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Local Pair Natural Orbital-Based Coupled-Cluster Theory through Full Quadruples (DLPNO–CCSDTQ)

Journal Article · · Journal of Chemical Theory and Computation
 [1];  [2];  [3];  [1];  [1];  [3];  [1]
  1. University of Georgia, Athens, GA (United States)
  2. Southern Methodist University, Dallas, TX (United States)
  3. Georgia Institute of Technology, Atlanta, GA (United States)
+ Show Author Affiliations
In this work, we implement a local pair natural orbitalbased coupled-cluster method through the full treatment of quadruple excitations (CCSDTQ). The domain-based local pair natural orbital (DLPNO) approach, which has successfully been applied to lower levels of coupled-cluster theory, is utilized in our algorithm, and thus our algorithm is called DLPNO-CCSDTQ. For simplicity in the working equations and in the implementation, we t1-dress the twoelectron integrals as well as Fock matrix elements. Our method can recover CCSDTQ-CCSDT and CCSDTQ-CCSDT(Q) energy differences on the order of 0.01−0.05 kcal mol−1, even at a loose quadruples natural orbital (QNO) occupation number cutoff of 3.33 × 10−6. To highlight the capabilities of our code and its potential future applications, we showcase computations that would be intractable with canonical CCSDTQ, such as the benzene dimer, (H2O)17, and adamantane. With sufficient computing resources, computations up to 15 heavy atoms (40 atoms overall) may be feasible for fully bonded 3D systems.
Research Organization:
University of Georgia, Athens, GA (United States)
Sponsoring Organization:
US National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0018412
Other Award/Contract Number:
2236869
17-SC-20-SC
2410879
CHE-2143725
MRI-1828187
OAC-2410877
OSTI ID:
3024412
Journal Information:
Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 6 Vol. 22; ISSN 1549-9626; ISSN 1549-9618
Publisher:
American Chemical Society (ACS)Copyright Statement
Country of Publication:
United States
Language:
English

References (164)

An Introduction to Coupled Cluster Theory for Computational Chemists book January 2000
Linear scaling local correlation approach for solving the coupled cluster equations of large systems journal December 2001
W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods journal July 2017
Isomerism of CH2SO: Accurate structural, energetic, and spectroscopic characterization journal December 2023
Improvements on the direct SCF method: Improved Direct SCF Method journal January 1989
Comparison of the boys and Pipek-Mezey localizations in the local correlation approach and automatic virtual basis selection journal June 1993
Accurate molecular structures of small‐ and medium‐sized molecules journal July 2016
Astronomical complex organic molecules: Quantum chemistry meets rotational spectroscopy journal September 2016
Ionization energies of water from PNO-CI calculations journal January 1971
Simplifications in the generation and transformation of two-electron integrals in molecular calculations journal October 1977
Analytical gradients for the coupled-cluster method journal March 1984
The versatility of the Cholesky decomposition in electronic structure theory journal October 2023
Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems journal December 1983
The coupled-pair approximation in a basis of independent-pair natural orbitals journal August 1976
Convergence acceleration of iterative sequences. the case of scf iteration journal July 1980
Localizability of dynamic electron correlation journal September 1983
Accelerating the convergence of the coupled-cluster approach journal October 1986
Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods journal February 1990
The convergence of coupled-cluster methods for Be2 journal July 1991
Use of approximate integrals in ab initio theory. An application in MP2 energy calculations journal June 1993
Integral approximations for LCAO-SCF calculations journal October 1993
A direct atomic orbital driven implementation of the coupled cluster singles and doubles (CCSD) model journal September 1994
A fifth-order perturbation comparison of electron correlation theories journal May 1989
Why CCSD(T) works: a different perspective journal December 1997
RI-MP2: optimized auxiliary basis sets and demonstration of efficiency journal September 1998
The Configuration Interaction Method: Advances in Highly Correlated Approaches book January 1999
Basis set convergence of high-order coupled cluster methods up to CCSDTQ567 for a highly multireference molecule journal December 2019
Post-CCSD(T) corrections in the S66 noncovalent interactions benchmark journal March 2025
Diving for Accurate Structures in the Ocean of Molecular Systems with the Help of Spectroscopy and Quantum Chemistry journal February 2018
