Symmetry-Adapted Perturbation with Half-Projection for Spin Unrestricted Geminals

Mihálka, Zs. É.; Śurján, Péter R.; Szabados, Ágnes

doi:10.1021/acs.jctc.1c00305

Cited by 4 publications

(2 citation statements)

References 113 publications

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“…They reported improvement of the unrestricted geminals through the spin-projection technique. [39][40][41][42] We verified the extension of geminals in terms of spin functions in this study. Besides the ⟨Sz⟩ = 0 type triplet two-electron functions mixed, e.g., in the USSG, general triplet functions, ⟨Sz⟩ = 0 and also ±1 types, could be included in geminals.…”

Section: Communicationsupporting

confidence: 72%

A geminal theory based on the generalized electron pairing

Nakatani

Sato

2023

J. Chem. Phys.

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As in the hierarchy of the Hartree-Fock theory in terms of spin symmetry, the extension of spin functions in a theory of two-electron units or geminal, was developed in this study. A trial wave function is constructed as an antisymmetrized product of geminals, in which singlet and triplet two-electron functions are fully mixed. We present a variational optimization method for this generalized pairing wave function in the strong orthogonality condition. The present method is considered an extension of the antisymmetrized product of strongly orthogonal geminals or perfect pairing generalized valence bond methods, maintaining the compactness of the trial wave function. The obtained brokensymmetry solutions were similar to the unrestricted Hartree-Fock wave functions in terms of spin contamination while giving lower energy due to the inclusion of the electron correlation effect in geminals. The degeneracy of the obtained broken-symmetry solutions in the Sz space is reported for the tested four-electron systems.

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Section: Communicationsupporting

confidence: 72%

A geminal theory based on the generalized electron pairing

Nakatani

Sato

2023

J. Chem. Phys.

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“…This is the case of the half-projected strongly localized geminals (HPSLG) [51], applied to H 4 , diradicals, and benzynes, confirming the spin properties already mentioned of the HPHF wave function. To obtain more correlation energy, the HPSLG method has been extended to perturbation theory [52] and tested in the case of singlet-triplet gaps of biradicaloids, leading to very promising results. The HPHF method has been also extended in the variant of semiempirical methods [35,53] and was used to calculate biradical species.…”

Section: A Historical Review Of the Hphf Methodsmentioning

confidence: 99%

Half‐Projected Hartree–Fock method: History and application to excited states of the same symmetry as the ground state

Ruiz

2022

Int J of Quantum Chemistry

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Spin projected wave functions are generalizations of the Hartree-Fock wave function. Among them, the Half-Projected Hartree-Fock (HPHF) wave function is a nearly pure wave function of spin and recovers a small part of the spin correlation energy. This paper reviews the history of the HPHF theory, not only from the conceptual point of view but also providing a compilation of the publications of this method over the years until now. In addition, the extension of the HPHF method to the calculation of excited states with the same symmetry as the ground state will be discussed. The possible variational collapse during the calculation of a singlet excited state of the same symmetry as the ground state is avoided by orthogonalizing a pair of corresponding orbitals, one occupied and one virtual orbital, at every step of the variational process. As an example, the potential energy surfaces of the S0 ground and 1S1(n, π*) first excited state of the formic acid HCOOH are calculated.

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Pivot invariance of multiconfiguration perturbation theory via frame vectors

Szabados

Margócsy

Śurján

2022

The Journal of Chemical Physics

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Multiconfiguration perturbation theory (MCPT) is a general framework for correcting a reference function of arbitrary structure. Variants of MCPT introduced so far differ in the specification of the zero-order Hamiltonian, i.e. the partitioning. A common characteristic of MCPT variants is that no numerical procedure is invoked when handling the overlap of the reference function and determinants spanning the configuration space. This comes at the price of pinpointing a principal term in the determinantal expansion of reference, rendering the PT results dependent on this choice.It is here shown, that pivot dependence of MCPT can be eliminated by using the overcomplete set of projected determinants in the space orthogonal and complementary to the reference. Projected determinants form a so-called frame, a generalization of the notion of basis, allowing for redundancy of the set. Simple structure of the frame overlap matrix facilitates overlap treatment in closed form, a feature shared by previous MCPT variants. In particular, Moore-Penrose inverse of singular matrices appearing in frame-based MCPT can be constructed without the need of any pivoting algorithm or numerical zero threshold.Pilot numerical studies are performed for the singlet-triplet gap of biradicaloid systems, relying on geminal based, incomplete model space reference function. Comparison with previous MCPT variants as well as illustration of pivot invariance is provided.

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Symmetry-Adapted Perturbation with Half-Projection for Spin Unrestricted Geminals

Cited by 4 publications

References 113 publications

A geminal theory based on the generalized electron pairing

A geminal theory based on the generalized electron pairing

Half‐Projected Hartree–Fock method: History and application to excited states of the same symmetry as the ground state

Pivot invariance of multiconfiguration perturbation theory via frame vectors

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