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I was trying to calculate the resonance energy of benzene by using Argus Lab. These values are weird and very different from the experimental data. I have two questions regarding them.

  1. What is the difference between Final SCF Energy and heat of formation?

    When I tried to calculate the energy, It gave me two kinds of energy - Final SCF Energy and Heat of Formation. I know the definition of heat of formation. But what I found weird is that Heat of Formation of $\ce{H2}$ molecule was $\pu{-13.3564 kcal/mol}$. It should be zero instead.

  2. Is there any mistake in following procedure:

    a. I calculated the energy of cyclohexane($x$), cyclohexene($y$), and benzene ($z$).
    b. Energy change while converting cyclohexane to cyclohexene ($a$) $= y-x$
    c. Expected energy for benzene ($b$) $= x+3a$
    d. Resonance energy of benzene = $z-b$
    (Answer should be negative, implying that resonance energy is stabilizing in nature)

    By using the SCF Energy data, I got resonance energy $\pu{415 Kcal/mol}$ and while using the heat of formation data I got $\pu{-41.8 Kcal/mol}$.

Here is the data (in $\pu{Kcal/mol}$) -: $$ \begin{array}{|l|c|c|c|} \hline \text{Energy type} & \mathrm x & \mathrm y & \mathrm z\\ \hline \text{SCF Energy using PM3} & {-21556.7995} & {-20680.6471} & -18512.6189 \\ \text{Heat Of Formation} & {-37.43} & {-3.0101 } & 23.96 \\ \hline \end{array} $$

Is this a reliable software for calculating the resonance energy as there is a difference about $\pu{5 Kcal/mol}$ or I am doing some mistake by overlooking any concept?

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  • $\begingroup$ You are modelling hydrogenations, but I do not see any hydrogen in your equations. Even in quantum chemistry you have to use stoichiometric equations. $\endgroup$ – awvwgk Apr 3 '18 at 21:43
  • $\begingroup$ I think "a" is the energy difference between 2 C-H bonds and C=C Pi bond. $\endgroup$ – Aditya Shrivastav Apr 5 '18 at 13:35
  • $\begingroup$ A reaction you can model is $C_6H_{10} + H_2 \to C_6H_{12}$. But you have to consider the hydrogen, so $a = E_\text{SCF}(C_6H_{12}) - E_\text{SCF}(C_6H_{10}) - E_\text{SCF}(H_2)$. $\endgroup$ – awvwgk Apr 6 '18 at 17:46
  • $\begingroup$ Also keep in mind that you have calculated energies. When comparing with (free) enthalpies measured by experiment you have to consider this. $\endgroup$ – awvwgk Apr 6 '18 at 17:52
  • $\begingroup$ Ok got my mistake in case of SCF energy.I earlier assumed that SCF of H2 is 0. Leave it. My question is regarding the "heat of formation", at least heat of formation of H2 is 0. So it should give precise results. $\endgroup$ – Aditya Shrivastav Apr 8 '18 at 13:32

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