skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Driven similarity renormalization group: Third-order multireference perturbation theory

Abstract

Here, a third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N6) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F2, H2O2, C2H6, and N2 along the F–F, O–O, C–C, and N–N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (ΔST = ET–ES) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic ΔST is 3.9 kcal mol–1, a value that is within 0.1 kcal mol–1 from multireference coupled cluster results.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Emory Univ., Atlanta, GA (United States)
Publication Date:
Research Org.:
Emory Univ., Atlanta, GA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1351290
Grant/Contract Number:  
SC0016004
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 12; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; driven similarity renormalization group; multireference theories; perturbation theory

Citation Formats

Li, Chenyang, and Evangelista, Francesco A. Driven similarity renormalization group: Third-order multireference perturbation theory. United States: N. p., 2017. Web. doi:10.1063/1.4979016.
Li, Chenyang, & Evangelista, Francesco A. Driven similarity renormalization group: Third-order multireference perturbation theory. United States. https://doi.org/10.1063/1.4979016
Li, Chenyang, and Evangelista, Francesco A. 2017. "Driven similarity renormalization group: Third-order multireference perturbation theory". United States. https://doi.org/10.1063/1.4979016. https://www.osti.gov/servlets/purl/1351290.
@article{osti_1351290,
title = {Driven similarity renormalization group: Third-order multireference perturbation theory},
author = {Li, Chenyang and Evangelista, Francesco A.},
abstractNote = {Here, a third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N6) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F2, H2O2, C2H6, and N2 along the F–F, O–O, C–C, and N–N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (ΔST = ET–ES) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic ΔST is 3.9 kcal mol–1, a value that is within 0.1 kcal mol–1 from multireference coupled cluster results.},
doi = {10.1063/1.4979016},
url = {https://www.osti.gov/biblio/1351290}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 12,
volume = 146,
place = {United States},
year = {2017},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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


Coupled-cluster method in Fock space. II. Brueckner-Hartree-Fock method
journal, August 1985


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


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


The size consistency of multi-reference Møller–Plesset perturbation theory
journal, February 1998


Molecular Electronic-Structure Theory
book, August 2000


Combined coupled-cluster and many-body perturbation theories
journal, January 2004


Full implementation and benchmark studies of Mukherjee’s state-specific multireference coupled-cluster ansatz
journal, February 2010


Quasidegenerate perturbation theories. A canonical van Vleck formalism and its relationship to other approaches
journal, December 1980


Application of Hilbert-space coupled-cluster theory to simple ( H 2 ) 2 model systems: Planar models
journal, April 1993


Third-order generalized Van Vleck perturbation theory variant of multireference perturbation theory for electron correlation
journal, January 2009


In-Medium Similarity Renormalization Group For Nuclei
journal, June 2011


Quantum chemistry in Fock space. II. Effective Hamiltonians in Fock space
journal, November 1983


Multireference second-order perturbation theory: How size consistent is “almost size consistent”
journal, January 2005


Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators
journal, April 2016


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


A new internally contracted multi-reference configuration interaction method
journal, August 2011


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


Multireference equation-of-motion coupled cluster theory
journal, November 2012


A second order multiconfiguration SCF procedure with optimum convergence
journal, June 1985


Configuration interaction calculations on the nitrogen molecule
journal, January 1974


Qualitative intruder-state problems in effective Hamiltonian theory and their solution through intermediate Hamiltonians
journal, June 1987


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


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


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


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


Applications of level shift corrected perturbation theory in electronic spectroscopy
journal, December 1996


Coupled-cluster method in Fock space. I. General formalism
journal, August 1985


A sequential transformation approach to the internally contracted multireference coupled cluster method
journal, May 2012


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


Normal order and extended Wick theorem for a multiconfiguration reference wave function
journal, July 1997


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


Molecular Applications of a Size-Consistent State-Specific Multireference Perturbation Theory with Relaxed Model-Space Coefficients
journal, March 1999


A state-specific multi-reference coupled cluster formalism with molecular applications
journal, May 1998


Multiconfiguration perturbation theory: Size consistency at second order
journal, March 2005


Renormalization of Hamiltonians
journal, December 1993


General spin adaptation of open‐shell coupled cluster theory
journal, February 1996


Quantum chemistry in Fock space. III. Particle‐hole formalism
journal, January 1984


A state-specific multi-reference coupled cluster formalism with molecular applications
journal, May 1998


n -electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants
journal, November 2002


Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods
journal, April 2016


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


Intruder states in multireference perturbation theory: The ground state of manganese dimer
journal, February 2009


