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12 Nov 2019

(a) Draw an MO energy-level diagram for the MOs that would arisein a diatomic molecule from the combination of unhybridized dorbitals. Label the AOs being combined and the resulting MOs. Letthe z-axis lie along the σ bond.
(b) Sketch the shape of each of these orbitals.

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Collen Von
Collen VonLv2
30 Jun 2019

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Related questions

1. In this problem, you will construct molecular orbitals for the triatomic molecule H3 in the isosceles triangular geometry. The molecular orbitals will be constructed from a linear combinations of the 1s atomic orbitals:

Ψ(r) = c11sA(r) + c21sB (r) + c31sC (r)

The nuclei are labeled A, B, and C.

a) How many MOs will be formed?
b) Draw the MO energy levels ( straight lines corresponding to the energy levels, not the full MO diagram) and sketches of the corresponding MOs. Make sure your MO sketches agree with the molecular symmetry.
c) Now assume that the two longer bonds further increase in length, and the other bond de- creases in length. Describe how the changes in bond lengths will change the energy of each of your MOs.
d) Label the molecular orbitals ψ1, ψ2, ...ψn. Draw the corresponding stick diagram showing the occupancy of the molecular orbitals with arrows.
e) Write the three-electron independent particle wave function Ψ(r1, r2, r3, σ1, σ2, σ3) for the H3 molecule in the ground state in the form of a Slater determinant in terms of the MOs ψn and the electron spin wavefunctions α and β (recall that σn are spin variables). You do not have to expand the determinant.

Linear H4 is a hypothetical molecule used to illustrate concepts in Group Theory. Take a linear combination of the outermost H atoms and do the same for the inner H atoms to generate the associated group orbitals.

Construct a MO diagram by properly combining the two sets of group orbitals you generated. Sketch the molecular orbitals generated from these four 1s orbitals using signs to indicate their respective phasing (+ - + -). Properly label the symmetry of each MO in the diagram. Taking into account only the number of nodes, place these MOs in order of increasing energy.

Describe the bonding that occurs in this hypothetical molecule once the electrons are placed into the MO diagram.

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