Abstract: The calculation of thermal neutron cross section for thermal neutron scattering materials in the field of nuclear engineering is based on the first principle. This study utilizes Al and Bi metals as examples for the determination of thermal neutron cross sections. The frozen phonon method and density functional perturbation method are applied to calculate the thermal neutron cross sections for Al and Bi, respectively. Phonon dispersion relation and phonon density of state are computed using VASP and PHONONY. Subsequently, coherent scattering for Bi is incorporated into LEAPR using NJOY to generate the thermal neutron scattering cross-section libraries for Al and Bi. The results reveal that, in the case of Al, the thermal neutron scattering cross section obtained using the density functional perturbation theory is in better agreement with ENDF8.0 compared to the frozen phonon method. Conversely, for Bi, the density functional perturbation method eliminates the imaginary frequency phenomenon observed in the frozen phonon method, resulting in thermal neutron scattering results that align well with experimental data. The paper proposes a more fundamental and predictable method for generating thermal neutron cross-sections by exploring the internal characteristic mechanism of the material, thus laying a theoretical foundation for studying the thermal mechanisms of new reactor nuclear materials..