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

Title: Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.5100022· OSTI ID:1613023
 [1];  [2]; ORCiD logo [3]; ORCiD logo [4]
  1. Q-Chem, Inc., Pleasanton, CA (United States); Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
  2. Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
  3. Johannes Gutenberg Univ., Mainz (Germany)
  4. Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry; Johannes Gutenberg Univ., Mainz (Germany)
+ Show Author Affiliations

We present a general formulation of analytic nuclear gradients for the coupled-cluster with single and double substitution (CCSD) and equation-of-motion (EOM) CCSD energies computed using Cholesky decomposition (CD) representations of the electron repulsion integrals. By rewriting the correlated energy and response equations such that the storage of the largest four-index intermediates is eliminated, CD leads to a significant reduction in disk storage requirements, reduced I/O penalties, and an improved parallel performance. CD thus extends the scope of the systems that can be treated by (EOM-)CCSD methods, although analytic gradients in the framework of CD are needed to extend the applicability of (EOM-)CCSD methods in the context of geometry optimizations. This paper presents a formulation of analytic (EOM-)CCSD gradient within the CD framework and reports on the salient details of the corresponding implementation. The accuracy and the capabilities of analytic CD-based (EOM-)CCSD gradients are illustrated by benchmark calculations and several illustrative examples.

Research Organization:
Univ. of Southern California, Los Angeles, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0018910
OSTI ID:
1613023
Journal Information:
Journal of Chemical Physics, Vol. 151, Issue 1; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 24 works
Citation information provided by
Web of Science

References (110)

