MadSci Network: Chemistry


Date: Tue Mar 1 02:58:05 2011
Posted By: Ed Stammel, Faculty, Computer, SUNY Delhi
Area of science: Chemistry
ID: 1298814951.Ch

First let me start by stating that I have not taught quantum mechanics in 
a very long time and I ask that any readers carefully analyze my 
statements in light of more current research.

Part of the problem comes from the way we are being taught bonding. If we 
think in terms of "electron dot" models of bonding, we are able to put 
the "dots" wherever we wish. We might try to arrange them in a triangle 
with double bonds between each atom and the extra electrons distributed 
around the oxygens. We are further taught to follow the electron pair 
repulsion concept where all of the pairs repel each other. It would end up 
looking kind of like an equilateral triangle with 3 double bonds. In this 
model each atom would have access to 12 electrons. This violates the 
octete rule.

By playing around with various combinations of single and double bonds we 
can come up with a logical, though incorrect, solution.We can create a 
structure with some double and some single bonds. We then say that this 
structure "resonates". That is the locations of the single and double 
bonds change, through time, always giving each atom access to eight 
electrons. Seems like a good idea but unfortunately in the early part of 
the twentieth century our model of the atom changed dramatically.

Enter quantum mechanics. The electrons are not, as we might think, able to 
go wherever we wish them. They are strictly bound by rules generated by 
energy, relativistic wave properties, charge, and mass. It comes out that 
electrons must "occupy" distinct regions around the atom. In the lowest 
possible energy state oxygen atom's outer electrons are in the 2s2 2p4 
configuration. This state gives us the classic bent molecule of H20 with 
single bonds between oxygen and hydrogen. This, however, is not the case 
with ozone.

By allowing the one s electron to gain a bit of energy and 2 p electrons 
to lose a bit, there appears a new "hybrid" sp2 structure. Although the 
nature of the bonds is beyond an elementary discussion, let it be said 
that the sp2 hybrid orbitals line in a flat plane separated by an angle of 
120 degrees and that the remaining electrons float in orbitals above and 
below that plane. Drawing this structure requires a good artist since it 
must be three dimensional. But let me try to describe it.

Each oxygen lies in a flat plane ... let us say the x-z plane for the sake 
of discussion. There exists a bonding orbital between each atom, referred 
to as a sigma bond, occupied by 2 electrons each. Above and below this 
plane is a "y shaped" cloud of electrons referred to as the PI cloud for 
each atom. These interact to form one complete "y shaped" cloud with some 
extra PI ears at each atom. The sigma bonds contain 1 electron from each 
atom. Each atom also has 2 unbonded s orbitals containing 2 electrons 
each. Therefore each atom has 5 s electrons. The remaining electron 
resides in the PI cloud. The PI cloud, therefore, has 3 total electrons. 
The electrons arrange themselves in the cloud in such a manner that the PI 
clouds are equal.

A discerning reader might think that the clouds are unsymmetrical because 
at any one moment one cloud must have 1 and the other 2 electrons. This is 
the wonder and mystery of quantum mechanics. In fact each cloud has "sort 
of" 1 1/2 electrons. Since you can't split an electron, I leave it to the 
reader to discover how this occurs.

E Stammel
SUNY Delhi

PS: I will post an image on my website at

[Admin Note: Image is also included below. - RJS]

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