The Stability of Carbonium Ions

Organic chemists are taught that carbonium ion stability is predominantly due to electronic factors such as whether they are primary, secondary, tertiary, allylic, benzylic etc. What is mentioned much less is that their relative stability is also very sensitive to their geometries, and in particular the angles of the three substituents at the carbon. We will use a technique known as Molecular Mechanics to predict the relative stabilities of the species shown below.

The only surprising result is that the MM method predicts that the tertiary carbonium ion is actually LESS stable than the preceeding primary ion, which is surprising to say the least. Clearly, electronic factors must be playing an important role as well. Suffice to say that even without ANY consideration of electronic factors, the MM2 method does not do too badly in its prediction of relative stabilities of this set of carbonium ions. This re-inforces the conclusion that bond angles in carbonium ions are just as important as substitution! Take a look for example at the angle contribution to the MM energies, which varies most. Also included are the semii-empirial (PM3) energies, which take into account lots of other factors, including effects such as hyper-conjugation, and p conjugation. In this particular system, the differences in these effects are only secondary in controlling the stability. 


stretch         =    0.868        angle           =   19.173
stretch bend    =   -0.672        dihedral        =    6.497
improp torsion  =    0.155        van der Waals   =    2.663
electrostatics  =   -1.341        hydrogen bond   =    0.000
The energy of the final structure is 27.342 kcal/mol. 
(Final QM heat of formation = 249.11 Kcal/mol) 

stretch         =    0.447        angle           =   18.758
stretch bend    =   -0.078        dihedral        =    6.916
improp torsion  =    1.124        van der Waals   =    1.622
electrostatics  =    0.000        hydrogen bond   =    0.000
The energy of the final structure is 28.788 kcal/mol. 
(Final QM heat of formation = 232.62 Kcal/mol)   

stretch         =    0.571        angle           =    5.694
stretch bend    =   -0.027        dihedral        =    7.179
improp torsion  =    0.009        van der Waals   =    5.678
electrostatics  =   -0.545        hydrogen bond   =    0.000
The energy of the final structure is 18.559 kcal/mol. 
(Final QM heat of formation = 211.67 Kcal/mol)   

stretch         =    0.512        angle           =    3.439
stretch bend    =   -0.153        dihedral        =    6.662
improp torsion  =    0.002        van der Waals   =    3.872
electrostatics  =    0.683        hydrogen bond   =    0.000
The energy of the final structure is 15.017 kcal/mol. 
(Final QM heat of formation = 195.79 Kcal/mol)