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Abstract
Hund’s term rules are only valid for isolated atoms, but have no generalization for molecules or clusters of several atoms. We present a benchmark calculation of Al2 and Al3, for which we find the high and low-spin ground states 3Πu and , respectively. We show that the relative stabilities of all the molecular terms of Al2 and Al3 can be described by simple rules pertaining to bonding structures and symmetries, which serve as guiding principles to determine ground state terms of arbitrary multi-atom clusters.
Highlights
Hund’s term rules are only valid for isolated atoms, but have no generalization for molecules or clusters of several atoms
We show that the relative stabilities of all the molecular terms of Al2 and Al3 can be described by simple rules pertaining to bonding structures and symmetries, which serve as guiding principles to determine ground state terms of arbitrary multi-atom clusters
Because the Coulomb correlation effects are similar for all terms, Coulomb correlation does not alter the relative stability of them, and the discussion above of term stability based on Fermi correlations and wavefunction nodal structure is sufficient
Summary
Hund’s term rules are only valid for isolated atoms, but have no generalization for molecules or clusters of several atoms. The highest spin multiplicity (Hund’s first) rule does not follow any of the potential energy components Ven, Vee, and Vnn, the Ξ terms, when observed for spin-triplet and spin-singlet states individually, exhibit the following trends Inclusion of Coulomb correlation via CAS-SCF un-stabilizes the spin-quadruplet terms despite their possession of two electrons in 3pσ type orbitals (a1 and b2 for 4A2 and two a1s for 4B1) on the Al3 molecular plane.
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