Draw the lewis structure for XeF4 and describe its structure using VSEPR (why it has a D4h symmetry)

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a) Draw the lewis structure for XeF4 and describe its structure using VSEPR (why it has a D4h symmetry)

b) The XeF4 molecular orbital diagram is shown below, where there are four valence atomic orbitals for all the atoms but the F 2s orbitals do not take part in bonding

i) Why are there 20 molecular orbitals?

ii) How many bonding molecular orbitals are there? How many antibonding? How many non bonding?

iii) Which orbital is the HOMO and what is its bonding nature and character? (i.e. sigma-bonding, pi-antibonding, nonbonding, mostly Xe or O, etc?)

iv) which orbital is the LUMO? Bonding nature and character?

v) how many non-bonding electron pairs are there? on which atoms? How does this compare with the lewis structure?

vi) Qualitatively sketch one 2eu and the 2a2u orbital.

The Correct Answer and Explanation is :

a) Lewis Structure for XeF4

Lewis Structure:

  1. Valence Electrons:
  • Xenon (Xe) is in group 18 and has 8 valence electrons.
  • Fluorine (F) is in group 17 and each fluorine atom has 7 valence electrons. With four fluorine atoms, the total is (4 \times 7 = 28) valence electrons.
  • Total valence electrons: (8 + 28 = 36) valence electrons.
  1. Bonding:
    Xenon will form bonds with the four fluorine atoms, using 8 electrons (two electrons per bond). Each fluorine atom will also have three lone pairs to complete its octet.
  2. Lone Pairs on Xenon:
    After forming four bonds with fluorine atoms, xenon will have (36 – 8 = 28) electrons left, which will be placed as lone pairs. Xenon can accommodate more than 8 electrons in its valence shell due to its position in period 5, where it has d-orbitals available. This leaves Xenon with two lone pairs. Thus, the Lewis structure of XeF4 is:
        F
        |
   F - Xe - F
        |
        F

Lone Pairs on Xenon:
Xenon has two lone pairs positioned opposite each other in the structure, and the fluorine atoms are bonded to xenon.

VSEPR Structure and Symmetry of XeF4

  • The electron pair geometry of XeF4 is octahedral, as there are 6 regions of electron density (4 bonding pairs and 2 lone pairs).
  • The molecular geometry, however, is square planar. This is because the lone pairs on xenon will occupy positions opposite each other, forcing the four fluorine atoms to occupy the equatorial positions in a square shape, while the lone pairs are in the axial positions.
  • D4h symmetry arises because of this square planar arrangement and the specific symmetry of the electron pairs. The lone pairs occupy positions that maintain a high degree of symmetry, leading to the D4h point group (which corresponds to a square planar structure with an axis of symmetry).

b) Molecular Orbital Diagram for XeF4

  1. Why are there 20 molecular orbitals? The XeF4 molecule involves bonding between one xenon atom and four fluorine atoms. The total number of molecular orbitals is calculated by adding up the number of atomic orbitals involved in the bonding process. Xenon provides 4 valence orbitals (due to its position in the periodic table), and each fluorine atom contributes 4 valence orbitals. This gives:
    [
    4 \text{ (from Xe)} + 4 \times 4 \text{ (from F)} = 20 \text{ molecular orbitals}.
    ]
  1. How many bonding, antibonding, and nonbonding molecular orbitals are there? The 20 molecular orbitals can be divided as follows:
  • Bonding orbitals: These are lower energy orbitals that result from constructive interference between atomic orbitals. Typically, the bonding orbitals are filled first.
  • Antibonding orbitals: These arise from destructive interference between atomic orbitals, and these orbitals are higher in energy than the bonding orbitals.
  • Nonbonding orbitals: These are orbitals that do not participate in bonding but are still part of the molecule’s overall orbital set. Generally, in a molecular orbital diagram:
  • There will be a combination of bonding and antibonding orbitals.
  • Bonding orbitals: 10
  • Antibonding orbitals: 10
  • Nonbonding orbitals: Typically, the nonbonding orbitals are degenerate and may be the result of lone pairs or the participation of atomic orbitals that do not contribute to bonding.
  1. Which orbital is the Highest Occupied Molecular Orbital (HOMO), and what is its bonding nature and character? The HOMO is the highest energy orbital that still contains electrons. It is usually an antibonding molecular orbital with the highest energy. For XeF4, the HOMO is likely to be a 2a2u orbital or similar orbital from the fluorine atoms, which can be a pi-antibonding orbital. It involves a combination of fluorine 2p orbitals, which are largely fluorine in character but with some contribution from xenon.
  1. Which orbital is the Lowest Unoccupied Molecular Orbital (LUMO)? The LUMO is the lowest energy orbital that is unoccupied by electrons. For XeF4, the LUMO is likely to be a sigma-antibonding orbital or similar, originating from xenon’s 5p orbitals, which interact with the fluorine orbitals.
  1. How many non-bonding electron pairs are there, and on which atoms? How does this compare with the Lewis structure? In XeF4, the xenon atom will have two non-bonding electron pairs (lone pairs). These lone pairs are non-bonding because they do not contribute to the bonding between xenon and fluorine. This is consistent with the Lewis structure, where xenon has two lone pairs. The fluorine atoms will not have any non-bonding pairs in the molecular orbital diagram because all their electrons are involved in bonding.
  1. Qualitatively sketch one 2eu and one 2a2u orbital.
  • 2eu orbital: This is a pair of degenerate orbitals that are typically formed from combinations of atomic orbitals with symmetry corresponding to the (e) irreducible representation in the D4h point group. They typically involve p-orbitals.
  • 2a2u orbital: This orbital arises from combinations of orbitals with symmetry corresponding to the (a_2u) irreducible representation. It is typically a combination of p-orbitals with antibonding character.

Here are the sketches for the orbitals:

  • 2eu orbital: The lobes would have a shape that reflects symmetry around the square plane, with two lobes pointing in opposite directions, forming a typical (p)-orbital shape.
  • 2a2u orbital: The shape of the orbital would be a more complex combination of the xenon and fluorine orbitals, with antibonding characteristics.

These are qualitative shapes, as exact details depend on the detailed molecular orbital theory calculations.

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