Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states

Piecuch, Piotr; Kowalski, Karol; Pimienta, Ian S. O.; Fan, Peidong; Lodriguito, Maricris D.; McGuire, Michael J.; Kucharski, S.; Kuś, Tomasz; Musiał, Monika

doi:10.1007/s00214-004-0567-2

Cited by 198 publications

(264 citation statements)

References 4 publications

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“…The Cl-Cl and Cl-SiH 3 charts have a wider −16 to 16 mhartree range to accommodate larger errors. The CCL method recovers the FCI results to within less than 1 mhartree error in the region R =1-3R e for the H -SiH 3 , H-Cl, H 3 Si-SiH 3 , Cl-CH 3 , H-CH 3 , and H 3 C -SiH 3 bonds; it has slightly larger but no more than 2 mhartree errors in the R =1−3R e regions for the Cl-Cl, Cl-SiH 3 , and H 3 C-CH 3 bonds. The small absolute CCL errors quantitatively illustrate the excellent agreement between the CCL and FCI PES.…”

Section: -2mentioning

confidence: 73%

“…The second type ͑e.g., Cl-CH 3 ͒ is a bell shape, in which the CCSD error first increases with the stretching bond length and then decreases to nearly zero at 3R e . In the third type ͑e.g., H -CH 3 and H 3 C-CH 3 ͒, the CCSD error increases with the bond length and then decreases to eventually become negative before the error levels off.…”

Section: -2mentioning

confidence: 98%

“…3 The completely renormalized ͑CR͒ CCSD͑T͒ method developed by Kowalski and Piecuch 4 performs much better than CCSD͑T͒ for stretched bonds, but somewhat worse at nearequilibrium geometries. 3,4 Recently, Piecuch and co-workers developed the size-extensive "left-eigenvalue ͑L͒" CR-CCSD͑T͒ L or CR-CC͑2,3͒ method ͑hereinafter called CCL͒, which belongs to a larger CR-CC͑m , n͒ family based on the biorthogonal formulation 5 of the method of moments coupled-cluster equations 3,4 and which is expected to be as accurate as CCSD͑T͒ for near-equilibrium geometries while outperforming CR-CCSD͑T͒ in the bond-breaking region. 5 CCL is a single-reference approach whose computational costs are on the same order as those of CCSD͑T͒ calculations.…”

Section: Introductionmentioning

confidence: 99%

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Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

Gordon

Piecuch

2007

The Journal of Chemical Physics

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The recently developed [P. Piecuch and M. Wloch, J. Chem. Phys.123, 224105 (2005)] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2SiSiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R=1-3Re for all of the studied single bond-breaking reactions, whereR and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1mhartree in the region R=1-3Reof the H-SiH3, H-Cl, H3Si-SiH3, Cl-CH3, H-CH3, and H3C-SiH3bonds. The maximum errors are −2.1, 1.6, and 1.6mhartree in the R=1-3Re region of the H3C-CH3, Cl-Cl, and H3Si-Clbonds, respectively, while the discrepancy for the H2SiSiH2 double bond-breaking reaction is 6.6 (8.5)mhartree at R=2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T). Keywords Chemical bonds, Hydrogen reactions, Hydrogen bonding, Nuclear reaction models, Chemical vapor deposition Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 127 (2007) The recently developed ͓P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 ͑2005͔͒ size-extensive left eigenstate completely renormalized ͑CR͒ coupled-cluster ͑CC͒ singles ͑S͒, doubles ͑D͒, and noniterative triples ͑T͒ approach, termed CR-CC͑2,3͒ and abbreviated in this paper as CCL, is compared with the full configuration interaction ͑FCI͒ method for all possible types of single bond-breaking reactions between C, H, Si, and Cl ͑except H 2 ͒ and the H 2 Siv SiH 2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R =1-3R e for all of the studied single bond-breaking reactions, where R and R e are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R =1-3R e of the H -SiH 3 , H-Cl, H 3 Si-SiH 3 , Cl-CH 3 , H-CH 3 , and H 3 C -SiH 3 bonds. The maximum errors are −2.1, 1.6, and 1.6 mhartree in the R =1-3R e region of the H 3 C-CH 3 , Cl-Cl, and H 3 Si-Cl bonds, respectively, while the discrepancy for the H 2 Siv SiH 2 double bond-breaking reaction is 6.6 ͑8.5͒ mhartree at R =2͑3͒R e . CCL also predicts more accurate relative energies than the conventional CCSD and CCSD͑T͒ approaches, and the predecessor of CR-CC͑2,3͒ termed CR-CCSD͑T͒.

