Symmetrized combinations of s-, p-, d-, f-spinors for study of electronic structure of physical systems

Usually, atom-like functions of $s$-, $p$- and $d$-type (linear combinations of atom-like orbitals – LCAO method) are used for study of electronic structure of molecules, crystals end nanoobjects. It is necessary to enlarge the basis by including atom-like functions of f-type for more precise calculations and for study of compounds with heavy atoms. Taking into account the spin-orbit interaction, the basis ought be composed by the products of coordinate and spin functions (or spinors). Symmetrized combinations of $s$-, $p$-, $d$-, $f$-type functions are built and presented in this article (with and without spin multiplier) by means of compact tables. The symmetrization is made according to irreducible representations of usual and double point groups with axes up to six order.