chem 241 final - 1
What is molecular orbital theory?
Method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.
Why is MO theory considered closer to reality?
It is closer to reality, but it becomes quite complex with larger molecules, so computation is required and approximations are often used.
How do you judge how accurate a result from MO modeling is?
Compare the result to experimental data, then interpret.
How does valence bond theory differ from MO theory?
Valence bond theory treats bonding more as 2 atoms sharing 2 bonding electrons and is commonly used with VSEPR and hybridization. MO theory says molecular bonds can contain contributions from many atoms.
What does MO theory make us care about?
The whole molecule, not just orbitals on individual atoms.
Over how many atoms can MO bonding occur?
MO bonding can occur over more than 2 atoms.
Why are valence bond theory, VSEPR, and hybridization still the day-to-day tools?
Because MO orbitals are complex and require calculations, so valence bond theory, VSEPR, and hybridization are more practical for routine use.
When is MO theory especially required?
For π systems and transition metal systems.
When do bonding interactions occur?
When atomic orbitals overlap with the correct direction, relative energy, and number of electrons.
What determines the number of molecular orbitals formed?
The number of MOs equals the number of atomic orbitals used to construct the MOs.
How are molecular orbitals filled?
MOs are of different energy and are filled with valence electrons in the same manner as atomic orbitals.
How do we consider an MO in the simplest case?
As a linear combination of atomic orbitals.
What happens when atomic wavefunctions are in phase?
They add, which is stabilizing, and gives a bonding MO.
What is the expression for an in-phase MO combination?
ψMO = N[ψ1 + ψ2]
What kind of MO results from addition of atomic wavefunctions?
A bonding molecular orbital.
What happens when atomic wavefunctions are out of phase?
They subtract, which is destabilizing, and gives an antibonding MO.
What is the expression for an out-of-phase MO combination?
ψ*MO = N*[ψ1 − ψ2]
What kind of MO results from subtraction of atomic wavefunctions?
An antibonding molecular orbital.
What are N and N* in the MO expressions?
Normalization factors.
What does normalization mean here?
The integral of ψ² over all space equals 1.
What is the simplest MO example discussed?
H2.
How do you start drawing the MO energy level diagram for H2?
Draw the valence orbital energy levels for the bonding atoms on the left and right, here 2 H atoms.
What valence orbital does each H atom contribute in H2?
Each H has one valence electron and one valence atomic orbital, 1s.
What two molecular orbitals form when two H 1s orbitals combine?
A σ bonding MO and a σ* antibonding MO.
How does the σ bonding MO in H2 arise?
From adding the two 1s atomic orbitals in phase.
How does the σ* antibonding MO in H2 arise?
From subtracting the two 1s atomic orbitals, so they are out of phase.
Why are the electrons in the H2 MO lower in energy than the single electrons in each H atom orbital?
Because they experience attractions to both nuclei.
What does the σ symbol mean here?
It refers to a bonding MO with most electron density along the H–H axis.
What is the phase relationship in the H2 σ bonding MO?
All the same phase.
Where is the electron density concentrated in the H2 σ bonding MO?
In the space along the H–H axis, between the nuclei.
Why is the H2 σ bonding MO stabilizing?
Because constructive overlap concentrates electron density between the nuclei, giving attraction to both nuclei.
Why is antibonding destabilizing?
Because the phases do not match, so there is no bonding overlap and electron-electron repulsion destabilizes.
What is true about antibonding orbitals and phase?
They are of opposite phase.
Where is electron density found in the antibonding MO?
Outside the bonding region, not concentrated between the nuclei.
What special feature exists in an antibonding orbital?
A nodal plane.
Where is the nodal plane in the H2 σ* antibonding orbital?
Perpendicular to the H–H atom-atom axis.
How are molecular orbitals filled in general?
In order of energy, like atomic orbitals.
What is the stability idea for molecules in MO language?
Molecules with all bonding MOs filled are the equivalent of having full valence electrons and are stable.
What does the symbol g mean in MO labels?
Same.
What does the symbol u mean in MO labels?
Opposite.
Is understanding MO theory important beyond H2?
Yes, especially for transition metal chemistry.
Why is MO theory a fundamental basis of transition metal chemistry?
Because it is required to understand σ-bonding and π-back bonding in transition metal systems.
