[xshadow]

Hi All!!

In general chemistry and inorganic chemistry  courses i  studied the MO-theory to understand how to mix the O.A in order to form the MO's of a molecule.

But now that i'm studying "the whole" quantomeccanic theory in Physical Chemistry i have some doubt.

For example one LCAO of HF molecule of the valence shell(using some approximation about energy and symmetry is given by mixing:

a) 1s(H)
b)2pz(F)

So when i mix  2OA i'll get 2MO.
In general chemistry i have studied that these two MO  are given by:

psi+ = 1s + 2pz
psi- = 1s- 2pz

But now studying physical chemistry i know that there is no reason to think that the coefficinets in these  two linear combinations are:

psi+ --->  c2=c1
psi-  --->  c2=-c1

In fact i have checked and the two coefficients doesn't have the same value in module (they have the same value only in the homonuclear diatomic molecules!! )

So why in general chemistry i suppose that c1=c2 (in module) for a case that  doesn't involve a    homonuclear diatomic molecule??

Is  it an approximation or what??

Thanks!!!

[Corribus]

The coefficients are only equal when the orbital energies are equal. In a molecule like HF, the electrons are attracted far more to the fluorine than the nitrogen. This is reflected in the HOMO, which has a lot more fluorine AO character than hydrogen AO character. Conversely, the LUMO, an antibonding orbital, has more hydrogen character than fluorine character. You can do some basic theoretical treatments and show that the coefficients are related to the energy differences between the two mixing AOs.

In polyatomic molecules, even when the AOs have the same energies, the coefficients are frequently not equal in magnitude, reflecting the fact that electrons naturally spend more time near certain nuclei than others. This is as much a matter of geometry as anything else.

[xshadow]

so for HF isn't correct the expressions:

psi+ = 1s + 2pz
psi- = 1s- 2pz
(used in the general  chemistry course to write then the OM DIAGRAM)

Because the orbitals involved don't have the same  energy...
right??

it would be better t9 write:

psi+ = C1*1s + C2*2pz
psi- = C1*1s- C2*2pz

where C1 is usually not the same of C2
Right??

[Corribus]

Yes. In general chemistry they just want you to know that the molecular orbital wavefunctions are additive and subtractive combinations of the atomic orbital wavefunctions.

[xshadow]

Yes. In general chemistry they just want you to know that the molecular orbital wavefunctions are additive and subtractive combinations of the atomic orbital wavefunctions.

thanks

[Corribus]

Note that even in the event of equal contributions of both orbitals, the coefficients aren't equal to 1 because the wavefunction must be normalized.

ΣC_n² = 1

Therefore, for equal sharing C₁ = C₂ = 1/SQRT(2)

In the event that one of the atoms is so electronegative that there is no sharing at all (ionic limit), then the coefficients would be 0 and 1 - the bonding electrons both are completely in the atomic orbital of the electronegative atom. Of course, this model completely neglects the fact that the presence of multiple electrons in the vicinity of each other changes the nature of the atomic orbitals being used to make the molecular orbitals. This is a fundamental limitation of the LCAO approximation. But in many cases it works pretty well, at least for qualitative descriptions of what is going on.

[xshadow]

Well!!

thanks very much