We present new analytic representations of ab initio interaction potentials for Li3, Na3, and K3. The analytic representations are based on a functional form that has the correct analytic behavior in its dependence on the nuclear coordinates, even in the vicinity of D3h conical intersections and for collinear geometries, and that reduces, when one atom is removed to infinity, to an accurate diatomic potential energy curve. We show that the new representation can be used to predict excited-state energies by analytic continuation of ground-state energies to a second Riemann sheet. We also report pseudorotation barriers, Jahn-Teller stabilization energies, and harmonic vibration frequencies.
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