Quantum Mechanics of a Simulated Tri-hydrogen Dication

The Schroedinger equation is solved exactly within the Born-Oppenheimer approximation for a simulacrum of the $H_3^{++}$-ion. The ion is assumed to form an isosceles triangle and the ground state energy is obtained over its geometrical parameter space. No multi-center molecular integrations are required. We indicate how the approximation to the actual molecule can be improved systematically.