Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom

Abstract

Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed region the corresponding $N$-fermion quantum state has a significantly simpler structure. We recall the recently proposed natural extension of the Hartree-Fock ansatz based on this structural simplification. This variational ansatz is tested for the lithium atom. Intriguingly, the underlying mathematical structure yields universal geometrical bounds on the correlation energy reconstructed by this ansatz.

arXiv commentContribution to the special issue dedicated to professor Michael Springborg on the occasion of his 60th birthday, 7 pages

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• Relating correlation measures: the importance of the energy gap
• Experimental Data from a Quantum Computer Verifies the Generalized Pauli Exclusion Principle
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• On the time evolution of fermionic occupation numbers
• Static correlated functionals for reduced density matrix functional theory
• Quantum marginals from pure doubly excited states
• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study
• A toolbox of spin-adapted generalized Pauli constraints