View source for More about the stability of a molecule

<p>You can test directly the stability of a molecule, you just have to choose '''Job style''' --> '''Stability'''. And then test with a singulet or a triplet.<br>

'''But in this case what you are looking for is the stability of the wave function!'''<br/>

For the example of propene, we get the same, the too exist but at different energy.</p>

<pre>
For the singulet
 SCF Done:  E(UHF) =  -117.022407343     A.U. after   19 cycles
             Convg  =    0.9626D-08             -V/T =  1.9986
             S**2   =   0.1527

</pre>

<pre>
For the triplet
 SCF Done:  E(UHF) =  -116.910538298     A.U. after   15 cycles
             Convg  =    0.1887D-08             -V/T =  1.9942
             S**2   =   2.0203

</pre>

<p>So the results suggest that in term of energy the singulet is the more stable because it has got the lowest energy.
</p>

<p>But with the example of '''O<sub>2</sub>''' you get different results.<br/>


O<sub>2</sub>   HF   6-21G<br/>

Singulet
<pre>
 The wavefunction has an RHF -> UHF instability.
</pre>

Triplet
<pre>
The wavefunction is stable under the perturbations considered.
</pre>

So here the singulet state does not exist.
</p>

<p>Consider the energy of the two forms (singulet and triplet) of O<sub>2</sub>.<br/>

<pre>
For the singulet
 SCF Done:  E(RHF) =  -148.686490556     A.U. after    8 cycles
             Convg  =    0.2240D-08             -V/T =  2.0032
             S**2   =   0.0000

</pre>

<pre>
For the triplet
 SCF Done:  E(UHF) =  -148.768525186     A.U. after    9 cycles
             Convg  =    0.4772D-08             -V/T =  2.0031
             S**2   =   2.0195

</pre>

So if we just have a look at the energy we deduce that the triplet has a lower energy so it is the more stable... it is not in contradiction to our results concerning the stability of the wave function, but it is two different questions!</p>

<p>And if we consider the theory that we know about the orbital diagram of O<sub>2</sub> the filling is : <math>\sigma</math>1s<sup>2</sup> <math>\sigma</math>*1s<sup>2</sup>  <math>\sigma</math>2s<sup>2</sup> <math>\sigma</math>*2s<sup>2</sup> <math>\sigma</math>2px<sup>2</sup> <math>\pi</math>2pz<sup>2</sup> <math>\pi</math>2py<sup>2</sup> <math>\pi</math>*2pz<sup>1</sup> <math>\pi</math>*2py<sup>1</sup> <math>\sigma</math>*2px<sup>0</sup>
</p>
<p>So it is quite logical that O<sub>2</sub> is more stable as a triplet because of the repartition of the electrons.

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