Total energy from KS-DFT: How reliable is it and why?

Question

As the title suggests, my question is fundamental - How reliable are the total energy values from Kohn-Sham Density Functional Theory, and why. I acknowledge that absolute values of energies are useless, but relative values are often used to compute several quantities across different applications. For instance:

1. Atomization Energies - For a simple molecule AB, the atomization energy can be calculated directly from $E_{AB}$ - $E_{A}$ - $E_{B}$.
2. Magnetic materials - Difference of total energy values for systems in different spin configurations (say FM and AFM), can indicate which magnetic configuration is more stable.

To word my question differently: There are many more applications where total energies are used. What I find weird is many research works rarely delve into the validity of this quantity. Why is one able to do this? Note: I also acknowledge that there might be functional-dependent errors in calculation of these quantities, but my question is not about that. Instead, my question is more generic.

Answer 1

The main issue here is that the calculated energy is a potential energy, that's why the absolute value is useless. As potential energy always depends on a reference system, you can only use the absolute value in comparison (as you do the calculations using exactly the same conditions) or in quantities that are obtained by substractions of these energies like binding energies or the examples you gave.

Answer 2

Your question is on absolute energies, but all of your physical examples are relative energies. One could also add properties to the list; however, these are again not determined by the total energy, but rather as its derivatives with respect to some perturbation... which are again energy differences, just now between the perturbed and unperturbed system. This means that lots of systematical errors in the absolute energy end up cancelling in most situations.

Answer 3

In fact, in some situations, if you are chasing "chemical accuracy" (1 kcal/mol $\approx$ 40 meV/atom) you do need total energy calculation beyond DFT. For example:

• Total energy differences with ”chemical accuracy”: Atomization, formation energies, reaction barriers, etc.

• Van der Waals interactions.

• Bandstructure of metals and largish gap systems, and some problematic cases in-between.

To obtain the total energy beyond DFT, you usually need to consider the total energy at the RPA level. The following screencast is summarized from this paper: J. Harl and G. Kresse, PRL 103, 056401 (2009), from which you can see the RPA total energy calculations are more in good agreement with the experimental data than the PBE total energy calculations.

For more information, you can take a look at this slide.

Hope it helps.