[tom.snelling.90]

This slide on Benzene shows 6 different contributions of atomic orbitals to the molecular orbitals. Please could somebody explain why only 4 of the 6 2pz atomic orbitals contribute to the pi molecular orbitals for 2 of the contributions and why there is a total of 6 different contributions?

Thanks

[Corribus]

There are six total molecular orbitals because there are six atomic orbitals that combine to make them.

Note that there are only four energy states. This means that two pairs of orbitals have the same energy (we call these orbitals degenerate). For either of the pairs, the two orbitals have the same energy but are simply oriented in perpendicular directions. There is some freedom into how we define these directions because (due to symmetry) the energy of the orbitals doesn't change depending on what direction their facing with respect to the molecule. You asked why two of the orbitals don't appear to have anything situated on two carbons. This indicates that there is a node that runs through the two orbitals in this configuration. This is more convention than anything else. In the other orbital in each pair, there is also a node, but it bisects two carbons rather than runs through them.

[tom.snelling.90]

There are six total molecular orbitals because there are six atomic orbitals that combine to make them.

Note that there are only four energy states. This means that two pairs of orbitals have the same energy (we call these orbitals degenerate). For either of the pairs, the two orbitals have the same energy but are simply oriented in perpendicular directions. There is some freedom into how we define these directions because (due to symmetry) the energy of the orbitals doesn't change depending on what direction their facing with respect to the molecule. You asked why two of the orbitals don't appear to have anything situated on two carbons. This indicates that there is a node that runs through the two orbitals in this configuration. This is more convention than anything else. In the other orbital in each pair, there is also a node, but it bisects two carbons rather than runs through them.

Thank you for your in-depth reply. Different textbooks seem to illustrate the positions of the positive and negative lobes with respect to each other differently. For example, this image compared to the one in my previous post.



This doesn't matter because energy of the orbitals doesn't change depending on what direction their facing as long as the number of nodal planes and bonding, anti-bonding interactions is correct. Is that correct? Personally I struggle to visualise where the nodal planes are in each configuration.

With respect to not showing the two orbitals in the configuration because of the node which runs through them - Is that what it looks like?



Thanks

[Corribus]

This doesn't matter because energy of the orbitals doesn't change depending on what direction their facing as long as the number of nodal planes and bonding, anti-bonding interactions is correct. Is that correct? Personally I struggle to visualise where the nodal planes are in each configuration.

First of all, it is typically the energies that are used to compute the orbital coefficients, not the other way around. Also note that these are only diagrams to help illustrate the relative contributions of atomic orbitals to the molecular orbitals. I wouldn't get too caught up in the way they are actually drawn. Be aware that there aren't actually p atomic orbitals on the carbon atoms any more, even though they are drawn as such here. In reality, they are blended together to form molecular orbitals that span the entire molecule.

A node will occur any time there is a flip in the polarity (sign) of the contributing atomic orbitals.

With respect to not showing the two orbitals in the configuration because of the node which runs through them - Is that what it looks like?

I'm afraid I don't understand the question, or what you're attempting to draw.

[tom.snelling.90]

This doesn't matter because energy of the orbitals doesn't change depending on what direction their facing as long as the number of nodal planes and bonding, anti-bonding interactions is correct. Is that correct? Personally I struggle to visualise where the nodal planes are in each configuration.

First of all, it is typically the energies that are used to compute the orbital coefficients, not the other way around. Also note that these are only diagrams to help illustrate the relative contributions of atomic orbitals to the molecular orbitals. I wouldn't get too caught up in the way they are actually drawn. Be aware that there aren't actually p atomic orbitals on the carbon atoms any more, even though they are drawn as such here. In reality, they are blended together to form molecular orbitals that span the entire molecule.

A node will occur any time there is a flip in the polarity (sign) of the contributing atomic orbitals.

With respect to not showing the two orbitals in the configuration because of the node which runs through them - Is that what it looks like?

I'm afraid I don't understand the question, or what you're attempting to draw.

Thank you. I understand now. The drawing attempt I agree was poor - It was showing the plane as a vertical line through carbon 1 and carbon 4.