This paper presents an optimized norm-conserving Vanderbilt pseudopotential (OV) method for electronic structure calculations. The approach improves upon the traditional Kleinman-Bylander (KB) method by incorporating a systematic optimization of convergence with the plane-wave basis size. The OV method allows for the use of positive-energy scattering states and enforces greater continuity in the pseudopotential. It generalizes norm-conservation to multiple projectors and improves the accuracy of pseudopotentials in reproducing all-electron results. The paper compares the performance of all-electron, one-projector, and two-projector norm-conserving pseudopotentials for a variety of solids, including those with ionic, covalent, and metallic bonding. The OV method is shown to yield better agreement with all-electron results, particularly for cases involving shallow core states. The method also improves the convergence of the total energy with respect to the plane-wave cutoff energy. The paper discusses the optimization of the residual kinetic energy, which is crucial for accurate electronic structure calculations. The optimization involves a systematic approach to minimize the residual kinetic energy while satisfying the norm-conservation condition. This is achieved by introducing a set of residual basis functions and using a quadratic optimization procedure. The paper also addresses the issue of scattering properties of pseudopotentials, showing that the OV method produces scattering properties that are essentially identical to those calculated from scattering pseudo wave functions. The method is shown to be robust and effective in improving the accuracy of pseudopotentials, particularly for cases where the ground-state configuration of an atom cannot be used to generate the pseudopotential. The paper concludes that the OV method is a competitive choice for accuracy and computational efficiency compared to ultrasoft and projector-augmented-wave potentials. The open-source ONCVPSP code is freely available and provides a reliable implementation of the OV method. The results demonstrate that the accuracy of two-projector OV pseudopotentials is primarily limited by the accuracy of the underlying density functional approximations. The paper also highlights the importance of treating outermost core electrons as valence electrons for accurate results in group 1 and group 2 elements, as well as for transition-metal elements.This paper presents an optimized norm-conserving Vanderbilt pseudopotential (OV) method for electronic structure calculations. The approach improves upon the traditional Kleinman-Bylander (KB) method by incorporating a systematic optimization of convergence with the plane-wave basis size. The OV method allows for the use of positive-energy scattering states and enforces greater continuity in the pseudopotential. It generalizes norm-conservation to multiple projectors and improves the accuracy of pseudopotentials in reproducing all-electron results. The paper compares the performance of all-electron, one-projector, and two-projector norm-conserving pseudopotentials for a variety of solids, including those with ionic, covalent, and metallic bonding. The OV method is shown to yield better agreement with all-electron results, particularly for cases involving shallow core states. The method also improves the convergence of the total energy with respect to the plane-wave cutoff energy. The paper discusses the optimization of the residual kinetic energy, which is crucial for accurate electronic structure calculations. The optimization involves a systematic approach to minimize the residual kinetic energy while satisfying the norm-conservation condition. This is achieved by introducing a set of residual basis functions and using a quadratic optimization procedure. The paper also addresses the issue of scattering properties of pseudopotentials, showing that the OV method produces scattering properties that are essentially identical to those calculated from scattering pseudo wave functions. The method is shown to be robust and effective in improving the accuracy of pseudopotentials, particularly for cases where the ground-state configuration of an atom cannot be used to generate the pseudopotential. The paper concludes that the OV method is a competitive choice for accuracy and computational efficiency compared to ultrasoft and projector-augmented-wave potentials. The open-source ONCVPSP code is freely available and provides a reliable implementation of the OV method. The results demonstrate that the accuracy of two-projector OV pseudopotentials is primarily limited by the accuracy of the underlying density functional approximations. The paper also highlights the importance of treating outermost core electrons as valence electrons for accurate results in group 1 and group 2 elements, as well as for transition-metal elements.