Matter Modeling Stack Exchange is a question and answer site for materials modelers and data scientists. It only takes a minute to sign up.
Sign up to join this community
Note added afterwards: This question also has excellent answers on the Chemistry Stack Exchange: Is density functional theory an ab initio method?
I have very little experience with DFT, but coming from more of a coupled-cluster background, where the improvements are "systematic", to me it seems that the choice of functional in DFT is somewhat trial-and-error based and also problem specific, perhaps requiring "chemical intuition". Therefore, can DFT truly be considered an ab initio method?
This is a good question. The term ab initio literally means 'from the beginning,' "implying that the only inputs into an ab initio calculation are physical constants." (Wikipedia)
However, this term is often used to describe methods that involve empirical approximations (like LDA, GGA) or derived quantities (like pseudopotentials). And DFT is commonly referred to as an ab initio method, including on the DFT Wikipedia entry:
In the context of computational materials science, ab initio (from first principles) DFT calculations allow the prediction and calculation of material behaviour on the basis of quantum mechanical considerations, without requiring higher-order parameters such as fundamental material properties. In contemporary DFT techniques the electronic structure is evaluated using a potential acting on the system’s electrons.
There are techniques, like quantum Monte Carlo, or directly solving the Schrodinger equation, that are truly from first principles, but these techniques are so computationally expensive that they are rarely useful for modelling an actual material at any scale, and are also rarely referred to as ab initio. DFT is ab initio relative to other more empirical methods like molecular mechanics.
As pointed out by several people already, some information can be found elsewhere, as in here. And also the differentiation between DFT (exact) and density functional approximations (DFAs), as pointed out regularly by Mel Levy, can be found there.
However, I think there is one aspect missing, and here I would like to quote my late PhD supervisor Jaap Snijders. The most important aspect to know if a method is ab initio or not, is related to the integrals. If the integrals can be computed from the beginning, the method is ab initio; if not, then not. In DFT, DFAs and wavefunction methods, the integrals can be computed, and hence, these methods are ab initio. In semi-empirical methods (AM1, PM3, DFTB, xtb), some of the integrals are either estimated or approximated (from e.g. DFA results in case of DFTB/xtb), and therefore, these methods are not ab initio. Likewise for e.g. the Empirical Valence Bond method, which like the name already indicates, is empirical.
Whether or not a method gives the exact energy is a different aspect. In that case only Full CI with infinite basis set and DFT give the exact energy, all other methods are approximations. By choosing a basis set of a certain size, one is approximating; by using "only" CCSD(T), one is approximating; by using a density functional like PBE, B3LYP or r2SCAN, one is approximating; etc.
In principle, DFT is exact, so it's an ab initio method. However, because we don't have an universal functional and work only with approximated functionals, we have to know a priori what functional performs well with our system in study and also compare results with experiment or high-level wavefunction methods. Then, we could say that is a "semi-empirical" approach, but some could argue with that name.
