Triple excitations in state-specific multireference coupled cluster theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

2008 ◽  
Vol 128 (12) ◽  
pp. 124104 ◽  
Author(s):  
Francesco A. Evangelista ◽  
Andrew C. Simmonett ◽  
Wesley D. Allen ◽  
Henry F. Schaefer ◽  
Jürgen Gauss
Keyword(s):  
Model Systems ◽  
Coupled Cluster ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Theory Application

Excitonic Coupled-cluster Theory: Part I, General Formalism

2017 ◽  
Author(s):  
Yuhong Liu ◽  
Anthony Dutoi
Keyword(s):  
Electron Correlation ◽  
Degrees Of Freedom ◽  
Model Systems ◽  
Coupled Cluster ◽  
Effective Hamiltonian ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
High Level ◽  
Fragment Interaction

<div> <div>A shortcoming of presently available fragment-based methods is that electron correlation (if included) is described at the level of individual electrons, resulting in many redundant evaluations of the electronic relaxations associated with any given fluctuation. A generalized variant of coupled-cluster (CC) theory is described, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction is pre-computed and permanently folded into the effective Hamiltonian. This article provides a high-level description of the CC variant, establishing some useful notation, and it demonstrates the advantage of the proposed paradigm numerically on model systems. A companion article shows that the electronic Hamiltonian of real systems may always be cast in the form demanded. This framework opens a promising path to build finely tunable systematically improvable methods to capture precise properties of systems interacting with a large number of other systems. </div> </div>

Excitonic Coupled-cluster Theory: Part I, General Formalism

2017 ◽  
Author(s):  
Yuhong Liu ◽  
Anthony Dutoi
Keyword(s):  
Electron Correlation ◽  
Degrees Of Freedom ◽  
Model Systems ◽  
Coupled Cluster ◽  
Effective Hamiltonian ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
High Level ◽  
Fragment Interaction

<div> <div>A shortcoming of presently available fragment-based methods is that electron correlation (if included) is described at the level of individual electrons, resulting in many redundant evaluations of the electronic relaxations associated with any given fluctuation. A generalized variant of coupled-cluster (CC) theory is described, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction is pre-computed and permanently folded into the effective Hamiltonian. This article provides a high-level description of the CC variant, establishing some useful notation, and it demonstrates the advantage of the proposed paradigm numerically on model systems. A companion article shows that the electronic Hamiltonian of real systems may always be cast in the form demanded. This framework opens a promising path to build finely tunable systematically improvable methods to capture precise properties of systems interacting with a large number of other systems. </div> </div>

Excitonic Coupled-cluster Theory: Part II, Electronic Hamiltonian

2017 ◽  
Author(s):  
Anthony Dutoi ◽  
Yuhong Liu
Keyword(s):  
Electron Exchange ◽  
Error Tolerance ◽  
Model Systems ◽  
Coupled Cluster ◽  
Electronic Systems ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
Complete Basis ◽  
Single Fragment

<div> <div> <div>Generic equations were presented in a companion article for a variant of coupled-cluster theory that operates directly on fragment excitation coordinates (excitonic CC), and its promise was illustrated on model systems. Three conditions were asserted for the excitonic CC framework to be valid and practicable; these concerned (1) the existence of an appropriate fragment-decomposed complete basis, (2) the existence of single-fragment fluctuation operators referencing that basis, and (3) the existence and complexity of the Hamiltonian resolved in terms of strings of those operators. In this article, we take on these assertions specificially for fragment-decomposed electronic systems, proceeding ultimately to explicit recipes for resolving the Hamiltonian in a systematically improvable manner. Though framed in the context of excitonic CC theory, the derivations here are applicable to the general inter-fragment electron-exchange problem. The number of terms in the exactly transformed Hamiltonian formally scales quartically, but this can be reduced to quadratic within an arbitrary error tolerance. The vast majority of these terms are outside of exchange range and may be decomposed efficiently in terms of single-fragment information. </div> </div> </div>

Excitonic Coupled-cluster Theory: Part II, Electronic Hamiltonian

2017 ◽  
Author(s):  
Anthony Dutoi ◽  
Yuhong Liu
Keyword(s):  
Electron Exchange ◽  
Error Tolerance ◽  
Model Systems ◽  
Coupled Cluster ◽  
Electronic Systems ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
Complete Basis ◽  
Single Fragment

<div> <div> <div>Generic equations were presented in a companion article for a variant of coupled-cluster theory that operates directly on fragment excitation coordinates (excitonic CC), and its promise was illustrated on model systems. Three conditions were asserted for the excitonic CC framework to be valid and practicable; these concerned (1) the existence of an appropriate fragment-decomposed complete basis, (2) the existence of single-fragment fluctuation operators referencing that basis, and (3) the existence and complexity of the Hamiltonian resolved in terms of strings of those operators. In this article, we take on these assertions specificially for fragment-decomposed electronic systems, proceeding ultimately to explicit recipes for resolving the Hamiltonian in a systematically improvable manner. Though framed in the context of excitonic CC theory, the derivations here are applicable to the general inter-fragment electron-exchange problem. The number of terms in the exactly transformed Hamiltonian formally scales quartically, but this can be reduced to quadratic within an arbitrary error tolerance. The vast majority of these terms are outside of exchange range and may be decomposed efficiently in terms of single-fragment information. </div> </div> </div>

Excitonic Coupled-cluster Theory: Part I, General Formalism

2017 ◽  
Author(s):  
Yuhong Liu ◽  
Anthony Dutoi
Keyword(s):  
Electron Correlation ◽  
Degrees Of Freedom ◽  
Model Systems ◽  
Coupled Cluster ◽  
Effective Hamiltonian ◽  
Coupled Cluster Theory ◽  
Cluster Theory ◽  
Companion Article ◽  
High Level ◽  
Fragment Interaction

<div> <div>A shortcoming of presently available fragment-based methods is that electron correlation (if included) is described at the level of individual electrons, resulting in many redundant evaluations of the electronic relaxations associated with any given fluctuation. A generalized variant of coupled-cluster (CC) theory is described, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction is pre-computed and permanently folded into the effective Hamiltonian. This article provides a high-level description of the CC variant, establishing some useful notation, and it demonstrates the advantage of the proposed paradigm numerically on model systems. A companion article shows that the electronic Hamiltonian of real systems may always be cast in the form demanded. This framework opens a promising path to build finely tunable systematically improvable methods to capture precise properties of systems interacting with a large number of other systems. </div> </div>

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