Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations

Qiu, Yunhai; Henderson, Thomas M.; Scuseria, Gustavo E.

doi:10.1063/1.4963082

Cited by 31 publications

(44 citation statements)

References 27 publications

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“…The particlehole form of singlet spin-projected UHF has also been recognized for quite some time, [18] though only recently has it been realized that the SUHF wave function can be written as a polynomial of single and double excitation operators. [17,20] This work shows that the singlet SGHF also has such a polynomial form, though now we need not only single excitation operators (T 1 ) and double excitation operators (C 2 ) to define the polynomial, we must also include triple (C 3 ) and quadruple excitation operators (K 4 ), but apparently no further. These higher excitations appear only once the Thouless transformation from RHF to symmetry-broken Hartree-Fock has more than one mode (i.e.…”

Section: Discussionmentioning

confidence: 94%

“…N = 30), though we cannot guarantee that they are correct for still higher excitation levels. It is important to note that where SUHF contains only single and double excitations and powers of them [17,18,20], SGHF additionally has triple and quadruple excitations which arise from the additional S z projections and which may have significant energetic consequences (see below). Table I provides numerical values for the coefficients λ ijk through octuple excitations, to give an idea of how rapidly the coefficients decay, and compares to the analogous coefficients in coupled cluster theory.…”

Section: The Sghf Wave Functionmentioning

confidence: 99%

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Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Henderson

Scuseria

2017

Phys. Rev. A

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The past several years have seen renewed interest in the use of symmetry-projected HartreeFock for the description of strong correlations. Unfortunately, these symmetry-projected mean-field methods do not adequately account for dynamic correlation. Presumably, this shortcoming could be addressed if one could combine symmetry-projected Hartree-Fock with a many-body method such as coupled cluster theory, but this is by no means straightforward because the two techniques are formulated in very different ways. However, we have recently shown that the singlet S 2 -projected unrestricted Hartree-Fock wave function can in fact be written in a coupled cluster-like wave function: that is, the spin-projected unrestricted Hartree-Fock wave function can be written as a polynomial of a double-excitation operator acting on some closed-shell reference determinant. Here, we extend this result and show that the spin-projected generalized Hartree-Fock wave function (which has both S 2 and Sz projection) is likewise a polynomial of low-order excitation operators acting on a closed-shell determinant, and provide a closed-form expression for the resulting polynomial coefficients. The spin projection of the generalized Hartree-Fock wave function introduces connected triple and quadruple excitations which are absent when spin-projecting an unrestricted Hartree-Fock determinant. We include a few preliminary applications of the combination of this spin-projected Hartree-Fock and coupled cluster theory to the Hubbard Hamiltonian, and comment on generalizations of the methodology. Results here are not for production level, but a similarity-transformed theory that combines the two offers the promise of being accurate for both weak and strong correlation, and may offer significant improvements in the intermediate correlation regime where neither projected Hartree-Fock nor coupled cluster is particularly accurate.

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Section: Discussionmentioning

confidence: 94%

Section: The Sghf Wave Functionmentioning

confidence: 99%

Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Henderson

Scuseria

2017

Phys. Rev. A

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“…E i a is an excitation which leaves both S and M S unchanged, while S i a is an excitation that leaves M S unchanged but increases S by 1 [25,35]. Combining these two excitations in the exponential ansatz [Eq.…”

Section: Theory a Symmetry-adapted Formalismsmentioning

confidence: 99%

“…In selecting particular terms corresponding to the target quantum numbers from the exponential, the projection operator creates a new polynomial, F , in which highorder particle-hole excitations are expressed in terms of products of lower-order ones by some non-exponential formula. We have found in previous works that projecting out spin symmetry in this way leads to a hyperbolic sine function [35], and that projecting out number symmetry for the reduced BCS Hamiltonian results in a modified Bessel function of the first kind [23]. Attempts to model these functions with an exponential ansatz will fail and this is at the root of why single-reference restricted coupled cluster is unstable under strong correlation.…”

Section: Theory a Symmetry-adapted Formalismsmentioning

confidence: 99%

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Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

2017

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The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected meanfield wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

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Employing broken symmetry effects from unrestricted coupled cluster wave function to determine dynamic and non‐dynamic electron correlation during triple bond breaking in the N₂ molecule

Toboła

2018

Int J of Quantum Chemistry

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The cluster structure of the singlet full symmetric component of the unrestricted Hartree‐Fock (UHF)‐based CCSD wave function describing the triple bond breaking in the nitrogen molecule has been subjected to a detailed analysis for the possibility of determining the dynamic and near‐degeneracy electron correlation. The results obtained show that the spin and symmetry contaminations are not responsible only for the appearance of the artificial hump in the potential energy curve (PEC) generated by the UHF‐based CCSD calculations. A theoretical analysis of this issue indicates that the UHF‐based CCSD wave function and its singlet full symmetric component have a multi‐reference structure. This form of the wave function allows to explain the mechanism for creating cluster contributions in the projected UHF‐based CCSD wave function, which also provides the opportunity to explain the cause of the hump in the nitrogen PEC generated by the UCCSDecCCSD method.

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Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations

Abstract: Articles you may be interested inProjected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

Cited by 31 publications

References 27 publications

Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Employing broken symmetry effects from unrestricted coupled cluster wave function to determine dynamic and non‐dynamic electron correlation during triple bond breaking in the N₂ molecule

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Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations

Abstract: Articles you may be interested inProjected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

Cited by 31 publications

References 27 publications

Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Employing broken symmetry effects from unrestricted coupled cluster wave function to determine dynamic and non‐dynamic electron correlation during triple bond breaking in the N2 molecule

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Employing broken symmetry effects from unrestricted coupled cluster wave function to determine dynamic and non‐dynamic electron correlation during triple bond breaking in the N₂ molecule