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Section: -2mentioning

confidence: 73%

Section: -2mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

Gordon

Piecuch

2007

The Journal of Chemical Physics

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“…Among the most representative examples are the CR-CC (Completely Renormalized Coupled Cluster) and CR-EOMCC (Completely Renormalized Equation of Motion Coupled Cluster) approaches [18][19][20][21][22], the active-space CC and EOMCC methods [23][24][25][26], the EA/IP-(Electron Affinity/Ionization Potential) and DEA/DIP-(Double EA/IP) EOMCC models [27], and the spin-flip CC/EOMCC formalism [28][29][30]. A different, computationally feasible approach suitable for strongly-correlated systems uses seniority-zero wavefunctions to describe the static/nondynamic part of the electron correlation en-ergy.…”

Section: Introductionmentioning

confidence: 99%

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

Boguslawski

Tecmer

2017

J. Chem. Theory Comput.

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Wavefunctions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allow us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multi-reference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori linearized coupled cluster correction on top of AP1roG against CR-CCSD(T) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the N2, C2, and BN dimers against MRCI-SD and MRCI-SD+Q reference data. Our numerical results indicate that the best performance is obtained from a linearized coupled cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG allow us to reliably model molecular systems dominated by static/nondynamic as well as dynamic electron correlation.

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“…31 The CCL method belongs to a larger CR-CC(m, n) family based on the biorthogonal formulation 29,30 of the method of moments coupled-cluster equations. [32][33][34][35] CCL has been shown to reproduce full configuration interaction (FCI) PESs with small errors for the single-bond-breaking reactions of nine closed-shell C-H-Si-Cl molecules. [29][30][31] The restricted open-shell CCL (ROCCL) method has been shown to properly break the OH and F 2 + bonds within reasonable accuracy.…”

Section: Introductionmentioning

confidence: 99%

Breaking Bonds of Open-Shell Species with the Restricted Open-Shell Size Extensive Left Eigenstate Completely Renormalized Coupled-Cluster Method

Gordon

Piecuch

et al. 2008

J. Phys. Chem. A

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The recently developed restricted open-shell, size extensive, left eigenstate, completely renormalized (CR), coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as ROCCL, is compared with the unrestricted CCSD(T) [UCCSD(T)] and multireference second-order perturbation theory (MRMP2) methods to assess the accuracy of the calculated potential energy surfaces (PESs) of eight single bond-breaking reactions of open-shell species that consist of C, H, Si, and Cl; these types of reactions are interesting because they account for part of the gas-phase chemistry in the silicon carbide chemical vapor deposition. The full configuration interaction (FCI) and multireference configuration interaction with Davidson quadruples correction [MRCI(Q)] methods are used as benchmark methods to evaluate the accuracy of the ROCCL, UCCSD(T), and MRMP2 PESs. The ROCCL PESs are found to be in reasonable agreement with the corresponding FCI or MRCI(Q) PESs in the entire region R = 1−3Re for all of the studied bond-breaking reactions. The ROCCL PESs have smaller nonparallelity error (NPE) than the UCCSD(T) ones and are comparable to those obtained with MRMP2. Both the ROCCL and UCCSD(T) PESs have significantly smaller reaction energy errors (REE) than the MRMP2 ones. Finally, an efficient strategy is proposed to estimate the ROCCL/cc-pVTZ PESs using an additivity approximation for basis set effects and correlation corrections. The recently developed restricted open-shell, size extensive, left eigenstate, completely renormalized (CR), coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as ROCCL, is compared with the unrestricted CCSD(T) [UCCSD(T)] and multireference second-order perturbation theory (MRMP2) methods to assess the accuracy of the calculated potential energy surfaces (PESs) of eight single bond-breaking reactions of open-shell species that consist of C, H, Si, and Cl; these types of reactions are interesting because they account for part of the gas-phase chemistry in the silicon carbide chemical vapor deposition. The full configuration interaction (FCI) and multireference configuration interaction with Davidson quadruples correction [MRCI(Q)] methods are used as benchmark methods to evaluate the accuracy of the ROCCL, UCCSD(T), and MRMP2 PESs. The ROCCL PESs are found to be in reasonable agreement with the corresponding FCI or MRCI(Q) PESs in the entire region R ) 1-3R e for all of the studied bond-breaking reactions. The ROCCL PESs have smaller nonparallelity error (NPE) than the UCCSD(T) ones and are comparable to those obtained with MRMP2. Both the ROCCL and UCCSD(T) PESs have significantly smaller reaction energy errors (REE) than the MRMP2 ones. Finally, an efficient strategy is proposed to estimate the ROCCL/cc-pVTZ PESs using an additivity approximation for basis set effects and correlation corrections.

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Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states

Cited by 198 publications

References 4 publications

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

Breaking Bonds of Open-Shell Species with the Restricted Open-Shell Size Extensive Left Eigenstate Completely Renormalized Coupled-Cluster Method

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