[Meter]

For the image above, does σ2p_z simply denote the p-orbital that is involved in the formation of the σ-bond, and does  the placement of p_x, p_y and p_z in the orbital matter as long as all three are included, or will  p_x, p_y always be involved in π-bonding and p_z in σ-bonding?

Also, I've seen MO diagrams where the placement of the bonding and anti-bonding orbitals alternates between bonding/anti-bonding, whereas here it doesn't. What is the most correct way to do it?

I understand how to draw an MO, but this notation confuses me a little.

Thanks.

[Orcio_87]

For the image above, does σ2pz simply denote the p-orbital that is involved in the formation of the σ-bond

Yes, it is σ bonding orbital created by overlap of two p_z atomic orbitals.

and does  the placement of px, py and pz in the orbital matter as long as all three are included, or will  px, py always be involved in π-bonding and pz in σ-bonding?

Default orientation assume that atoms lies on YZ plane with Z as principal axis.

Different orientation of atoms will change character of molecular orbitals (σ can be π and vice versa).

Also, I've seen MO diagrams where the placement of the bonding and anti-bonding orbitals alternates between bonding/anti-bonding, whereas here it doesn't.

Are you blind ? Anti-bonding orbitals are marked with upper * sign.

[Meter]

For the image above, does σ2pz simply denote the p-orbital that is involved in the formation of the σ-bond

Yes, it is σ bonding orbital created by overlap of two p_z atomic orbitals.

and does  the placement of px, py and pz in the orbital matter as long as all three are included, or will  px, py always be involved in π-bonding and pz in σ-bonding?

Default orientation assume that atoms lies on YZ plane with Z as principal axis.

Different orientation of atoms will change character of molecular orbitals (σ can be π and vice versa).

Also, I've seen MO diagrams where the placement of the bonding and anti-bonding orbitals alternates between bonding/anti-bonding, whereas here it doesn't.

Are you blind ? Anti-bonding orbitals are marked with upper * sign.

I meant like this:

[Babcock_Hall]

I am not sure that I understand the question.  The σ_u* orbital is below the π_g orbital in the diagram, but I just assumed that this was done strictly on the basis of which is lower in energy.

[Corribus]

The reason is because any atomic orbitals and molecular orbitals with appropriate symmetry can interact with each other, and the strength of the interactions between orbitals depends on their respective energy separations. Those various energy gaps change as a function of the nuclear core charges and electron configurations. I.e., orbital interactions are complex, even for diatomics. The end result is that there comes a point going down the series X₂ where the ordering of the 2p pi and sigma bonding orbitals flip (the 2pi bonding orbitals are lower in energy than the 2sigma bonding orbitals). See the diagram at this link, under the section "Quantum patterns". Of those with a "flipped" configuration, dinitrogen is really the only one with practical relevance.

EDIT: Basically, the atomic s orbitals don't just interact with atomic s orbitals, even though we erroneously draw MO diagrams that way in introductory chemistry. Atomic s orbitals also have the appropriate symmetry to interact with atomic p_z orbitals if they are aligned appropriately, which they are in a diatomics. Sometimes those interactions are strong, sometimes not, depending on the mutual energies of the s and p orbitals. And those energies change quite a bit as the nuclear core charges change going across the periodic table. The bonding sigma orbital energies are very sensitive to this, as you can see in the diagram linked to above.

[Meter]

Excellent insight, Corribus.

My takeaway from that is I probably shouldn't worry about it right now (on my 2nd semester).

Thanks for the help to all of you. It cleared some things up.

[Corribus]

My recollection is that at general chemistry level you just need to know (1) that those two bonding orbitals (2sigma and 2pi) flip in ordering going across the homonuclear series, with lighter elements being inverted and (2) that nitrogen is the last "inverted" one. If you remember this, you can accurately predict various properties of the homonuclear diatomics (bond order, stability, paramagnetism, etc.). The quantum mechanical reason behind it all is interesting, but not really important until you're in physical chemistry.

[Meter]

My recollection is that at general chemistry level you just need to know (1) that those two bonding orbitals (2sigma and 2pi) flip in ordering going across the homonuclear series, with lighter elements being inverted and (2) that nitrogen is the last "inverted" one. If you remember this, you can accurately predict various properties of the homonuclear diatomics (bond order, stability, paramagnetism, etc.). The quantum mechanical reason behind it all is interesting, but not really important until you're in physical chemistry.

As far as I know, that is not on this year's curriculum. I will, however, begin quantum chemistry already next year, so I'm sure I'll have to take these things into consideration in due time.

For now, it seems that the purpose of these exercises (other than learning the basics of MO diagrams) is to utilize the Aufbau principle, Madelung's ordering rules and Hund's rule on something other than the electron configuration of elements. Furthermore, also realizing why molecular bonding is favorable at all (sort of).