Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study

Abstract

Most {\em ab initio} calculations on fullerene molecules have been carried out based on the paradigm of the Hückel model. This is consistent with the restricted nature of the independent-particle model underlying such calculations, even in single-reference-based correlated approaches. On the other hand, previous works on some of these molecules using model Hamiltonians have clearly indicated the importance of short-range inter-atomic spin-spin correlations. In this work, we consider {\em ab initio} non-collinear Hartree--Fock (HF) solutions for representative fullerene systems: the bowl, cage, ring, and pentagon isomers of C${}_{20}$, and the larger C${}_{30}$, C${}_{36}$, C${}_{60}$, C${}_{70}$, and C${}_{84}$ fullerene cages. In all cases but the ring we find that the HF minimum corresponds to a truly non-collinear solution with a torsional spin density wave. Optimized geometries at the generalized HF (GHF) level lead to fully symmetric structures, even in those cases where Jahn-Teller distortions have been previously considered. The nature of the GHF solutions is consistent with the $\pi$-electron space becoming polyradical in nature: each $p$-orbital remains effectively singly occupied. The spin frustration, induced by the pentagon rings in an otherwise anti-ferromagnetic background, is minimized at the HF level by aligning the spins in non-collinear arrangements. The long-range magnetic ordering observed is reminiscent of the character of broken symmetry HF solutions in polyacene systems.

arXiv comment16 figures

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• Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C${}_{36}$ Fullerene and an Iron Porphyrin Model Complex
• Zero-temperature magnetic response of small fullerene molecules at the classical and full quantum limit
• Challenges for variational reduced-density-matrix theory with three-particle N-representability conditions
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• Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• Ground state magnetic response of two coupled dodecahedra
• Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach
• Exploring Spin Symmetry-Breaking Effects for Static Field Ionization of Atoms: Is There an Analog to the Coulson-Fischer Point in Bond Dissociation?
• $\mathbf{\Delta }$S${}^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C${}_{60}$: Origin and the role of symmetry
• Influence of the biquadratic exchange interaction in the classical ground state magnetic response of the antiferromagnetic icosahedron
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