What industrial example was mentioned to show the importance of MO theory?
The Haber-Bosch process: N2 + 3H2 ⇌ 2NH3 with Fe as catalyst.
What role does Fe play in the Haber-Bosch example discussed here?
Fe is a nanoparticle catalyst.
Why is H2 bonding to Fe discussed?
Because it shows, on a molecular level, how MO theory explains activation of ligands in transition metal chemistry.
What is a ligand?
Any atom or group of atoms bonding to a metal.
What happens in H2–Fe bonding with the filled H–H σ bonding MO?
The filled H–H σ bonding MO donates σ-bonding electrons to an empty atomic orbital on Fe.
What kind of Fe orbitals can accept this donation?
An empty σ orbital on Fe, for example orbitals with the correct symmetry such as combinations involving s, px, or dx²−y² depending on the axis and metal orbital makeup.
Why is the Fe acceptor orbital sometimes described as a combination?
Because in metallic Fe the MO is likely some combination of orbitals, and computations are needed to know the proportions.
What is this donation from H2 to Fe called?
σ donation from the H–H σ bonding orbital to an empty orbital on Fe.
Why is it called σ bonding in the metal-ligand interaction?
Because it involves metal σ orbitals and occurs along the axis between the metal centre and the ligand.
What effect does σ donation from H2 to Fe have on the H–H bond?
It weakens the H–H bond by depleting electrons from the H–H bonding orbital.
What other interaction occurs between Fe and H2?
π-back bonding from filled Fe d orbitals into the H–H σ* antibonding orbital.
What specific Fe orbital was highlighted for π-back bonding in the notes?
A filled dxy orbital on Fe.
Why is it called π-back bonding in the notes?
Because the metal dxy π orbital can bond with and donate into the empty H–H σ* orbital due to its orientation above and below the Fe–H2 axis.
What effect does putting electrons into an antibonding orbital have?
It weakens the corresponding bonding interaction.
How does π-back bonding affect the H–H bond?
π-back bonding from Fe dxy to H–H σ* weakens the H–H bond.
What happens when σ donation and π-back bonding are both complete?
The H–H bond breaks.
What general point does this example show about transition metal centres?
This is how transition metal centres activate many types of ligands.
Does He2 exist according to MO theory?
No.
Why does MO theory predict He2 does not exist?
Because the σ bonding and σ* antibonding MOs are both filled, so bonding and antibonding effects cancel.
What is the bond order formula?
Bond order = (# electrons in bonding MOs − # electrons in antibonding MOs) / 2
What is the bond order of He2?
(2 − 2) / 2 = 0 for the 1s-derived interaction, so no net bond.
What is the conclusion for He2?
He2 does not exist.
Does Li2 exist according to MO theory?
Yes.
What orbitals are important for bonding in Li2?
The 2s-derived MOs.
What happens with the 1s-derived MOs in Li2?
They form filled bonding and filled antibonding orbitals, so they cancel and do not contribute net bonding.
What happens with the 2s-derived MOs in Li2?
Only the bonding 2s-derived MO is filled.
What is the net bond order of Li2?
(4 bonding electrons − 2 antibonding electrons) / 2 = 1, or considering only the net 2s contribution, a single bond.
What does MO theory predict for Li2?
Li–Li exists with a single bond.
Is this prediction correct experimentally?
Yes, but the Li–Li bond is weak.
Does Be2 exist according to MO theory as presented here?
No.
Why does MO theory predict Be2 does not exist?
All σ bonding and σ* antibonding MOs are full, so bonding and antibonding cancel.
What is the bond order of Be2?
(4 − 4) / 2 = 0
What is the conclusion for Be2?
MO theory predicts that Be2 does not exist, and that is true.
What is the simplest memory rule for bond order?
Bonding helps, antibonding hurts, divide the difference by 2.
How can you quickly remember whether a molecule exists in simple MO problems?
If bond order is greater than 0, it exists; if bond order is 0, it does not.
What is the simplest memory rule for phase?
Same phase gives overlap and stabilization; opposite phase gives a node and destabilization.
What is the simplest memory rule for σ donation and π-back bonding in H2 activation by Fe?
Donate out of H–H σ, donate into H–H σ*, and the H–H bond weakens until it breaks.