Microscopically there is no such thing as a fractionally occupied site. You need to create a supercell and place atoms at the correct fraction of symmetry equivalent sites. There is a full explanation in the responses to this question:

https://www.researchgate.net/post/How_I_can_add_Occupancies_of_atoms_in_as_here_Bi1-xCaxFe1-xTiO3_for_x02_Qunatum_espresso_input_file

And some details in the response to this question:

https://www.researchgate.net/post/Occupancy_of_atom_in_Castep_has_no_effect

There are two possible approaches:

1) You create a set of different structures of which the ensemble shows the fractional occupation. So in practice, you will end up trying to find out possible configurations of the sites with and without occupation. In the end you then will have to combine the results of the different calculations into a single result (story).

2) You can look into Special Quasi Random structures, in which you use one single supercel (with a complicated shape and no symmetry) which contains different occupied/unoccupied configurations.

(an example of what I mean can be found in this older paper:

Article Density functional theory study of La_ {2} Ce_ {2} O_ {7}: D...

A short and somewhat muddy explanation: It's not a problem of VASP itself - to my knowledge, no ab initio atomistic code (VASP, WIEN2K, abinit, QuantumEspresso, CASTEP, LMTO...) can treat partially occupied sites, by nature of the approach: Crystallographic models from diffraction experiments average diffraction data over the entire sample, so it's possible to assign site occupation factors for *regular* antisite/vacancy defects. In first-principle calculations, your code of choice makes use of an ideal unit cell with periodic boundary conditions, with the individual basis functions of all the atoms contributing to the system's total wavefunction (somewhat simply put), and taking a given site with an occupation factor

Dimitri Bogdanovski writes, "keep in mind that the lower the concentration of defects is, the larger your supercell will have to be to keep the stoichiometric ratio as needed, driving up the computational cost." which is an excellent point. In fact, any fractional concentration that can not be reasonably represented by a ratio of small integers is likely going to require an expensive calculation.

Dear Sebin, you can try our SOD code (https://github.com/gcmt-group/sod). SOD generates the list of symmetrically distinct configurations compatible with the overall composition you want, creates all the VASP input files, and then helps post-processing the results for the ensemble using statistical mechanics.

Ricardo Grau-Crespo, what a great idea for a code! Thanks for bringing it to our attention.

On Dimitri's point "keep in mind that the lower the concentration of defects is, the larger your supercell will have to be to keep the stoichiometric ratio as needed, driving up the computational cost", I just want to add that it is possible to represent a very low concentration of vacancies using a grandcanonical approach: your ensemble in this case will be a combination of cells with no vacancies and cells with vacancies. That keeps the size of the supercell down. On how to use cell configurations within the same ensemble, i.e. the grandcanonical formulation, please have a look at our paper:

Article Thermodynamics of hydrogen vacancies in MgH2 from first-prin...