The primary production methods of FHI-aims are density functional theory as well as many-body methods and higher-level quantum chemistry approaches. For the exchange - correlation treatment, local (LDA), semi-local (e.g., PBE, PBEsol), meta-GGA, and hybrid (e.g., HSE06, B3LYP) functionals have been implemented. The resulting orbitals can be used within the framework of many-body perturbation theory, such as Møller-Plesset perturbation theory or the GW approximation. Moreover, thermodynamic properties of the molecules and solids are accessible via Born-Oppenheimer molecular dynamics and path integral molecular dynamics methods. The first step is to expand the Kohn-Sham orbitals packages ψ ψ i ( r ) into a set of basis functions { ϕ ϕ j ( r ) } ψ ψ i ( r ) = ∑ ∑ j C i j ϕ ϕ j ( r ) . Since FHI-aims is an all-electron full-potential code that is computationally efficient without compromising accuracy, the choice of basis function is crucial in order to achieve the said accuracy. Therefore, FHI-aims is based on numerically tabulated atom-centered orbitals (NAOs) of the form: ϕ ϕ j ( r ) = μ μ j ( r ) r Y l m ( Ω Ω ) . As the name implies, the radial shape μ μ j ( r ) is numerically tabulated and, therefore, fully flexible. This allows the creation of optimized element-dependent basis sets that are as compact as possible while retaining a high and transferable accuracy in production calculations up to meV-level total energy convergence. To obtain real-valued ϕ ϕ j ( r ) , Y l m ( Ω Ω ) here denotes the real parts ( m = 0 , … … , l ) and imaginary parts ( m = − − l , … … , − − 1 ) of complex spherical harmonics, with l an implicit function of the radial function index j .