[TheWhiteSpark]

Hey everyone,

I'm hoping this is a fairly simple question, but i'm confused about the molecular orbits for butadiene ( and other 4 orbital molecules).

I looked online, and it seems that it has four different orbitals, all closed down, up up down down, up down down up, and up down up down.

Haha, i hope that makes sense.

Why aren't there up down down down, and down down down up? I thought there would be and then you would add together and cancel out the two outer pi clouds or something, i dunno. What am i missing?

[phth]

What type of a mathematical function describes an orbital?

[TheWhiteSpark]

Umm, I have no idea. Are you asking about the wave-like behavior of electrons?

[Rutherford]

Because the Π-Π and the Π*-Π* MO of the double bonds can combine only in these four ways:


(To get the orbital you proposed, you need to combine Π and Π* which don't have the right symmetry and energy difference to do so)

[Corribus]

@OP

To answer this appropriately, you have to understand standing waves, which is the classical analog of the wave function. If you had an MO that was up-down-down-down, destructive interference would destroy the wavefunction. To see this in a practical sense, tie a string to a wall and try to access the various harmonics by moving the string up and down.  Where are the nodes? And do you notice that the string oscillates around those nodes? You can't have a single node 3/4 of the way down the string and still get a standing wavefunction. Destructive interference would destroy the wave. Molecular wavefunctions behave essentially the same way.

[TheWhiteSpark]

Awesome, thank you all for the great responses, i think i understand the standing wave and interference issue. Can someone explain what this means then though, obviously a different molecule than butadiene.

Edit for clarity: the bottom chalkboard has some sort of adding thing and it forms the 1 node orbital for that molecule. What is happening?

[Corribus]

Here you have a single node which is located on the central carbon nucleus. Compare this to butadiene, in which case the nodes are always between nuclei. This is just due to the even/odd effect. (Like, if you have 4 apples, you can evenly divide them between two people, but if you have 3 apples, one has to be split in half.)

Remember, at this point you don't' really have atomic orbitals any more - they are only drawn for demonstration. What you really have are molecular orbitals that span the entire molecule.

[Irlanur]

There COULD BE something like up-down-down-down.  Why? the "Basis" u choose are the four pi-orbitals (of course there are others, but the pi orbitals can often tell you something). if you don't want to calculate anything, you can do a lot of qualitative understanding with so-called "symmetry adapted MO's". these are the ones you are normally talking about. BUT (now it gets technical) the fock operator is invariant under unitary transformations. This basically means that the Energy doesn't change if you recombine the orbitals. Since in Calculations the only thing you actually care about are the Energy or its derivatives, one just takes the mathematically most easy ones, which are the symmetry adapted ones.

Bottom line: there could be an MO up-down-down-down. but it's inconvenient. so choose a symmetry adapted Basis.

PS: symmetry adapted: all MO's are either symmetric or antisymmetric with respect to any symmetry operation of the point group of the molecule.