Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

Tsuchimochi, Takashi; Ten‐no, Seiichiro

doi:10.1063/1.4939585

Cited by 39 publications

(65 citation statements)

References 39 publications

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“…If all the EPV terms R ab ij are completely neglected, we obtain a large cancellation between the unlinked terms in Eq. (15). This is historically called CEPA(0), 29,46 and is equivalent to linearized CC theory (LCC).…”

Section: B Pair-energy and Several Approximationsmentioning

confidence: 99%

“…[17][18][19] The dynamical part of the correlation energy is then treated by either perturbation theory 12 or configuration interaction (CI). 15,16 Among these developments, it was shown that spin-extended CI with single and double substitutions (ECISD) can produce accurate results for systems where the static correlation plays an important role. The success of this method is a result of its effective MR-CI nature, which comes from the MC character of SUHF.…”

Section: Introductionmentioning

confidence: 99%

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Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Tsuchimochi

Ten‐no

2017

J. Chem. Theory Comput.

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We propose a size-consistent generalization of the recently developed spin-extended configuration interaction with singles and doubles (ECISD), where a CI wave function is explicitly spin-projected. The size-consistent effect is effectively incorporated by treating quadruples within the formulation of coupled electron pair approximation. As in coupled-cluster theory, quadruple excitations are approximated by a disconnected product of double excitations. Despite its conceptual similarity to the standard single-and multireference analogues, such a generalization requires careful derivation, as the spin-projected CI space is non-orthogonal and overcomplete. Although our methods generally yield better results than ECISD, size-consistency is only approximately retained because the action of a symmetry-projection operator is size-inconsistent. In this work, we focus on simple models where exclusion-principle-violating terms, which eliminate undesired contributions to the correlation effects, are either completely neglected or averaged. These models possess an orbital-invariant energy functional that is to be minimized by diagonalizing an energy-shifted effective Hamiltonian within the singles and doubles manifold. This allows for a straightforward generalization of the ECISD analytical gradients needed to determine molecular properties and geometric optimization. Given the multireference nature of the spin-projected Hartree-Fock method, the proposed approaches are expected to handle static correlation, unlike single-reference analogues. We critically assess the performance of our methods using dissociation curves of molecules, singlet-triplet splitting gaps, hyperfine coupling constants, and the chromium dimer. The size-consistency and size-extensivity of the methods are also discussed.

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Section: B Pair-energy and Several Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Tsuchimochi

Ten‐no

2017

J. Chem. Theory Comput.

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“…Thence, there is a big interest in combining both worlds, aiming at what is known as a black‐box description. Recently Tsuchimochi and Ten‐no have provided a very promising combination of the CI method and spin‐projection, specifically, they considered the spin projection of a singly and doubly excited UHF determinant:

∣ Ψ_{ECISD} false〉 = \overset{P}{true} (()|||, c_{0}, normalΦ false〉 + \sum_{IA} c_{I}^{A}, Φ_{I}^{A} false〉 + \underset{\begin{matrix} I < J \\ A < B \end{matrix}}{false\sum} c_{IJ}^{A B}, Φ_{I J}^{A B} false〉) .

…”

Section: Spin‐extended Configuration Interactionmentioning

confidence: 99%

The practical implementation of Löwdin's method for spin projection

Pons

2018

Int J of Quantum Chemistry

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Based on Löwdin's projector for recovering the Strue^ 2 symmetry of an Unrestricted Hartree‐Fock Slater determinant, a robust and efficient method, which simplifies the multi‐determinantal character of the original expansion, is deduced. It has a direct application as a Projection after Variation scheme, providing the exact expected values of spin‐projected operators in polynomial time. In the presented approach the (exactly) projected Hamiltonian admits a simple explicit expression when it is written in the “Corresponding Orbitals” basis. This simplicity makes possible to optimize the projected determinant, Variation after Projection, by a direct minimization of the projected energy. Recent successful results obtained from the combination of a projected symmetry broken Slater determinant and post Hartree‐Fock methods has strengthen the attention on Projective Methods. In order to achieve a simple application of the reported formalism to the Interaction Configuration method (CI), a new rotation of the CI basis has been proposed and justified.

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“…Besides our own efforts, [11][12][13] there have also been other attempts to combine SUHF with residual correlation methods. [40][41][42] In this work, we take a new approach, exploiting our recent formulation of SUHF for singlet states as a polynomial similarity transformation of particle-hole excitations out of a symmetry-adapted reference determinant. [11,13] Although some of the details of the PoST SUHF formulation are not key to this work, we need to establish that CC and SUHF can be written in a common language in order to justify modifying the CC equations based on the structure of the PoST SUHF equations.…”

Section: Projected Hartree Fockmentioning

confidence: 99%

Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory

2017

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In electronic structure theory, restricted single-reference coupled cluster (CC) captures weak correlation but fails catastrophically under strong correlation. Spinprojected unrestricted Hartree-Fock (SUHF), on the other hand, misses weak correlation but captures a large portion of strong correlation. The theoretical description of many important processes, e.g. molecular dissociation, requires a method capable of accurately capturing both weak-and strong correlation simultaneously, and would likely benefit from a combined CC-SUHF approach. Based on what we have recently learned about SUHF written as particle-hole excitations out of a symmetry-adapted reference determinant, we here propose a heuristic coupled cluster doubles model to attenuate the dominant spin collective channel of the quadratic terms in the coupled cluster equations. Proof of principle results presented here are encouraging and point to several paths forward for improving the method further.

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Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures

Cited by 39 publications

References 39 publications

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation

The practical implementation of Löwdin's method for spin projection

Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory

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