Question

3. The trihydrogen cation, H3, has been experimentally observed, but its geometry is the subject of some controversy. The two most commonly proposed structures are linear or cyclic, as shown in the figure here: a. Construct an MO diagram for linear H3. Use the D2h point group to identify the symmetry of each atomic orbital, group orbital, and molecular orbital. Include a sketch of each MO in your diagram. b. Construct a modified MO diagram for cyclic H3t. Use the D3h point group to determine the symmetry of the three MOs for cyclic H3 (Note: Here our process for determining group orbital symmetry can be used to determine the symmetry of each MO). Order these MOs from low to high energy, and include a sketch of each MO. c. Compare your two MO diagrams. Which structure do you think most closely matches the true geometry of H3*? Explain your choice.

Answer 1

a) Construct mo diagram of Hat (linear) a) Linear structure - H o me HT=15° (3 cent te ze) Hals' Bonding -> [mid H] [Group Orbitala same phase) of Hydrogen 2000 MOMO E 15o anomag I BMO homo ①0 . н н н Central ht atom - H Group Orbitals of Hydrogen HGH 2 Center, Lelectron Only group Orbitals and central atown orbitals cuith the same symetry and similar Energy will start interact g orbitals interact while u orbitals in non bonding

(b) Construct MO diagram of cyclie Hay h found by J. J Thomsan (1911) Dah l E 26, 362 On 25; 30w H À This 3 o 13o1 aiii !! i ! E' 12-10 2 - 0 IH, Reduces Alte' 3 Mck) to i h .I AM O IL BMO BMD of to's fill Hat has ae (Bonding to de regio totally degenerate symmetric set of Combination Mo's formed from Combi- -nation of His Ad's y we can determine exactly how the As's should be combined to form the di proof to free and E Mo's using the projection operator Method. The Result of that Process I do ta (Ha that He ) - 0 t Malesa ta (2HA - He-He) - © The last e combination can be determi- - ned from the fact that each orbital most contribut equally across all set Also since First EMO contain I node 2/3 34€) = Ya CHo-HC ) QMA gives; A X most

Only the because lowest Mo Matters, Only that mo is occupied in Hat so the triangular version in achich pled mo es louler in energy is better. CU 7 o'o linear closely structure is most matches the toue geomety 3/3