[samuel]

Hello from Barcelona,

I've found an interesting result (at least interesting for me ) calculating the energy of different carbocations with gamess. The basis is STO-3G
NOTE: I'm just a 4th year chemistry student and I've not so much experience with computational chemistry.

The results are:
Comparing the satability of the following serie of carbocations
H₂C(CH₃)⁺ ; H₂C(CH₂CH₃)⁺;H₂C(CH₂CH₂CH₃)⁺ ; H₂C(CH₂C₂CH₂CH₃)⁺ etc

So here the parameter is the length of the chain. What I was expecting was that stability increases while the length of the chain increases. And, in fact, that's true, but my surprise comes from that I've found a linear correlation between them showed in the figure.

My questions are:

1.- I thought that the correlation would be similar to a function like y=1/(chain length) so that the energy difference between H₂C(CH₃)⁺    H₂C(CH₂CH₃)⁺ would be higher than the difference between (for example) H₂C(CH₂CH₂CH₂CH₂CH₃) ⁺  H₂C(CH₂CH₂CH₂CH₂CH₂CH₃) ⁺. But according to the linear correlation, that wouldn't be true. Who's wrong, Me or the computer?¿  (I think that there is an effect of electronic density donation by the carbon chain to the carbocation, but I don't think that this effect has a linear relation with the length of the chain).

2.- The value of energy that the program gives (in Hartrees), which reference do they have? (which is the "zero" energy reference for that value?).

I hope that the discussion will be interesting,

Samuel Núñez

[Corribus]

Just curious, what if you normalize the energy value for chain length?  (That is, divide each value by the value of n.)

[Babcock_Hall]

I know just enough about this branch of chemistry to be dangerous, but I would question the correctness of comparing the energies of chemical species with different numbers of atoms.

[opsomath]

If you want to do this properly, you should take the energy difference between the parent alkane and the carbocation and plot that vs. chain length.

What you are basically doing here is showing that energy of formation increases with the size of the molecule, which is a given.

[samuel]

Firts answering to Corribus:
I've done that "normalization". The results are showed in the first picture. It shows that the energy of formation/number of carbons keeps constant which agree whith the "non-normalized" plot. In fact, I don't see which new information brings .

About your interesting comments "Babcock_Hall" and "opsomath" :

I see your point, and I understand that is the correct way to understand the tendency of carbocations stability. My surprise comes again when I calculated the ∆E between carbocation and alcane (the second picture). It is more or less constant without a clear tend. What can explain that?

Thanks for all your interesting comments.

[opsomath]

Means that the length of chain isn't a big factor in the energy difference, which is what I would have predicted so it makes sense

I also think that your n=4 result is some kind of a mistake. A Hartree is about 600 kcal/mol, so you're saying that the n=4 carbocation is about 400 kcal/mol more stable than the n=3 one. People with experience using these units are already laughing now.

To give you an idea of what I mean, let's calculate the ratio of equilibrium constants in those two at 300 K;

ΔG = RT ln K so ΔΔG = RT (ln K1- ln K2) = RT ln K1/K2)

K1/K2 = e^(ΔΔG/RT) = e^(400 kcal/mol / (2x10^-3 kcal/mol-K * 300 K) )  = e^666 (Eee! Devil number!)

In other words, this would imply that there's such a big difference between those two cations that we need an inconceivably large number to even describe it. That, obviously, isn't true. So you probably messed up your calculation somewhere.

[samuel]

Jajajaja ok I will review the number (I probably made a mistake while selecting gabedit options). I'm not sure about if the devil number it's defined in an exponential jajaja (Just bad luck :-) ).

I see the meanig of the values with your explanations. Thank's again

[Babcock_Hall]

Another exercise that may help is to calculate the energies of isomeric carbocations, such as a primary, secondary, and tertiary butyl carbocation.  That controls for the number of atoms and the result is well known in advance.  The energy differences might be helpful as well.

[samuel]

Yes the results are as all of us would have predicted comparing the following carbocations Vs alcanes:

Butane-primary butane carbocation

Butane-secondary butane carbocation

Isobutane- tertiary isobutane carbocation

(With a basis 3-31G) => Figure