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

@article{Qiu2016CommunicationPH, title={Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations}, author={Yiheng Qiu and Thomas M. Henderson and Gustavo E. Scuseria}, journal={Journal of Chemical Physics}, year={2016}, volume={145}, pages={111102} }

Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion…

## 23 Citations

Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

- Physics
- 2017

Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster theory, in contrast, does…

Spin polynomial similarity transformation for repulsive Hamiltonians: interpolating between coupled cluster and spin-projected unrestricted Hartree-Fock.

- Physics, MedicinePhysical chemistry chemical physics : PCCP
- 2017

This manuscript adapts earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial similarity transformation (SpinPoST) interpolation, which parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansätze self consistently and is a spin-symmetry adapted model which involves only single and double excitations.

Projected coupled cluster theory.

- Physics, MedicineThe Journal of chemical physics
- 2017

This work combines and tries to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions by providing a solution via a disentanglement framework theory that can be approximated rigorously and systematically.

Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations.

- Computer Science, MedicineThe Journal of chemical physics
- 2019

A new, polynomial product wavefunction ansatz is introduced that incorporates information from symmetry projection into standard coupled-cluster theory in a way that attempts to mitigate the effects of the lack of size extensivity and size consistency characteristic of symmetry-projected methods.

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

- Physics, Chemistry
- 2017

ABSTRACT In electronic structure theory, restricted single-reference coupled cluster (CC) captures weak correlation but fails catastrophically under strong correlation. Spin-projected unrestricted…

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian.

- Physics, MedicineThe Journal of chemical physics
- 2017

It is shown how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram.

Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems.

- Medicine, Computer ScienceThe Journal of chemical physics
- 2018

This study takes a minimalist approach and truncate the Taylor series of the exponential ansatz at a certain order such that the approximation safely recovers the traditional CC without spin-projection, and shows that the approach is rigorously orbital-invariant and provides more accurate results than its configuration interaction and linearized CC analogues for chemical systems.

Half-projection of the strongly orthogonal unrestricted geminals' product wavefunction.

- Medicine, PhysicsJournal of chemical theory and computation
- 2019

Half-projection of a wavefunction built as a product of singlet-triplet mixed two-electron fragments (geminals) is explored, allowing for single covalent bond breaking in a spin pure manner.

Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms.

- Physics, MedicineThe Journal of chemical physics
- 2019

The proposed unitary CC formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS and can be extended to any type of CAS representing an arbitrary energy window of a quantum system.

Influence of broken-pair excitations on the exact pair wavefunction

- Physics
- 2017

ABSTRACT Doubly occupied configuration interaction (DOCI), the exact diagonalisation of the Hamiltonian in the paired (seniority zero) sector of the Hilbert space, is a combinatorial cost wave…

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