# When it comes to bond energy or molecular binding energy, do people mean enthalpy?

When calculating bond energy or molecular binding energy, which value should I use, enthalpy or total energy?

For example, A+B=C

Should it be C's enthalpy of formation minus (A's+B's)enthalpies of formation, or C's total energy minus (A's+B's) total energies?

When in doubt, consult IUPAC Gold Book for definitions (italics below is mine).

bond-dissociation energy, $D$

The enthalpy (per mole) required to break a given bond of some specific molecular entity by homolysis, e.g. for $\ce{CH4 -> CH3^{.} + H^{.}}$, symbolized as $D(\ce{CH3−H})$.

bond energy (mean bond energy)

The average value of the gas-phase bond dissociation energies (usually at a temperature of 298 K) for all bonds of the same type within the same chemical species. The mean bond energy for methane, for example, is one-fourth the enthalpy of reaction for: $$\ce{CH4_{(g)} -> C_{(g)} + 4H_{(g)}} \, .$$ Tabulated bond energies are generally values of bond energies averaged over a number of selected typical chemical species containing that type of bond.

So, yes, conceptually you should use enthalpy. Note, however, that the enthalpy of a molecular specie in gas phase at, say 298K, is calculated as follows $$H_{298} = E_{\mathrm{e}} + E_\mathrm{ZPE} + H_{\mathrm{trans}} + H_{\mathrm{rot}} + H_{\mathrm{vib}} + RT \, ,$$ where

• $E_{\mathrm{e}}$ is the electronic energy;
• $E_\mathrm{ZPE}$ is the zero point energy;
• $H_{\mathrm{trans}}$, $H_{\mathrm{rot}}$ and $H_{\mathrm{vib}}$ are the temperature-dependent contributions to enthalpy from translation, rotational and vibrational motion, respectively.

And the problem (as Martin mentioned in comments) is that basically only the first term out of this five can be calculated accurately enough when the ultimate goal is to calculate energies (bond energies in our case) with the so-called "chemical accuracy" which is about $\pm 1$ kcal/mol. For relatively large molecules harmonic frequencies and consequently $E_\mathrm{ZPE}$, as well as a rigid-rotor harmonic-oscillator approximation used to calculate thermal corrections, become inaccurate, and thus, the change of electronic energy should always be used as a reference.

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• In computational chemistry it is never wise to only use the enthalpy values. The goldbook is unfortunately not a very good address for these kinds of questions. Aug 31 '14 at 15:19
• @Martin could you elaborate a little bit more? Do you mean that a rigid-rotor harmonic-oscillator approximation used to calculate thermal corrections is not suitable for relatively large systems? Aug 31 '14 at 15:56
• Amongst others, yes. When systems go large, harmonic frequencies become more inaccurate. Tiny inaccuracies may lead to big errors. Numerical treatment can be a big problem. It may depend much more on implementation and approximation used in the different qc programms. The pure electronic energy should always be used as a reference. Aug 31 '14 at 16:26
• @Martin, surely, that is a good point. I added relevant info to my answer. Aug 31 '14 at 18:22
• These terms has more of historical value. In early theoretical chemistry they needed practical experimental values that can be reasonably inquired by the the methods, can cover wide range of (organic) chemistry and cannot be calculated by simple empirical equations. This kind of thermochemical data were just right for e.g. semi-empirical methods. That time I believe they were happy if they could compare electronic energies, and fit parameters for the electronic calculations, and didn't really care the other contributions.
– Greg
Aug 31 '14 at 18:43