogen Atom−Hydrocarbon Radical Association Kinetics
journal, June 2005

  • Harding, Lawrence B.; Georgievskii, Yuri; Klippenstein, Stephen J.
  • The Journal of Physical Chemistry A, Vol. 109, Issue 21
  • DOI: 10.1021/jp0508608

Partitioning technique, perturbation theory, and rational approximations: PARTITIONING TECHNIQUE
journal, January 1982

  • Löwdin, Per-Olov
  • International Journal of Quantum Chemistry, Vol. 21, Issue 1
  • DOI: 10.1002/qua.560210105

A driven similarity renormalization group approach to quantum many-body problems
journal, August 2014

  • Evangelista, Francesco A.
  • The Journal of Chemical Physics, Vol. 141, Issue 5
  • DOI: 10.1063/1.4890660

CNT-Confinement Effects on the Menshutkin S N 2 Reaction: The Role of Nonbonded Interactions
journal, July 2016

  • Giacinto, Pietro; Zerbetto, Francesco; Bottoni, Andrea
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 8
  • DOI: 10.1021/acs.jctc.6b00260

Multireference perturbation theory for large restricted and selected active space reference wave functions
journal, April 2000

  • Celani, Paolo; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 112, Issue 13
  • DOI: 10.1063/1.481132

A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency
journal, August 2002

  • Weigend, Florian
  • Physical Chemistry Chemical Physics, Vol. 4, Issue 18
  • DOI: 10.1039/b204199p

Comparison of fully internally and strongly contracted multireference configuration interaction procedures
journal, August 2016

  • Sivalingam, Kantharuban; Krupicka, Martin; Auer, Alexander A.
  • The Journal of Chemical Physics, Vol. 145, Issue 5
  • DOI: 10.1063/1.4959029

Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) Time
journal, July 2013

  • Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.
  • The Journal of Physical Chemistry B, Vol. 117, Issue 42
  • DOI: 10.1021/jp4021905

Multireference Driven Similarity Renormalization Group: A Second-Order Perturbative Analysis
journal, April 2015

  • Li, Chenyang; Evangelista, Francesco A.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 5
  • DOI: 10.1021/acs.jctc.5b00134

Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics
journal, August 2009

  • Ufimtsev, Ivan S.; Martinez, Todd J.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 10
  • DOI: 10.1021/ct9003004

Test of a new multi-reference Møller-Plesset perturbation theory
journal, June 1994

The multi-state CASPT2 method
journal, May 1998

Analytical energy gradients for internally contracted second-order multireference perturbation theory
journal, September 2003

  • Celani, Paolo; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 119, Issue 10
  • DOI: 10.1063/1.1597672

State-specific multireference perturbation theory: development and present status: State-specific multireference perturbation theory
journal, February 2016

  • Chattopadhyay, Sudip; Chaudhuri, Rajat K.; Mahapatra, Uttam Sinha
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 6, Issue 3
  • DOI: 10.1002/wcms.1248

Theoretical Analysis of Concerted and Stepwise Mechanisms of Diels−Alder Reaction between Butadiene and Ethylene
journal, February 2000

  • Sakai, Shogo
  • The Journal of Physical Chemistry A, Vol. 104, Issue 5
  • DOI: 10.1021/jp9926894

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction
journal, January 2017

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 146, Issue 3
  • DOI: 10.1063/1.4973840

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units
journal, October 2017

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 147, Issue 16
  • DOI: 10.1063/1.4997997

Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory
journal, February 2015

  • MacLeod, Matthew K.; Shiozaki, Toru
  • The Journal of Chemical Physics, Vol. 142, Issue 5
  • DOI: 10.1063/1.4907717

Second-order perturbation theory with a CASSCF reference function
journal, July 1990

  • Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O.
  • The Journal of Physical Chemistry, Vol. 94, Issue 14
  • DOI: 10.1021/j100377a012

Generalized Mo/ller–Plesset and Epstein–Nesbet perturbation theory applied to multiply bonded molecules
journal, September 1992

  • Murphy, Robert B.; Messmer, Richard P.
  • The Journal of Chemical Physics, Vol. 97, Issue 6
  • DOI: 10.1063/1.463992

Analytical energy gradients for second-order multireference perturbation theory using density fitting
journal, March 2013

  • Győrffy, Werner; Shiozaki, Toru; Knizia, Gerald
  • The Journal of Chemical Physics, Vol. 138, Issue 10
  • DOI: 10.1063/1.4793737

A transformed framework for dynamic correlation in multireference problems
journal, March 2015

  • Sokolov, Alexander Yu.; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 142, Issue 12
  • DOI: 10.1063/1.4916315

A time-dependent formulation of multi-reference perturbation theory
journal, February 2016

  • Sokolov, Alexander Yu.; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 144, Issue 6
  • DOI: 10.1063/1.4941606

Local complete active space second-order perturbation theory using pair natural orbitals (PNO-CASPT2)
journal, September 2016

  • Menezes, Filipe; Kats, Daniel; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 145, Issue 12
  • DOI: 10.1063/1.4963019

Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2
journal, March 2013

  • Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.
  • The Journal of Chemical Physics, Vol. 138, Issue 12
  • DOI: 10.1063/1.4795514

Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation
journal, March 2009

  • Ufimtsev, Ivan S.; Martinez, Todd J.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 4
  • DOI: 10.1021/ct800526s

Third-order multireference perturbation theory The CASPT3 method
journal, October 1996

New perspectives in multireference perturbation theory: the n-electron valence state approach
journal, December 2006

  • Angeli, Celestino; Pastore, Mariachiara; Cimiraglia, Renzo
  • Theoretical Chemistry Accounts, Vol. 117, Issue 5-6
  • DOI: 10.1007/s00214-006-0207-0

Multireference Møller—Plesset method
journal, March 1992

Integral approximations for LCAO-SCF calculations
journal, October 1993

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity
journal, May 2016

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 144, Issue 17
  • DOI: 10.1063/1.4948438

Third-order multireference perturbation theory The CASPT3 method
journal, October 1996

Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory.
text, January 2017

  • Sharma, Sandeep; Knizia, Gerald; Guo, Sheng
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.21653

Deazaflavin reductive photocatalysis involves excited semiquinone radicals
text, January 2020

  • Graml, Andreas; Neveselý, Tomáš; Kutta, Roger Jan
  • Universität Regensburg
  • DOI: 10.5283/epub.43436

A time-dependent formulation of multi-reference perturbation theory
text, January 2015

Analytical derivative coupling for multistate CASPT2 theory
text, January 2017

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Making machine learning a useful tool in the accelerated discovery of transition metal complexes
    journal, July 2019

    • Kulik, Heather J.
    • WIREs Computational Molecular Science, Vol. 10, Issue 1
    • DOI: 10.1002/wcms.1439

    CASSCF linear response calculations for large open-shell molecules
    journal, May 2019

    • Helmich-Paris, Benjamin
    • The Journal of Chemical Physics, Vol. 150, Issue 17
    • DOI: 10.1063/1.5092613

    Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots
    text, January 2019

      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      FIG. 1 (p. 4)figure
      FIG. 2 (p. 9)figure
      FIG. 3 (p. 11)figure
      FIG. 4 (p. 13)figure
      FIG. 5 (p. 15)figure
      FIG. 6 (p. 16)figure
      FIG. 7 (p. 17)figure
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: