Subject: Re: CCL:sp^2 hybridization

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Mon, 13 Nov 2000 11:09:07 +0100

Eric Scerri:

> When we teach hybridization at an elementary level we say that sp^2
> hybridization involves the mixing of three pure atomic orbitals, s, py and pz.
> 
> However the formal expressions for the linear combinations of orbitals show an
> asymmetry in that one of the hybrid orbitals consists of contributions from s
> and Py only while the other two hybrid orbitals are genuine mixtures of all
> three pure A.O.
> 
> My question is whether it is possible to define the hybrid orbitals so that
> all three are guninely mixtures of the three pure A.O. and if so why is this
> not generally carried out?

Dear Eric Scerri,

I am not quite sure that I understand your problem.

Of course, the three sp2 hybrids are entirely equivalent, and a trigonal orbital
directed in the direction of 'a' has a normalized wavefunction

         1/2        1/2
S  = (1/3)  s + (2/3)  p
 a                      a

The three hybrids are frequently constructed from p orbitals directed along the 
two in-plane cartesian axes z and y. The orientation of the axes z and y is 
arbitrary. If you choose a = z, then you obtain the expressions 

         1/2        1/2
S  = (1/3)  s + (2/3)  p
 a                      z            

         1/2        1/2          1/2
S  = (1/3)  s - (1/6)  p  + (1/2)   p
 b                      z            y

         1/2        1/2          1/2
S  = (1/3)  s - (1/6)  p  - (1/2)   p
 c                      z            y 

These seem to be the simplest expressions in terms of cartesian p orbitals (and 
the three hybrids are of course still exactly equivalent). If you choose to 
orient the axes z and y such that they do not coincide with any of the trigonal 
axes a, b, and c, then you get three slightly more complicated expressions that 
each involve contributions from both p orbitals. Is this what you would prefer?

Yours, Jens >--<
                             
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JENS SPANGET-LARSEN         Phone:  +45 4674 2000  (RUC)
Department of Chemistry             +45 4674 2710  (direct)
Roskilde University (RUC)   Fax:    +45 4674 3011 
P.O.Box 260                 E-Mail: [email-masked]
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