Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD

Hollett, Joshua W.; Loos, Pierre‐François

doi:10.1063/1.5140669

Cited by 21 publications

(22 citation statements)

References 87 publications

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“…The latter in particular affords many useful characterization including its relationship to eigenvalues of the 2-RDM itself and to long-range order [95], its relationship to Von-Neumann entropy [96] and its relationship to various orders of cluster amplitudes for a Couple-Cluster (CC) based wavefunction ansatz [97]. It has been successfully used to probe electronic correlation in various problems [98][99][100] and very recently in capturing signatures of Van der Waals interaction [101].…”

Section: Discussionmentioning

confidence: 99%

Geometrical picture of the electron-electron correlation at the large-D limit

Ghosh,

Kais,

Herschbach

2021

Preprint

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In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electronelectron correlations and might give a bound on the correlation energy. The results at the large-D limit and at D= 3 indicate the feasibility of using the geometrical picture to get a bound on the electron-electron correlations.

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Section: Discussionmentioning

confidence: 99%

Geometrical picture of the electron-electron correlation at the large-D limit

Ghosh,

Kais,

Herschbach

2021

Preprint

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“…However, quantum chemists already have a multiplication to count this: the normal ordered product of particle-conserving operators. This is the fundamental reason why the normal ordered product must be used rather than the operator product in equations ( 10) and (11).…”

Section: Probabilistic Cumulantsmentioning

confidence: 99%

“…Another obvious difference between the generating functions for the additively separable probabilistic (2) and fermionic (11) quantities is that the probabilistic multiplicatively separable generating function (1) uses an exponential that has no counterpart in the "generating function" for the fermionic multiplicatively separable quantity, (8). This is due to fermionic antisymmetry eliminating a technicality in the probabilistic cumulants.…”

Section: Probabilistic Cumulantsmentioning

confidence: 99%

“…This is one of the primary reasons why cumulants are either parameterized or varied directly in many RDM-based theories. [6][7][8][9][10][11] In GNO, second quantized operators are decomposed into linear combinations of operators "normal ordered" with respect to an arbitrary reference, Ψ, via the Generalized Wick's Theorem. This theorem gives the expansion coefficients of the linear combination in terms of contractions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

Misiewicz

Turney

Schaefer

2020

J. Chem. Theory Comput.

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Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering, but the underlying formalism has remained mysterious. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical to equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and reduced density matrices are entirely combinatorial constructions, where the differences can be associated to changes in the notion of "multiplicative separability" for expectation values of random variables compared to reduced density matrices.We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present the simplest proof to date of the Generalized Normal Ordering formalism to explore the role of reduced density matrix cumulants therein.

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“…See DOI: 10.1039/cXCP00000x/ Systems presenting dynamic and nondynamic correlation have become one of the greatest challenges in modern electronic structure methods. The ability to simultaneously tackle both types of correlation is present in very few electronic structure methods, such as the complete active space with second-order perturbation theory (CASPT2), 35,36 multireference configuration interactions (MRCI) 37,38 or, most recently, the adiabatic-connection MCSCF (AC-MCSCF) 39 , ∆NO, 40 and GNOF. 41 Nevertheless, these methods are far from exact and their computational cost represents a big drawback.…”

Section: Introductionmentioning

confidence: 99%

Range separation of the Coulomb hole

Via-Nadal,

Rodríguez-Mayorga,

Ramos-Cordoba

et al. 2022

Preprint

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A range-separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations (h c I ) and the other at short distances (h c II ), is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that h c I , which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how h c I can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how h c II helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold the promise to aid in developing new electronic structure methods that efficiently capture electron correlation.of electron correlation per se goes hand in hand with developing efficient electronic structure methods. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Many types of electron correlation exist, nondynamic (or static) 2,23,24 and dynamic 2,24 being the most regularly used because electronic structure methods are usually classified according to their ability to retrieve them. Dynamic correlation is universally present in systems with at least two electrons, as it describes the motion of charged particles avoiding each other due to the electronic repulsion. Hence, this type of correlation increases with the number of electrons. A reference singledeterminant picture along with a large number of low-contributing configurations is usually sufficient to portray this contribution. It is thus natural that the electron density displays very small differences with respect to the reference HF density. 14,15,22 Due to its nature, dynamic correlation affects electrons that are close to each other (short-ranged), but it is also responsible for long-range dispersion forces. 25 Configuration interactions or coupled cluster with single and double excitations (CISD or CCSD), 26,27 Møller-Plesset second-order perturbation theory (MP2) 28 and density functional approximations (DFAs) 6,29 are methods that retrieve a large amount of dynamic correlation. On the other hand, nondynamic correlation is not universal and emerges in the presence of partiallyoccupied (near-)degenerate orbitals. It is characteristic of bond stretching, polyradical structures, entanglement, and high symmetries. The correct description of nondynamic correlation requires a wavefunction that mixes other largely-contributing configurations besides the ...

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Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD

Cited by 21 publications

References 87 publications

Geometrical picture of the electron-electron correlation at the large-D limit

Geometrical picture of the electron-electron correlation at the large-D limit

Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

Range separation of the Coulomb hole

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