One of the most powerful attractions of quantum chemical calculations over experiments is their ability to deal with any molecular system, stable or unstable, real or imaginary. Take as an example the legendary (but imaginary) kryptonite molecule. Its very name gives us a formula, KrO²₂ −, and the fact that this species is iso-electronic with the known linear molecule, KrF₂, suggests that it too should be linear.

a. Build KrF₂ as a linear molecule (F―Kr―F), optimize its geometry using the HF/6-31G* model, and calculate vibrational frequencies. Is the calculated Kr―F bond distance close to the experimental value (1.89 Å)? Does the molecule prefer to be linear or does it want to bend? Explain how you reached this conclusion.

b. Build KrO²₂ − as a linear molecule (or as a bent molecule if the preceding analysis has shown that KrF₂ is not linear), optimize its structure using the HF/6-31G* model, and calculate vibrational frequencies. What is the structure of KrO²₂−?