The ions H₂⁺ and H₃ᵗ have been observed in gas discharges.

a. H₂⁺ has been reported to have a bond distance of 106 pm and a bond dissociate enthalpy of 255 kJ/mol. Comparable values for the neutral molecule are 74.2 pm and 436 kJ/mol. Are these values for H₂⁺ in agreement with the molecular orbital picture of this ion? Explain.
b. Assuming H₃ᵗ to be triangular (the probable geometry), describe the molecular orbitals of this ion and determine the expected H-H bond order.