Accurate Reduced-Cost CCSD(T) Energies: Parallel Implementation, Benchmarks, and Large-Scale Applications journal January 2021
Near-Exact CCSDT Energetics from Rank-Reduced Formalism Supplemented by Non-iterative Corrections journal December 2021
Implementation of Occupied and Virtual Edmiston–Ruedenberg Orbitals Using Cholesky Decomposed Integrals journal July 2022
When Gold Is Not Enough: Platinum Standard of Quantum Chemistry with N7 Cost journal October 2022
Tensor Hypercontraction Form of the Perturbative Triples Energy in Coupled-Cluster Theory journal February 2023
Automatic Differentiation for Explicitly Correlated MP2 journal September 2024
Linear-Scaling Local Natural Orbital-Based Full Triples Treatment in Coupled-Cluster Theory journal February 2025
Scalable Electron Correlation Methods. 2. Parallel PNO-LMP2-F12 with Near Linear Scaling in the Molecular Size journal October 2015
Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD) journal July 2017
Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12) journal September 2017
Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde journal February 2018
Scalable Electron Correlation Methods. 5. Parallel Perturbative Triples Correction for Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals journal December 2017
P si 4N um P y : An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development journal May 2018
Optimization of the Linear-Scaling Local Natural Orbital CCSD(T) Method: Improved Algorithm and Benchmark Applications journal June 2018
Approaching the Basis Set Limit of CCSD(T) Energies for Large Molecules with Local Natural Orbital Coupled-Cluster Methods journal August 2019
Integral-Direct and Parallel Implementation of the CCSD(T) Method: Algorithmic Developments and Large-Scale Applications journal November 2019
Implementation of the Coupled-Cluster Method with Single, Double, and Triple Excitations using Tensor Decompositions journal November 2019
Coupled Cluster Benchmarking of Large Noncovalent Complexes in L7 and S12L as Well as the C60 Dimer, DNA–Ellipticine, and HIV–Indinavir journal June 2022
High-Accuracy Heats of Formation for Alkane Oxidation: From Small to Large via the Automated CBH-ANL Method journal January 2023
Ab Initio Computations and Active Thermochemical Tables Hand in Hand: Heats of Formation of Core Combustion Species journal August 2017
Highly Accurate CCSDT(Q)/CBS Reaction Barrier Heights for a Diverse Set of Transition Structures: Basis Set Convergence and Cost-Effective Approaches for Estimating Post-CCSD(T) Contributions journal July 2019
CCSD[T] Describes Noncovalent Interactions Better than the CCSD(T), CCSD(TQ), and CCSDT Methods journal November 2012
Accuracy of Quantum Chemical Methods for Large Noncovalent Complexes journal July 2013
Accuracy and Efficiency of Coupled-Cluster Theory Using Density Fitting/Cholesky Decomposition, Frozen Natural Orbitals, and a t 1 -Transformed Hamiltonian journal May 2013
Convergence of the Interaction Energies in Noncovalent Complexes in the Coupled-Cluster Methods Up to Full Configuration Interaction journal July 2013
Basis Set Convergence of the Post-CCSD(T) Contribution to Noncovalent Interaction Energies journal June 2014
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
Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory journal March 2015
Intrinsic Errors in Several ab Initio Methods: The Dissociation Energy of N2 journal March 1995
Coupled Cluster Theory and Multireference Configuration Interaction Study of FO, F 2 O, FO 2 , and FOOF journal October 2003
Ab Initio Studies of π···π Interactions:  The Effects of Quadruple Excitations † journal April 2004
Improved Design of Orbital Domains within the Cluster-in-Molecule Local Correlation Framework: Single-Environment Cluster-in-Molecule Ansatz and Its Application to Local Coupled-Cluster Approach with Singles and Doubles † journal August 2010
Accurate Determination of Barrier Height and Kinetics for the F + H 2 O → HF + OH Reaction journal August 2013
Accurate Coupled Cluster Calculations of the Reaction Barrier Heights of Two CH 3 • + CH 4 Reactions † journal October 2009
High-Level Ab Initio Electronic Structure Calculations of Water Clusters (H 2 O) 16 and (H 2 O) 17 : A New Global Minimum for (H 2 O) 16 journal October 2010
Interactions between large molecules pose a puzzle for reference quantum mechanical methods journal June 2021
Understanding discrepancies in noncovalent interaction energies from wavefunction theories for large molecules journal October 2025
Linear scaling local coupled cluster theory with density fitting. Part I: 4-external integrals journal January 2003
Connections between the accuracy of rotational constants and equilibrium molecular structures journal January 2023
