Common accuracy objectives.
| Property | Accuracy required |
|---|---|
| Heats of formation | 1a kcal mol−1 |
| 3b kcal mol−1 | |
| Heats of formation (“intensive”)c | 0.3a kcal mol−1 |
| 1.6b kcal mol−1 | |
| Conformational energies | 0.1d kcal mol−1 |
| Barrier heights | 1e kcal mol−1 |
| Ionization potentials | 1e kcal mol−1 |
| Band gaps | 0.1f eV |
| Excitation energies | 0.1f eV |
| Bond lengths | 1g pm |
| Vibrational frequencies | <3h cm−1 |
| Shielding constants | 0.5–5%i |
| Dipole moments | 0.1–0.2j D |
| Dipole polarizabilities | 0.5–1j a.u. |
| Electric field gradients | 0.1–0.2j a.u. |
Savin: mean value of the experimental uncertainties compiled in ref. 266 for over 500 molecules containing elements with Z < 18. See also ref. 267.
Savin: Q95, cf. contribution (3.3.12), obtained from the experimental uncertainties compiled in ref. 266 for over 500 molecules containing elements with Z < 18.
Savin: heat of formation divided by (the number of atoms −1), justified by the mean of the values obtained by detaching successively one atom after the other.
Grimme: molecular total energy difference for the same covalently bound structure but with different three-dimensional shape normally obtained by rotation around covalent bonds.
Schwerdtfeger: based on ref. 267.
Kronik: an experimental accuracy of 0.1 eV in band gap measurements is possible, as well as desirable, but not at all trivial and may require the combination of several measurement techniques. Many reported experimental results, especially for insulators, do not necessarily reach this level of accuracy. Also, some reported band gaps arise from correction terms to optical gap values. Furthermore, experimental band gaps are also influenced by electron-nucleus coupling, sometimes quite significantly. This should be taken into account when comparing to results of electronic structure theory that do not include such coupling.
Helgaker: the uncertainties in experimental bond lengths depend strongly on the experimental technique used – an accuracy of 1 pm for covalent bonds of first-row atoms is a reasonable target for computation. For benchmark data of wave-function methods, see ref. 268.
Draxl: for vibrational frequencies, even semilocal DFT does already very well, if computed consistently (i.e., for the optimized geometry269). The situation is more tricky for intensities, as these are typically not measured for solids. The situation may be different for molecules; thus a distinction would be needed. Note that intensities can’t be obtained by DFT alone.
Kaupp: the necessary and achievable accuracy for shieldings and relative shifts differs from nucleus to nucleus and for different applications. The best way to report the accuracy that allows a comparison between different nuclei, is to give relative deviations in %, normalized to the shielding or shift range of a given nucleus (either computed or experimental). For meaningful accuracy, this should not exceed a few percent, sub-percent accuracy is better, and is achievable at least for light main-group systems. This is not yet the case for transition-metal nuclei.