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"Chemical accuracy" in computational chemistry, is commonly understood to be $1~\mathrm{kcal\over mol}$, or about $4~\mathrm{kJ\over mol}$. Spectroscopic accuracy is $1~\mathrm{kJ\over mol}$, and that definition has intuitive sense. However, where does the $1~\mathrm{kcal\over mol}$ quantity come from?

From Wikipedia:

A particularly important objective, called computational thermochemistry, is to calculate thermochemical quantities such as the enthalpy of formation to chemical accuracy. Chemical accuracy is the accuracy required to make realistic chemical predictions and is generally considered to be 1 kcal/mol or 4 kJ/mol.

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Short answer: the goal of "thermochemical accuracy" for computational chemistry is to match or exceed experimental accuracy. Thus, ~1 kcal/mol comes from the typical error in thermochemical experiments.

The drive began with John Pople, who begin the modern effort to consider "Model Chemistries," comparing the accuracy of different methods across many molecules and often multiple properties. He realized that for thermodynamic properties, one could approach the accuracy of experiments. (See, for example his Nobel lecture).

As the model becomes quantitative, the target should be that data is reproduced and predicted within experimental accuracy. For energies, such as heats of formation or ionization potentials, a global accuracy of 1 kcal/mole would be appropriate.

He then started work on composite methods like G1, G2, G3, etc. that could approach predicting many chemical properties to this accuracy.

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    $\begingroup$ I tried fairly quickly to see if the 1 kcal/mol number is solely due to Pople or others suggested it previously. Certainly he pushed this threshold in his widely-used Gn methods. $\endgroup$ – Geoff Hutchison Nov 2 '16 at 1:47
  • $\begingroup$ I see, so in short, "thermochemical accuracy" became shortened to "chemical accuracy" over time, since that was the main area of chemistry quantum chemistry aimed to match in accuracy. $\endgroup$ – Samuel Tan Nov 2 '16 at 13:44
  • $\begingroup$ Exactly. Also, if you can reach 1 kcal/mol accuracy, that's ~0.05 eV, which would be fairly good for ionization potentials or electron affinities. (We're not there yet.) So it was a good target for other chemical properties. $\endgroup$ – Geoff Hutchison Nov 8 '16 at 17:24

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