I understand that electronic energy includes a combination of

  • electron-electron repulsion energy,
  • nuclear-nuclear repulsion energy, and
  • electron-nuclear attraction energy

at 0 K, and the energies are relative to a zero with all particles infinitely far apart.

So is this when it's appropriate to use electronic energies rather than enthalpies when determining reaction energies at 0K and when particles are infinitely far apart?

  • 2
    $\begingroup$ "determining reaction energies at 0K and when particles are infinitely far apart?" - this part of sentences make no sense at all. $\endgroup$
    – Mithoron
    Apr 13, 2018 at 16:41

1 Answer 1


In the case of atoms or molecules in a vacuum, at $0~\mathrm{K}$, and infinitely apart, the "reaction energy" of

$$ \ce{A + B -> A \bond{....}\bond{....}\bond{....} B}, $$

where $\ce{A \bond{....}\bond{....}\bond{....} B}$ is effectively at infinite separation, is

\begin{align*} E_{\text{rxn}} &= \sum_{i}^{\text{products}} E_{i} - \sum_{j}^{\text{reactants}} E_{j} \\ &= E_{\ce{A \bond{....}\bond{....}\bond{....} B}} - (E_{\ce{A}} + E_{\ce{B}}) \\ &= E_{\ce{A}} + E_{\ce{B}} - (E_{\ce{A}} + E_{\ce{B}}) \\ &= 0. \end{align*}

The reasoning is that energies are extensive, and there is no change in the total energy of the system. The total energy of infinitely separated particles is their sum, as there is no attractive or repulsive interaction between them. They're effectively completely isolated. In that sense, there is no reaction, which is I put reaction energy in scare quotes.

In practice, when you have a finite interaction such as a chemical reaction, the total interaction energy should include electronic, vibrational, rotational, and translational components, of which the latter 3 will grow as temperature increases. Most likely the thermal vibrational contribution is the only significant one.

One missing term that is not dependent on temperature and should be added is the zero-point (vibrational) energy, $$ E_{\text{ZPVE}} = \frac{1}{2} \hbar \sum_{c}^{\text{normal}\\\text{modes}} \omega_{c}, $$ which is the non-zero amount of non-electronic energy that molecules have even at zero kelvin and is purely quantum mechanical in nature. The ZPVE or ZPE can alter energy barriers non-linearly, since vibrations are not necessarily localized, and is the most significant non-electronic contribution to gas-phase reaction energies.

  • $\begingroup$ "Most likely the thermal vibrational contribution is the only significant one." I'm not sure I agree with this. The translational component typically has the largest magnitude unless the species is geometrically constrained (e.g. a species chemisorbed on a surface). Could you clarify? $\endgroup$
    – Argon
    Apr 19, 2018 at 4:53
  • $\begingroup$ I should be careful. I am referring the ideal gas kinetic energy, since thermochemical analysis in quantum chemistry is usually within the ideal gas approximation. At room temperature, $(3/2)k_{\mathrm{B}}T\approx\pu{311 cm^{-1}} < \pu{1 kcal/mol}$, which should be dwarfed by ZPE. Can you give a good ref that shows this isn't true in reality? I don't know much about actual thermochemistry. $\endgroup$ Apr 19, 2018 at 13:03

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