Chemistry - Is density functional theory an ab initio method?

Solution 1:

First note that the acronym DFA I used in my comment originates from Axel D. Becke paper on 50 year anniversary of DFT in chemistry:

Let us introduce the acronym DFA at this point for “density-functional approximation.” If you attend DFT meetings, you will know that Mel Levy often needs to remind us that DFT is exact. The failures we report at meetings and in papers are not failures of DFT, but failures of DFAs. Axel D. Becke, J. Chem. Phys., 2014, 140, 18A301.

So, there are in fact two questions which must be addressed: "Is DFT ab initio?" and "Is DFA ab initio?" And in both cases the answer depend on the actual way ab initio is defined.

• If by ab initio one means a wave function based method that do not make any further approximations than HF and do not use any empirically fitted parameters, then clearly neither DFT nor DFA are ab initio methods since there is no wave function out there.
• But if by ab initio one means a method developed "from first principles", i.e. on the basis of a physical theory only without any additional input, then
  • DFT is ab initio;
  • DFA might or might not be ab initio (depending on the actual functional used).

Note that the usual scientific meaning of ab initio is in fact the second one; it just happened historically that in quantum chemistry the term ab initio was originally attached exclusively to Hartree–Fock based (i.e. wave function based) methods and then stuck with them. But the main point was to distinguish methods that are based solely on theory (termed "ab initio") and those that uses some empirically fitted parameters to simplify the treatment (termed "semi-empirical"). But this distinction was done before DFT even appeared.

So, the demarcation line between ab initio and not ab initio was drawn before DFT entered the scene, so that non-wave-function-based methods were not even considered. Consequently, there is no sense to question "Is DFT/DFA ab initio?" with this definition of ab initio historically limited to wave-function-based methods only. Today I think it is better to use the term ab initio in quantum chemistry in its more usual and more general scientific sense rather then continue to give it some special meaning which it happens to have just for historical reasons.

And if we stick to the second definition of ab initio then, as I already said, DFT is ab initio since nothing is used to formulate it except for the same physical theory used to formulate HF and post-HF methods (quantum mechanics). DFT is developed from the quantum mechanical description without any additional input: basically, DFT just reformulates the conventional quantum mechanical wave function description of a many-electron system in terms of the electron density.

But the situation with DFA is indeed a bit more involved. From the same viewpoint a DFA method with a functional which uses some experimental data in its construction is not ab initio. So, yes, DFA with B3LYP would not qualify as ab initio, since its parameters were fitted to a set of some experimentally measure quantities. However, a DFA method with a functional which does not involve any experimental data (except the values of fundamental constants) can be considered as ab initio method. Say, a DFA using some LDA functional constructed from a homogeneous electron gas model, is ab initio. It is by no means an exact method since it is based on a physically very crude approximation, but so does HF from the family of the wave function based methods. And if the later is considered to be ab initio despite the crudeness of the underlying approximation, why can't the former be also considered ab initio?

Solution 2:

The convention used by many is that ab initio refers solely to wave-function based methods of various sorts and that first principles refers to either wave-function or DFT methods with little approximation.

I can't find a citation at the moment, but I know this convention is fairly widely used in, e.g., J. Phys. Chem. journals.

The IUPAC gold book doesn't have "first principles," but Google Scholar gives over 224,000 hits for "first principles DFT".