Mod:CO2 MO explanation
This page is an explanation/deeper analysis of the MOs of CO2, which will be useful for students in the IMM2 lab. Don't worry if you don't understand everything in here yet - you may not have covered all the required lectures yet. In marking the lab we do not assume you are able to do anwhere near this level of detail!
The calculated MOs
I have optimised CO2 with Guassian using the following input line: (Should be roughly equivalent to the method from the IMM2 lab.) # opt freq b3lyp/3-21g pop=(nbo,full)
Here are the MOs as viewed in Gaussview with an isovalue of 0.02:
Assigning the AO contributions
By simply inspecting the MOs most AOs contributions can be easily assigned, however in some cases it is difficult to tell exactly what is going on. This figure shows sketches of the AOs contributing to the MOs, with two options and a question mark where it is hard to tell what is contributing:
Buliding an MO diagram
To build up the MO diagram for CO2 we first need the MO diagram for the fragment O-.-O (CO2 without the C.):
Now we put the C in the middle of the 2 Os and interact the C AOs with any fragment orbitals (FOs) which have the same symmetry, and are closest in energy. From this MO diagram we can see that the best assigments of the "tricky" MOs above are the first of the two options suggested.
A note on nomenclature: typically when we say an MO is bonding, we mean the interaction between the two fragments in the final MO diagram is bonding. (Even if the interactions within the fragments are anti-bonding!) For example we would say MO9 is bonding, because the C-O interactions are bonding. Likewise we say MO10 is non-bonding overall, however we could also say it is anti-bonding with respect to the O atoms.
Mixing
However it is not completely as simple as the MO diagram shows. By looking in the .log file of the calculation and doing some simple processing in excel we can see some significant mixing between MO4 and MO6, and also between MO5 and MO9:
This explains why some of our MOs look like a cross between different AO assignments - because they are! The yellow contributions in MOs 14 and 18 are likely due to mixing with some of the higher MOs.