CHpt 8 html



		Chapter VIII. MO's of Small Building Blocks

		In the following we will first derive the MOs of AH, pyramidal along with planar AH₃, and tetrahedral AH₄ based upon the appropriate orbital interaction diagrams. What we are doing is building up a library of MOs for any organic molecule. For each pattern we will use a generic A atom which has s and p AOs and an electronegativity about the same as hydrogen (case B in the previous material). A. The AH System Here is the orbital interaction diagram when the electronega- tivity of HA.

		The mixing coefficients can be evaluated as -



			From a VB - bond orbital approach one can derive them as follows (work out the simplifications for the bond orbitals yourself)-


			Here are the MOs for HC and HF note the electronegativity differences



		B. The C_3v AH₃ System The MOs for this geometry can be constructed as follows (again the electronegativity of HA):




	C. D_3h AH₃ We have gone through this before-



		Let us now construct and analyze a Walsh diagram for AH₃ pyramidalization (going from D_3h to C_3v)



		So for a molecule with 6 valence electrons, BH₃, CH₃+, AlH₃, etc. a D_3h geometry is preferred, whereas, with 8 electrons (NH₃, PH₃, etc.) a C_3v geometry is expected. Notice that with 10 electrons (e.g. BrF₃) a D_3h structure is predicted to be stable.



	For the 8 electron case at D_3h we have a classic second order Jahn-Teller problem. That e⁽²⁾ correction is given by:



And we can easily find G_Q= a₂" a₁' = a₂"



It is that 2a₁' mixing into a₂" that sets the H-A-H angle and the inversion barrier



		Here is some hard data that indeed is consistent with this model.

H₃A Me₃A F₃A

A H-A-H DE_inv^a C-A-C F-A-F

N 106.7° 5.7 110.9° 102.4°

P 95.3° 34.7 98.8° 97.2°

As 94.5° 39.7 96.2° 95.5°

Sb 93.8° 44.9 94.2° 94.3°

Bi 92.5° 60.5 97.1° 94.8°

^aC_3v to D_3h inversion barriers in kcal/mol.

And for the following 7 electron AH₃ compounds:

A H-A-H DE_inv^a

C 120.0° 0.0

Si 112.7° 3.7

Ge 112.4° 3.8

Sn 110.6° 7.0

^aC_3v to D_3h inversion barriers in kcal/mol.



	D. Substituent Effects A very important concept in this course is that the MOs for the AH_n series that we have been developing can be used for a much, much larger set of molecules. The hydrogens with their s AOs are topologically identical to a p AO used to bond to A in a sigma fashion or an sp³ hybrid from some R group. So the 2a₁ MO for C_3v AH₃ has the same shape as the HOMO in NF₃ or N(CH₃)₃:



	There are, however, two factors which can modify the AH_n "picture" that we have developed. 1) electronegativity effects, e.g. NH₃ NF₃

	So what does this tell us about the F-A-F bond angle compared to H-A-H and the inversion barrier?

	2) p - bonding - this again can be added to the basic electronic structure. There are two situations possible. i) p-acceptor groups.



	E. AH₄molecules 1. The tetrahedral (T_d) geometry:


	An alternative representation of these MOs are also commonly used:



		A Walsh diagram for distortion to a D4h geometry is as follows:

		Notice that CH₄²⁺ and CH₄^2- (or more likely SH₄ or SF₄) are stable at D_4h, whereas, of course CH₄ is stable at T_d. There is an avoided crossing at work here:



		F. AH_n Generalizations There are some patterns here in the shape of the MOs:



		For AH_n, there are always n A-H bonding and antibonding MOs. Left behind are 4-n nonbonding ones localized on the central atom, pointing away from the hydrogen atoms. This can be formalized as:


		To build a stable molecule one should always fill the bonding MOs as well as the nonbonding ones (provided that they are not at a very high energy. Therefore one has 2 x (n + 4 - n) = 8 electrons. This is a very obscure way to "prove" the Lewis octet rule, but it has a direct bearing on material in the next Chapter. There is an experimental way to look at this series via PE spectroscopy:



		Why does the H_ii values not show stabilization for the s AO in all of the examples? Why is the b₁ MO not totally nonbonding??