The calculations of the structural and electronic properties of materials quantitatively which use only the fundamental physical constants, i.e., the Planck constant, the elementary charge, the electron mass, and the speed of light, as experimental values are called first-principles calculations. In particular, those which take account of the relativistic effects are called relativistic first-principles calculations. The relativistic first-principles calculations are indispensable to the quantitative calculations of the structural and electronic properties of the materials with heavy elements.
The highly precise evaluation of the electrostatic potential originated in the electron distribution in a material is very important to reliable calculations. The term "full-potential" means that the method calculates the electrostatic potential in high precision. The LCAO method is the one which expresses the wave functions in a materials as the linear combinations of the wavefunctions of the constituent atoms. The advantage of this method is that it is capable of calculating the structural and electronic properties of molecules and one, two, and three-dimensional solids using the same algorithm.
To take account of all the relativistic effects including spin-orbit coupling, one must solve the Dirac equation as the wave equation for electrons. This method enables us to calculate spin-orbit coupling very precisely so that it is suitable for the study of the magnetocrystalline anisotropy and the orbital magnetism in ferromagnetic materials. The method is called the fully relativistic full-potential LCAO (FFLCAO) method.
Although the FFLCAO method is useful for taking account of spin-orbit coupling, the disadvantage is its high computational cost. Spin-orbit coupling is, however, not very important to some purposes. For such purposes, one can reduce the computational cost dramatically by an appropriate averaging procedure of spin-orbit coupling. The method is called the scalar relativistic full-potential LCAO (SFLCAO) method.