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.
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.
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.
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.
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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?
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".
