Abstract
Half-projection of a wave function built as a product of singlet-triplet mixed two-electron fragments (geminals) is explored. The condition of strong orthogonality is imposed between geminals, the initial Ansatz accommodating the unrestricted Hartree-Fock (UHF) wave function as a special case. The here explored geminal product is more general than UHF, it allowing for single covalent bond breaking in a spin pure manner. The strong correlation present in two geminals simultaneously is accompanied by spin contamination at the geminal product level. Variation after half-projection leads to an eigenvalue problem of an effective two-electron Hamiltonian, conserving the computational economy of the initial model. While the resulting expressions are shown to violate size consistency, quantification reveals a suppressed error with half-projection as compared to the full spin projected then varied scheme. Spin contamination is also found to be diminished compared to the initial, unprojected wave function.
Highlights
Describing the so-called static part of electron correlation in an efficient manner is imperative when modeling the electronic structure of inherently multireference systems
The concepts of symmetry breaking and active spaces are interrelated: ⟨Ŝ2⟩ violation at the single determinantal level leads to a pairing of orbitals, revealing two-electron building blocks behind the unrestricted Hartree−Fock (UHF) wave function.[16−19] We mention passing some pair-functionbased methodologies that step beyond the concept of exclusive active spaces for pairs.[20−22]
Though efficient new techniques for full spin projection have been worked out since,[33,52,53] the appealing feature of the HP method compared to full projection remains to be its significantly reduced spin contamination[48,49,54,55] in Received: August 28, 2019
Summary
Describing the so-called static part of electron correlation in an efficient manner is imperative when modeling the electronic structure of inherently multireference systems. In accordance with reduced spin contamination, we have successfully applied perturbation theory (PT) correction to UNO based SLG (USLG) in cases where UMP fails.[61] We have observed that USLG based PT remains prone to UMP type breakdown where substantial spin contamination persists at the SLG level This is often connected with triplet components of two or more geminals coupling to a singlet representing an important contribution to the ground state singlet wave function. In analogy with UHF based approaches, spin projected varied SLG is a possible solution Initial studies along this line have been performed,[62] revealing violation of size consistency on the example of a H8 model system.
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