Fulminic acid: a quasibent spectacle journal January 2024
A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency journal August 2002
Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction ( T ) journal December 2000
Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) journal January 2001
Higher excitations in coupled-cluster theory journal August 2001
Shielding polarizabilities calculated at the coupled-cluster singles and doubles level augmented by a perturbative treatment of triple excitations journal January 2002
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
Low-order scaling local electron correlation methods. V. Connected triples beyond (T): Linear scaling local CCSDT-1b journal May 2002
Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations journal May 2003
Coulombic potential energy integrals and approximations journal May 1973
PNO–CI Studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane journal February 1973
Configuration‐Interaction Calculation of H 3 and H 2 journal February 1965
Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I journal October 1955
HEAT: High accuracy extrapolated ab initio thermochemistry journal December 2004
Coupled-cluster methods including noniterative corrections for quadruple excitations journal August 2005
Approximate treatment of higher excitations in coupled-cluster theory journal December 2005
High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification journal August 2006
An efficient implementation of the “cluster-in-molecule” approach for local electron correlation calculations journal August 2006
W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions journal October 2006
Linear scaling density fitting journal November 2006
Basis set convergence of post-CCSD contributions to molecular atomization energies journal August 2007
High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview journal March 2008
Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane journal April 2008
Cholesky decomposition of the two-electron integral matrix in electronic structure calculations journal May 2008
Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree–Fock case journal October 2008
Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method journal March 2009
Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis journal January 2009
Local correlation calculations using standard and renormalized coupled-cluster approaches journal September 2009
Performance of W4 theory for spectroscopic constants and electrical properties of small molecules journal October 2010
A general-order local coupled-cluster method based on the cluster-in-molecule approach journal September 2011
Basis set convergence of the coupled-cluster correction, δMP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases journal November 2011
PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. II. The molecules BeH 2 , BH, BH 3 , CH 4 , CH − 3 , NH 3 (planar and pyramidal), H 2 O, OH + 3 , HF and the Ne atom journal February 1975
A theory of self-consistent electron pairs. Computational methods and preliminary applications journal October 1976
On some approximations in applications of X α theory journal October 1979
A coupled cluster approach with triple excitations journal December 1984
A fast intrinsic localization procedure applicable for a b i n i t i o and semiempirical linear combination of atomic orbital wave functions journal May 1989
Triple and quadruple excitation contributions to the binding in Be clusters: Calibration calculations on Be 3 journal December 1990
Comparison of coupled‐cluster methods which include the effects of connected triple excitations journal October 1990
Coupled‐cluster method truncated at quadruples journal November 1991
The coupled‐cluster single, double, triple, and quadruple excitation method journal September 1992
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
Coupled‐cluster theory employing approximate integrals: An approach to avoid the input/output and storage bottlenecks journal July 1994
Coupled‐cluster calculations of nuclear magnetic resonance chemical shifts journal September 1995
Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants journal February 1996
Full configuration–interaction and state of the art correlation calculations on water in a valence double‐zeta basis with polarization functions journal May 1996
Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory journal July 2012
Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method journal April 1998
An efficient way to include connected quadruple contributions into the coupled cluster method journal June 1998
Tensor hypercontraction. II. Least-squares renormalization journal December 2012
Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions journal December 2012
An efficient and near linear scaling pair natural orbital based local coupled cluster method journal January 2013
Connected quadruples for the frequencies of O3 journal May 1999
Low-order scaling local electron correlation methods. I. Linear scaling local MP2 journal October 1999
Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations journal June 2000
An efficient linear-scaling CCSD(T) method based on local natural orbitals journal September 2013
Natural triple excitations in local coupled cluster calculations with pair natural orbitals journal October 2013
A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy journal February 2014
Equation-of-motion coupled cluster perturbation theory revisited journal May 2014
Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction journal May 2014
Non-orthogonal spin-adaptation of coupled cluster methods: A new implementation of methods including quadruple excitations journal February 2015
Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals journal July 2015
Communication: The performance of non-iterative coupled cluster quadruples models journal July 2015
Accelerating the convergence of higher-order coupled cluster methods journal November 2015
Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory journal January 2016
SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. IV. Linear-scaling second-order explicitly correlated energy with pair natural orbitals journal April 2016
SparseMaps—A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals journal May 2017
A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory journal April 2017
Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform journal June 2017
Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)] journal January 2018
Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions journal April 2019
Platinum, gold, and silver standards of intermolecular interaction energy calculations journal August 2019
Rank reduced coupled cluster theory. II. Equation-of-motion coupled-cluster singles and doubles journal October 2019
Linear scaling perturbative triples correction approximations for open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory [DLPNO-CCSD(T 0 /T)] journal January 2020
The ORCA quantum chemistry program package journal June 2020
Coupled-cluster techniques for computational chemistry: The CFOUR program package journal June 2020
P si4 1.4: Open-source software for high-throughput quantum chemistry journal May 2020
Effective basis set extrapolations for CCSDT, CCSDT(Q), and CCSDTQ correlation energies journal July 2020
Quintic-scaling rank-reduced coupled cluster theory with single and double excitations journal January 2022
Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes journal February 2022
Enthalpies of formation for Criegee intermediates: A correlation energy convergence study journal January 2023
Accurate and efficient open-source implementation of domain-based local pair natural orbital (DLPNO) coupled-cluster theory using a t1-transformed Hamiltonian journal August 2024
On the applicability of CCSD(T) for dispersion interactions in large conjugated systems journal March 2025
Linear-scaling quadruple excitations in local pair natural orbital coupled-cluster theory journal April 2025
Optimized virtual orbitals for correlated calculations: an alternative approach journal August 2005
Connected quadruple excitations in the coupled-cluster theory journal November 2010
Further benchmarks of a composite, convergent, statistically calibrated coupled-cluster-based approach for thermochemical and spectroscopic studies journal April 2012
The eight-valence-electron systems re-examined: convergence of the coupled-cluster series and performance of quasiperturbative methods for quadruple excitations journal November 2013
Accelerating the convergence of higher-order coupled-cluster methods II: coupled-cluster Λ equations and dynamic damping journal May 2020
Post-CCSD(T) corrections to bond distances and vibrational frequencies: the power of Λ journal September 2023
Note on an Approximation Treatment for Many-Electron Systems journal October 1934
Canonical Configurational Interaction Procedure journal April 1960
Localized Atomic and Molecular Orbitals journal July 1963
Coupled-cluster theory in quantum chemistry journal February 2007
Frozen Natural Orbitals: Systematic Basis Set Truncation for Coupled-Cluster Theory journal January 2005
Tensor Decompositions and Applications journal August 2009
Methylene: a turning point in the history of quantum chemistry and an enduring paradigm journal October 2025

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Related Subjects

Cluster chemistry
Electron correlation
Natural orbitals