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CH164: Atoms and Molecules
Week 5 tutorial: Molecules in space, Prof. Adrian Chaplin
1. Within 100,000 years of the Big Bang, the temperature of the Universe cooled sufficiently for He2+ and He+ ions to combine with free electrons and form neutral, atomic helium. Soon after, the first molecule HeH+ was produced by combination of helium with a proton. The presence of HeH+ in interstellar space was experimentally verified in 2019. The 1s orbital energies of He and H are –24.6 and –13.6 eV, respectively.
(a) Why are electrons bound more tightly in helium?
(b) Construct and label the molecular orbital energy level diagram for HeH+
.
(c) Calculate the bond order of HeH+ and sketch the associated molecular orbitals.
(d) HeH+ is often referred to as the helium “hydride” ion. By reference to your energy level diagram, discuss if this is an accurate description.
(e) Explain why the bond in HeH+
2. The most prevalent molecular ion to be found in the interstellar medium now is H3+ , in which the hydrogen atoms form an equilateral triangle. The molecular orbital energy level diagram for this triatomic molecule can be constructed by considering the interaction between the 1s orbital of one hydrogen atom with symmetry adapted combinations (SALCs) of the 1s orbitals of the other two.
(a) Complete the diagram below, by indicating the connectivity between all the orbitals/orbital combinations and occupancy of the molecular orbitals.
(b) Assign the nature of the interactions that give rise to the molecular orbitals as either bonding, antibonding, or non-bonding (i.e. the connecting lines).
(c) Indicate which is the HOMO in H3+ and provide a sketch of this molecular orbital.
(d) A linear geometry is less stable than the triangular geometry. With reference to the HOMO, explain why ring opening of triangular H3+ to give linear H3+ is electronically unfavourable.
3. Diatomic carbon is a diamagnetic molecule that is unstable at ambient temperature and pressure but occurs in the interstellar medium. For instance, it is the origin of the green “halo” observed for some comets. The valence energies of carbon are -11.3 (2p) and -24.4 (2s) eV.
(a) Draw a Lewis structure for C2 in which the octet rule is satisfied. What is the bond order?
(b) IGNORING sp-orbital mixing in the first instance, construct a molecular orbital energy level diagram for C2 . Ensure you label the energy levels.
(c) Explain why the energy ordering of the MOs you have predicted in part (b) is inconsistent with a closed shell electronic configuration.
(d) Show how your diagram can be perturbed to incorporate sp-orbital mixing and give an electronic configuration for C2 that is consistent with experiment.
(e) Calculate the bond order of C2 using this electronic configuration and contrast it with the bond order predicted in part (a). Draw a Lewis structure which more accurately captures the nature of the bonding in C2.