How do bonding and antibonding MOs coexist in molecular systems?

[HUMERA.S]

hello..
i have checked various resources but am unable to get a clear idea of how bonding and antibonding MO exist simultaneously? [following that bonding MO results due to in phase overlapping of atomic orbitals while antibonding MO results due to out of phase overlapping]

 

[coolhand]

[following that bonding MO results due to in phase overlapping of atomic orbitals while antibonding MO results due to out of phase overlapping]

that's kind of a simplified, cookie-cutter description of what is actually going on. To really understand what's going on you need to use either the LCAO (linear combination of atomic orbitals) or the VB (valence bond) models.

From either model, you would then need to write out the respective wavefunctions for each. Here's an example of a LCAO approximation for a homonuclear system for 1st period atoms:

σ_g1s=C_g [1s^A + 1s^B], for bonding
σ_u1s^*=C_u[1s^A-1s^B] for anti
where "g" stands for gerade (bonding) and "u" stands for ungerade (antibonding)

As a side-note, you can do similar approximations for ∏-bonds as well. Also, these models can be used for systems larger than simple diatomics.

The functions for both σ_g and σ_u can be used to determine the ΔP.E. for bonding vrs antibonding electrons. Therefore, given the mathematical relationship between the two functions above, you should be able to see that the bonding electrons result in -ΔE, where as antibonding electrons result in +ΔE.

Thus, you could think of bonding and antibonding electrons in MO's as if they were in competition. As they each have an equal and opposite effect on the ΔPE, they more or less cancel each other out (as given by the Bond Order equation).