Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems

Tribedi, Soumi; Chakraborty, Anish; Maitra, Rahul

doi:10.1021/acs.jctc.0c00736

Cited by 13 publications

(4 citation statements)

References 73 publications

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“…Szakács and Surján 5,6 , for the first time, demonstrated that the CC iteration scheme under an input perturbation shows chaotic dynamics. Some of the present authors had shown that the dynamics associated with a double similarity transformed CC [7][8][9] iterations follows the universality of time-discrete map of one-parameter family. The authors analysed the phase space trajectory under an input perturbation and demonstrated a full period-doubling bifurcation cascade that precedes the onset of the chaos.…”

Section: Introductionmentioning

confidence: 57%

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

Agarawal,

Patra,

Maitra

2021

Preprint

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The coupled cluster iteration scheme is analysed as a multivariate discrete-time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the entire set of the cluster amplitudes. These driver amplitudes enslave all other amplitudes through a synergistic inter-relationship, where the latter class of amplitudes behave as the auxiliary variables. The driver and the auxiliary variables exhibit vastly different time scales of relaxation during the iteration process to reach the fixed points. The fast varying auxiliary amplitudes are small in magnitude, while the driver amplitudes are large, and they have a much longer time scale of relaxation. Exploiting their difference in relaxation time-scale, we employ an adiabatic decoupling approximation, where each of the fast relaxing auxiliary modes are expressed as unique functional of the principal amplitudes. This results in a tremendous reduction in the independent degrees of freedom. On the other hand, only the driver amplitudes are determined accurately via exact coupled cluster equations. We will demonstrate that the iteration scheme has an order of magnitude reduction in computational scaling than the conventional scheme. With a few pilot numerical examples, we would demonstrate that this scheme can achieve very high accuracy with significant savings in computational time.

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Section: Introductionmentioning

confidence: 57%

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

Agarawal,

Patra,

Maitra

2021

Preprint

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“…We refer to eq as the Flexible Ansatz for the N -body Configuration Interaction (FANCI). As demonstrated elsewhere, this formulation includes not only conventional CI − and coupled cluster − (CC) approaches, but also matrix-product states, − tensor network states, − and a wide variety of wave functions based on composite bosons and composite fermions, including many flavors of geminals. − …”

Section: Introductionmentioning

confidence: 99%

Flexible Ansatz for N-Body Perturbation Theory

Miranda-Quintana,

Kim,

Lokhande

et al. 2024

J. Phys. Chem. A

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We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrodinger equation for arbitrary wave functions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are wellbehaved across a wide range of conditions, including static correlationdominated configurations and highly nonlinear wave functions.

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“…3 For weakly correlated systems where a single-reference (SR) wave function provides a good starting point, CC yields remarkably accurate results even with only single and double excitations (CCSD). Improved by approximate inclusion of triple excitations (such as CCSD[T], 4 CCSD(T) 5 or iCCSDn 6 ), this method can give results with chemical accuracy (∼1 kcal mol −1 error), motivating efforts toward numerical realization for systems of impressive size. 7,8 Deficiencies of the single determinantal reference may induce a breakdown of SR-based CC when when applied to strongly correlated systems (e.g., molecules with dissociating covalent bonds).…”

Section: Introductionmentioning

confidence: 99%

Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster

Margócsy

Szabados

2021

J. Chem. Theory Comput.

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A new scheme is introduced in Multi-Reference (MR) Coupled Cluster (CC) based on the MR Generalized Normal Ordering (MRGNO) and the corresponding MR Generalized Wick Theorem (MRGWT) of Kutzelnigg and Mukherjee. The key element is the identification of a structure in MRGWT generated terms, facilitated by Goldstone diagram techniques. This allows for bundling the many terms of the MRGWT expansion and introduces a hierarchy in the equations that can be harnessed in devising approximations. One-and two-particle interaction vertices are found to be uniformly substituted for their counterpart dressed by density cumulants. This allows for a straightforward rewriting of the ordinary energy expression of CC with interaction dressed (id) one-and two-particle terms and reveals the presence of threeand higher-rank dressed interaction vertices too. Cumulants appearing out of dressed interaction vertices contribute to the amplitude equations and can be interpreted to have an amplitude dressing role. Dressing of one-and two-particle interaction vertices is the most straightforward to implement and does not hinder computational feasibility, provided that the reference function involves strictly limited active space sizes. The Generalized Valence Bond wave function, underlying pilot numerical tests, fulfills this criterion. Results on multiple bond breaking scenarios point to the need of stepping beyond one-and two-particle id. An extremely simple version of incorporating amplitude dressing in addition to one-and two-particle id is seen to cure the potential energy curves remarkably, stimulating further investigations along this line.

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Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems

Cited by 13 publications

References 73 publications

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

Flexible Ansatz for N-Body Perturbation Theory

Dressing of Vertices by Cumulants in Multi-Reference Coupled Cluster

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