Reduced scaling in electronic structure calculations using Cholesky decompositions journal June 2003
An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations journal December 1988
Geometry optimizations with the coupled-cluster model CC2 using the resolution-of-the-identity approximation journal May 2003
Excitation energies from the coupled cluster singles and doubles linear response function (CCSDLR). Applications to Be, CH + , CO, and H 2 O journal September 1990
Coupled cluster response functions journal September 1990
Molecular Electronic-Structure Theory book August 2000
Principles for a direct SCF approach to LICAO - MO ab - initio calculations : Direct journal September 1982
Charge localization and Jahn–Teller distortions in the benzene dimer cation journal August 2008
An extension of the coupled cluster formalism to excited states (I) journal January 1981
Analytic CCSD(T) second derivatives journal September 1997
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples journal February 1982
Energy gradient in a multi-configurational SCF formalism and its application to geometry optimization of trimethylene diradicals journal August 1979
Analytical energy gradients for local coupled-cluster methodsElectronic Supplementary Information available. See http://www.rsc.org/suppdata/cp/b1/b105126c/ journal January 2001
A direct product decomposition approach for symmetry exploitation in many‐body methods. I. Energy calculations journal March 1991
Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency journal April 2009
Explicitly correlated local coupled-cluster methods using pair natural orbitals journal July 2018
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon journal January 1993
Rigorous integral screening for electron correlation methods journal November 2005
Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application journal November 1987
General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks journal October 2013
Improvements on the direct SCF method: Improved Direct SCF Method journal January 1989
The integral‐direct coupled cluster singles and doubles model journal March 1996
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
Density-Based Multilevel Hartree–Fock Model journal October 2017
Analytic evaluation of energy gradients for the singles and doubles coupled cluster method including perturbative triple excitations: Theory and applications to FOOF and Cr 2 journal January 1991
Analytical gradients of the second-order Møller-Plesset energy using Cholesky decompositions journal October 2013
Double Precision Is Not Needed for Many-Body Calculations: Emergent Conventional Wisdom journal June 2018
New implementation of high-level correlated methods using a general block tensor library for high-performance electronic structure calculations journal July 2013
Multi-level coupled cluster theory journal December 2014
Revisitation of Nonorthogonal Spin Adaptation in Coupled Cluster Theory journal May 2013
Analytic derivatives for the Cholesky representation of the two-electron integrals journal July 2008
Accurate ab initio density fitting for multiconfigurational self-consistent field methods journal July 2008
A fifth-order perturbation comparison of electron correlation theories journal May 1989
Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory journal February 2015
Analytic energy derivatives for coupled-cluster methods describing excited states: General formulas and comparison of computational costs journal July 1995
Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks journal February 2015
Density fitting with auxiliary basis sets from Cholesky decompositions journal July 2009
Analytical energy gradients for second-order multireference perturbation theory using density fitting journal March 2013
Calculation of excited-state properties using general coupled-cluster and configuration-interaction models journal November 2004
Derivative studies in hartree-fock and møller-plesset theories journal March 1979
Equation of motion coupled cluster method for electron attachment journal March 1995
Derivative studies in configuration–interaction theory journal April 1980
Analytic gradients from correlated wave functions via the two‐particle density matrix and the unitary group approach journal April 1980
A Lagrangian, integral-density direct formulation and implementation of the analytic CCSD and CCSD(T) gradients journal February 2003
Analytic first derivatives for general coupled-cluster and configuration interaction models journal August 2003
Analytic energy derivatives for the equation-of-motion coupled-cluster method: Algebraic expressions, implementation and application to the journal January 1995
Cholesky Decomposition Techniques in Electronic Structure Theory book January 2011
Single-Reference ab initio Methods for the Calculation of Excited States of Large Molecules journal January 2006
Coupled‐cluster open‐shell analytic gradients: Implementation of the direct product decomposition approach in energy gradient calculations journal August 1991
Analytic energy derivatives for the calculation of the first-order molecular properties using the domain-based local pair-natural orbital coupled-cluster theory journal September 2016
Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space journal May 2008
The effect of polarizable environment on two-photon absorption cross sections characterized by the equation-of-motion coupled-cluster singles and doubles method combined with the effective fragment potential approach journal October 2018
A linear response, coupled-cluster theory for excitation energy journal March 1984
Analytic gradients for coupled‐cluster energies that include noniterative connected triple excitations: Application to c i s ‐ and t r a n s ‐HONO journal May 1991
Simplifications in the generation and transformation of two-electron integrals in molecular calculations journal October 1977
Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method journal November 1994
Implementation of analytical energy gradients at third- and fourth-order Møller-Plesset perturbation theory journal July 1987
Many‐body methods for excited state potential energy surfaces. I. General theory of energy gradients for the equation‐of‐motion coupled‐cluster method journal December 1993
Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach journal June 1991
The multilevel CC3 coupled cluster model journal July 2016
Analytical energy gradients for local second-order Møller–Plesset perturbation theory using density fitting approximations journal July 2004
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory: Analytical calculation of energy derivatives journal September 2013
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
Analytical differentiation of the energy contribution due to triple excitations in fourth-order Møller-Plesset perturbation theory journal December 1988
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties journal May 1993
Coulombic potential energy integrals and approximations journal May 1973
Calibration of Cholesky Auxiliary Basis Sets for Multiconfigurational Perturbation Theory Calculations of Excitation Energies journal February 2010
On first-row diatomic molecules and local density models journal January 1979
Analytic second derivatives for general coupled-cluster and configuration-interaction models journal April 2004
Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of Co III (diiminato)(NPh) journal April 2008
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model journal February 2002
Unbiased auxiliary basis sets for accurate two-electron integral approximations journal September 2007
Excited state coupled cluster methods: Excited state coupled cluster methods journal November 2011
Integral-direct electron correlation methods journal February 1999
An efficient algorithm for Cholesky decomposition of electron repulsion integrals journal May 2019
Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions journal July 2016
Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc–Zn journal August 2005
Equation-of-motion spin-flip coupled-cluster model with single and double substitutions: Theory and application to cyclobutadiene journal January 2004
Low-scaling analytical gradients for the direct random phase approximation using an atomic orbital formalism journal December 2018
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules journal November 2005
MOLCAS 7: The Next Generation journal January 2010
Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis journal January 2009
Scalable Electron Correlation Methods I.: PNO-LMP2 with Linear Scaling in the Molecular Size and Near-Inverse-Linear Scaling in the Number of Processors journal January 2015
Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the density-fitting approximation journal July 2017
Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation journal September 2003
Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules: II. Force constants of water journal April 1970
Auxiliary basis expansions for large-scale electronic structure calculations journal April 2005
Q-Chem: an engine for innovation: Q-Chem: an engine for innovation journal November 2012
Analytical gradients of the state-average complete active space self-consistent field method with density fitting journal July 2015
Natural triple excitations in local coupled cluster calculations with pair natural orbitals journal October 2013
Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules : I. Theory journal January 1969
Static polarizabilities for excited states within the spin-conserving and spin-flipping equation-of-motion coupled-cluster singles and doubles formalism: Theory, implementation, and benchmarks journal November 2016
Coupled cluster energy derivatives. Analytic Hessian for the closed‐shell coupled cluster singles and doubles wave function: Theory and applications journal April 1990
Method specific Cholesky decomposition: Coulomb and exchange energies journal October 2008
Coupled-cluster theory and its equation-of-motion extensions: Coupled-cluster theory journal July 2011
A general multireference configuration interaction gradient program journal February 1992
Analytic energy gradients for the equation‐of‐motion coupled‐cluster method: Implementation and application to the HCN/HNC system journal March 1994
Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients journal June 1993
Communication: Exact analytical derivatives for the domain-based local pair natural orbital MP2 method (DLPNO-MP2) journal January 2018
Analytic second derivatives for the full coupled-cluster singles, doubles, and triples model: Nuclear magnetic shielding constants for BH, HF, CO, N[sub 2], N[sub 2]O, and O[sub 3] journal January 2002
RI-MP2: first derivatives and global consistency journal October 1997
Local treatment of electron correlation in coupled cluster theory journal April 1996
Analytic gradients for the spin-conserving and spin-flipping equation-of-motion coupled-cluster models with single and double substitutions journal June 2005
Use of 2h and 3h−p-like coupled-cluster Tamm–Dancoff approaches for the equilibrium properties of ozone journal August 2003
Integral approximations for LCAO-SCF calculations journal October 1993
Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation journal May 2016
Gradient techniques for open‐shell restricted Hartree–Fock and multiconfiguration self‐consistent‐field methods journal August 1979
Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ journal September 1998
Linear-Scaling Techniques in Computational Chemistry and Physics: Methods and Applications book January 2011

Cited By (4)

NWChem: Past, Present, and Future text January 2020
Accurate reproduction of strongly repulsive interatomic potentials journal March 2020
Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets journal January 2020
On the accurate reproduction of strongly repulsive interatomic potentials text January 2019

Figures / Tables (5)

TABLE I(p. 7)table TABLE I
TABLE II(p. 7)table TABLE II
FIG. 1(p. 8)figure FIG. 1
TABLE III(p. 8)table TABLE III
TABLE IV(p. 8)table TABLE IV

Similar Records

Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks
Journal Article · Sat Feb 14 00:00:00 EST 2015 · Journal of Chemical Physics · OSTI ID:1613023
Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks
Journal Article · Fri Mar 19 00:00:00 EDT 2021 · Journal of Chemical Physics · OSTI ID:1613023
+2 more
Complex absorbing potentials within EOM-CC family of methods: Theory, implementation, and benchmarks
Journal Article · Mon Jul 14 00:00:00 EDT 2014 · Journal of Chemical Physics · OSTI ID:1613023
+5 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Chemistry
Physics
Excited states
Coupled-cluster methods