This paper presents a study on the performance of numerical atomic orbitals (NAOs) in density-functional calculations for solids and molecules. The authors explore various schemes for generating NAO basis sets, aiming to optimize basis quality while maintaining strict localization of the orbitals for linear-scaling calculations. The best performance is achieved with a new scheme that flexibilizes previous proposals. The basis sets are tested against converged plane-wave calculations on a variety of systems, including covalent, ionic, and metallic. The results show satisfactory convergence with small basis sizes, outperforming previous schemes. The transferability of the basis sets is also tested and found to be satisfactory. The paper discusses the importance of basis set size, range, and radial shape in achieving efficient and accurate calculations. It describes different methods for generating NAOs, including the use of confinement potentials and the optimization of orbital parameters. The authors also compare different confinement schemes and find that the proposed scheme offers better performance than previous ones, avoiding known problems such as discontinuities in the derivative of the orbitals. The study shows that NAO basis sets can achieve high precision with relatively small basis sizes, and that the proposed scheme provides better results than previous methods. The results are validated by comparing them with plane-wave calculations and other established methods. The paper concludes that NAO basis sets are a promising approach for linear-scaling calculations, offering good accuracy and efficiency. The authors also highlight the importance of further research to systematically control the cutoff radii for improving efficiency without losing precision.This paper presents a study on the performance of numerical atomic orbitals (NAOs) in density-functional calculations for solids and molecules. The authors explore various schemes for generating NAO basis sets, aiming to optimize basis quality while maintaining strict localization of the orbitals for linear-scaling calculations. The best performance is achieved with a new scheme that flexibilizes previous proposals. The basis sets are tested against converged plane-wave calculations on a variety of systems, including covalent, ionic, and metallic. The results show satisfactory convergence with small basis sizes, outperforming previous schemes. The transferability of the basis sets is also tested and found to be satisfactory. The paper discusses the importance of basis set size, range, and radial shape in achieving efficient and accurate calculations. It describes different methods for generating NAOs, including the use of confinement potentials and the optimization of orbital parameters. The authors also compare different confinement schemes and find that the proposed scheme offers better performance than previous ones, avoiding known problems such as discontinuities in the derivative of the orbitals. The study shows that NAO basis sets can achieve high precision with relatively small basis sizes, and that the proposed scheme provides better results than previous methods. The results are validated by comparing them with plane-wave calculations and other established methods. The paper concludes that NAO basis sets are a promising approach for linear-scaling calculations, offering good accuracy and efficiency. The authors also highlight the importance of further research to systematically control the cutoff radii for improving efficiency without losing precision.