A review of canonical transformation theory
journal, April 2010


Reversible Bergman cyclization by atomic manipulation
journal, January 2016


Multiconfiguration perturbation theory with imaginary level shift
journal, August 1997


Perturbative triples corrections in state-specific multireference coupled cluster theory
journal, February 2010


Spinfree formulation of reduced density matrices, density cumulants and generalised normal ordering
journal, February 2010


Simplifications in the generation and transformation of two-electron integrals in molecular calculations
journal, October 1977


High-order excitations in state-universal and state-specific multireference coupled cluster theories: Model systems
journal, October 2006


Molpro: a general-purpose quantum chemistry program package: Molpro
journal, July 2011

  • Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2
  • https://doi.org/10.1002/wcms.82

On some approximations in applications of X α theory
journal, October 1979


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


A coupled-cluster approach to the many-body perturbation theory for open-shell systems
journal, March 1978


On the perturbation of multiconfiguration wave functions
journal, July 2003


Third-order generalized Van Vleck perturbation theory study of the ground and lowest excited states of C2
journal, October 2006


Cumulant expansion of the reduced density matrices
journal, February 1999


Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations
journal, May 2003


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


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


Coulombic potential energy integrals and approximations
journal, May 1973


Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods
journal, April 2009


Meaning and magnitude of the reduced density matrix cumulants
journal, June 2012


Coupled-cluster method in Fock space. IV. Calculation of expectation values and transition moments
journal, March 1988


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


Comparative study of multireference perturbative theories for ground and excited states
journal, November 2009


Psi4: an open-source ab initio electronic structure program : Psi4: an electronic structure program
journal, October 2011

  • Turney, Justin M.; Simmonett, Andrew C.; Parrish, Robert M.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 4
  • https://doi.org/10.1002/wcms.93

Multireference perturbation configuration interaction V. Third-order energy contributions in the M�ller?Plesset and Epstein?Nesbet partitions
journal, May 2002


In-medium similarity renormalization group with chiral two- plus three-nucleon interactions
journal, March 2013


Canonical transformation theory from extended normal ordering
journal, September 2007


Coupled-cluster theory in quantum chemistry
journal, February 2007


Rethinking linearized coupled-cluster theory
journal, April 2009


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


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


A study of cumulant approximations to n-electron valence multireference perturbation theory
journal, May 2009


A state-specific partially internally contracted multireference coupled cluster approach
journal, June 2011


Quantum chemistry in Fock space. I. The universal wave and energy operators
journal, September 1982


Canonical transformation theory for multireference problems
journal, May 2006


A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications
journal, April 1999


Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients
journal, January 1999


Intruder state avoidance multireference Møller-Plesset perturbation theory: Multireference Møller-Plesset Perturbation Theory
journal, May 2002


Selection of active spaces for multiconfigurational wavefunctions
journal, June 2015


The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
journal, March 2016


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
  • https://doi.org/10.1002/wcms.1248

An Introduction to Coupled Cluster Theory for Computational Chemists
book, January 2000


Linear scaling local coupled cluster theory with density fitting. Part I: 4-external integrals
journal, January 2003


Third-order multireference perturbation theory: The n-electron valence state perturbation-theory approach
journal, February 2006


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


Explication and revision of generalized Van Vleck perturbation theory for molecular electronic structure
journal, September 2002


Additional global internal contraction in variations of multireference equation of motion coupled cluster theory
journal, April 2013


Potential Energy Surface of the Chromium Dimer Re-re-revisited with Multiconfigurational Perturbation Theory
journal, March 2016


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


An algebraic proof of generalized Wick theorem
journal, June 2010


Comparison of low-order multireference many-body perturbation theories
journal, April 2005


Ultraviolet Photoelectron Spectroscopy of the o -, m -, and p- Benzyne Negative Ions. Electron Affinities and Singlet−Triplet Splittings for o -, m -, and p -Benzyne
journal, June 1998


Works referencing / citing this record:

Multireference perturbation theory with improved virtual orbitals for radicals: More degeneracies, more problems
journal, November 2018


Driven similarity renormalization group for excited states: A state-averaged perturbation theory
journal, March 2018


Perspective: Multireference coupled cluster theories of dynamical electron correlation
journal, July 2018


Dynamically weighted multireference perturbation theory: Combining the advantages of multi-state and state-averaged methods
journal, April 2019


A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation
journal, August 2019


Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory
journal, July 2019


The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges
journal, January 2020


Erratum: “Driven similarity renormalization group: Third-order multireference perturbation theory” [J. Chem. Phys. 146, 124132 (2017)]
journal, February 2018


Describing strong correlation with fractional-spin correction in density functional theory
journal, September 2018