This paper presents relativistic separable dual-space Gaussian pseudopotentials for all elements from hydrogen (H) to radon (Rn). The authors generalize the concept of nonrelativistic separable dual-space Gaussian pseudopotentials to the relativistic case, allowing for the construction of pseudopotentials for the entire periodic table. The relativistic pseudopotentials retain all the advantages of their nonrelativistic counterparts, including separability, optimal integration on real space grids, high accuracy, and a compact parameter set. The accuracy of the pseudopotentials is demonstrated through extensive molecular calculations. The pseudopotentials are constructed using a fully relativistic all-electron calculation, solving the two-component Dirac equation. The norm-conservation property is generalized to the relativistic case, and slight modifications to the analytic form of the pseudopotential are introduced. The parameters are given in the context of the local density approximation (LDA), and while they change slightly when using a generalized gradient approximation (GGA), molecular properties are less accurately described when using GGA. The pseudopotentials have an analytical form in both real and Fourier space, making them optimal for convergence in both spaces. The nonlocal part of the pseudopotential is separable and consists of terms involving spherical harmonics and Gaussians. The relativistic case includes spin-orbit coupling, which splits orbitals with l > 0 into spin-up and spin-down states. The pseudopotentials are constructed to include these spin-orbit effects. The parameters of the pseudopotentials are determined by minimizing the differences between eigenvalues and charges of all-electron and pseudo atoms. The parameters are derived from the all-electron eigenvalues and charges, leading to highly accurate and transferable pseudopotentials. The pseudopotentials are tested in extensive molecular calculations, showing good agreement with all-electron results and experimental data. The paper also discusses semi-core electrons, which are included in the pseudopotentials for elements where the core and valence orbitals overlap significantly. These semi-core electrons improve the description of highly charged ions. The inclusion of semi-core electrons increases computational effort but is necessary for accurate results in some cases. The pseudopotentials are shown to be highly accurate, with errors in bond lengths for first-row atoms being nearly ten times smaller than LDA errors and for heavier elements at least comparable to LDA errors. The results are comparable to other all-electron methods and are more accurate than standard Gaussian basis sets. The pseudopotentials are also shown to be transferable and can be used with various basis sets. The authors provide a complete set of relativistic LDA pseudopotentials for the entire periodic table, with parameters given in a table. The parameters are derived from all-electron calculations and are optimized for accuracy and transferability. The pseudopotentials are easy to use, with only a few parameters required, and are highly accurate and transferable. The paper concludes that these pseudopotentials are a valuableThis paper presents relativistic separable dual-space Gaussian pseudopotentials for all elements from hydrogen (H) to radon (Rn). The authors generalize the concept of nonrelativistic separable dual-space Gaussian pseudopotentials to the relativistic case, allowing for the construction of pseudopotentials for the entire periodic table. The relativistic pseudopotentials retain all the advantages of their nonrelativistic counterparts, including separability, optimal integration on real space grids, high accuracy, and a compact parameter set. The accuracy of the pseudopotentials is demonstrated through extensive molecular calculations. The pseudopotentials are constructed using a fully relativistic all-electron calculation, solving the two-component Dirac equation. The norm-conservation property is generalized to the relativistic case, and slight modifications to the analytic form of the pseudopotential are introduced. The parameters are given in the context of the local density approximation (LDA), and while they change slightly when using a generalized gradient approximation (GGA), molecular properties are less accurately described when using GGA. The pseudopotentials have an analytical form in both real and Fourier space, making them optimal for convergence in both spaces. The nonlocal part of the pseudopotential is separable and consists of terms involving spherical harmonics and Gaussians. The relativistic case includes spin-orbit coupling, which splits orbitals with l > 0 into spin-up and spin-down states. The pseudopotentials are constructed to include these spin-orbit effects. The parameters of the pseudopotentials are determined by minimizing the differences between eigenvalues and charges of all-electron and pseudo atoms. The parameters are derived from the all-electron eigenvalues and charges, leading to highly accurate and transferable pseudopotentials. The pseudopotentials are tested in extensive molecular calculations, showing good agreement with all-electron results and experimental data. The paper also discusses semi-core electrons, which are included in the pseudopotentials for elements where the core and valence orbitals overlap significantly. These semi-core electrons improve the description of highly charged ions. The inclusion of semi-core electrons increases computational effort but is necessary for accurate results in some cases. The pseudopotentials are shown to be highly accurate, with errors in bond lengths for first-row atoms being nearly ten times smaller than LDA errors and for heavier elements at least comparable to LDA errors. The results are comparable to other all-electron methods and are more accurate than standard Gaussian basis sets. The pseudopotentials are also shown to be transferable and can be used with various basis sets. The authors provide a complete set of relativistic LDA pseudopotentials for the entire periodic table, with parameters given in a table. The parameters are derived from all-electron calculations and are optimized for accuracy and transferability. The pseudopotentials are easy to use, with only a few parameters required, and are highly accurate and transferable. The paper concludes that these pseudopotentials are a valuable