If one wants to compare energies of different calculations the simplest approach is to use the total energy, but convergence is slow. In particular, differnt calculations use different energy zero, different treatments of relativity and some use pseudopotential. Thus we need to define derived energies that converge faster and are universally defined.
Some possible energies could be:
- MethodConsistentAtomizationEnergy: Total energy minus the energy of the same number of isolated atoms calculated with the same method (functional,...), basisset and accuracy.
- MethodConsistentFormationEnergy: Total energy minus the same number of atomic energies of the most stable form of the element calculated with the same method (functional,...), basisset and accuracy.
- ConvergedAtomAtomizationEnergy : Fully converged atom with the same pseudo potential, relativity treatment and exchange correlation treatment. Not as good as MethodConsistentAtomizationEnergy, as the basis set error will not cancel, however fewer calculations are needed.
An interesting approach that can be used if one has enough data, without requiring any other extra calculation, and also gives an upper bound for the accuracy of the previous methods could be:
- FittedComparableEnergy: Total energy minus the an atom dependent contibution that depends on method, periodicity, basisset and accuracy, fitted so that the spread of the resulting binding energies is minimized.
- FittedComparableEnergyV1: First version of the fit of the total energy minus the an atom dependent contribution that depends on method, periodicity, basis set and accuracy, fitted so that the spread of the resulting binding energies is minimized.
Having just the energy is not enough one needs also a measure of the convergence of this particular calculation, and ideally even against a true reference. We can define three classes of measures:
- EnergyConvergencePartialMeasure: a measure of the energy convergence (like the scf criteria)
- EnergyConvergenceMeasure: a measure of the convergence against the limit of the theory using the same description level
- EnergyConvergenceAbsoluteMeasure: a measure of the convergence against the theory limit (best description)
It is expected that with time we will be able to devise better ways to predict or approximate the second two classes (as Cottenier tries to do).