# How to calculate the resonance energy of thiophene?

How to calculate the Resonance energy of Thiophene?
I know how to calculate the resonance energy of Benzene. I am applying same procedure for thiophene, too. (Wikipedia: Resonance energy)

The values are taken from NIST Chemistry WebBook.

\begin{array}{lccc} \hline \frac{\text{Heat Of Formations}}{\pu{kcal mol-1}} & \text{Thiophene} & \text{Tetrahydrothiophene} & \text{2,5-Dihydrothiophene}\\ \hline \text{Experimental} & 27.82 & -8.03 & 20.86 \\ \text{Using Argus Lab (AM1)} & 29.65 & -13.7 & 15.31 \\ \hline \end{array}

From moving from tetrahydrothiophene to 2,5-dihydrothiophene, there is a change of $\pu{28.89 kcal/ mol}$, so ideally thiophene should have $28.89 \times 2 (=57.78) \pu{kcal/mol}$ more energy of formation, but it has only $\pu{35.85 kcal/mol}$ more. This difference should be called resonance energy, i.e. $\pu{35.85 kcal/mol} - \pu{57.78 kcal/mol} = \pu{-21.93 kcal/mol}$.
In the literature, the value is given as $\pu{-29 kcal/mol}$. (1) (2)

I applied the same method on furan, where I got an error within 1%, but in case of thiophene, I am getting an error of about $\pu{7 kcal/mol}$. Why? When using Argus lab the error even reaches above 50%.

I've posted this question on another forum also. I didn't get any satisfactory answer. Why in the cases of benzene and furan does this method work, but in case of thiophene I'm getting this error?

• Resonance energy is not a real measurable physical value anyway, so why bother. – Ivan Neretin Apr 18 '18 at 14:27
• @Ivan Neretin Hahaha, Right. But at least it gives us some insight into the stability of different molecules. Moreover, My teacher gave me this assignment to calculate the resonance energy using Argus Lab, but results are drastic. First, my teacher didn't know how to calculate it :3 , Then I tried to find it then I faced this problem. – Aditya Shrivastav Apr 18 '18 at 14:43
• Thiophene, 2,3-dihydro-: 21.68 kcal/mol -> R 23,57 kcal/mol. That's pretty good for guessing a random number. It is also clear that AM1 is not able to describe the heats of formation very well; I mean they are 5 kcal/mol off, that is a lot. Please add where you got your reference value of -29.1 kcal /mol from. In what context and how did they measure that? – Martin - マーチン Apr 18 '18 at 15:29
• @Martin I've added two references. Please check them. – Aditya Shrivastav Apr 18 '18 at 15:47