This paper presents a novel separable dual space Gaussian pseudo-potential for the first two rows of the periodic table. The pseudo-potential is designed to be efficient in numerical calculations using plane waves as a basis set. It has optimal decay properties in both real and Fourier space, allowing efficient computation of the nonlocal part of the pseudo-potential in real space. The pseudo-potential is separable and can be expressed with a small number of parameters, enabling fast and accurate calculations. The local part of the pseudo-potential is given by an analytic form involving error functions and exponentials, while the nonlocal part is a sum of separable terms involving spherical harmonics and Gaussians. The pseudo-potential parameters were determined through a least square fitting procedure, ensuring high accuracy and satisfying norm-conserving conditions. The parameters exhibit clear trends across the periodic table and are tabulated for easy implementation. The pseudo-potential is highly accurate, with errors in bond lengths for molecules containing first row atoms being extremely small, and for second row atoms being comparable to the LDA approximation. The pseudo-potential is easy to implement in both real and Fourier space, and its dual space Gaussian form ensures optimal efficiency. The paper also discusses the accuracy of the pseudo-potential in molecular calculations and compares it with other methods. The results show that the pseudo-potential provides high accuracy for molecules with first row atoms and is significantly more accurate than standard Gaussian basis sets. The pseudo-potential is also compared with Gaussian94 results for some difficult molecules, showing good agreement. The paper concludes that the proposed pseudo-potential is highly accurate and efficient for electronic structure calculations.This paper presents a novel separable dual space Gaussian pseudo-potential for the first two rows of the periodic table. The pseudo-potential is designed to be efficient in numerical calculations using plane waves as a basis set. It has optimal decay properties in both real and Fourier space, allowing efficient computation of the nonlocal part of the pseudo-potential in real space. The pseudo-potential is separable and can be expressed with a small number of parameters, enabling fast and accurate calculations. The local part of the pseudo-potential is given by an analytic form involving error functions and exponentials, while the nonlocal part is a sum of separable terms involving spherical harmonics and Gaussians. The pseudo-potential parameters were determined through a least square fitting procedure, ensuring high accuracy and satisfying norm-conserving conditions. The parameters exhibit clear trends across the periodic table and are tabulated for easy implementation. The pseudo-potential is highly accurate, with errors in bond lengths for molecules containing first row atoms being extremely small, and for second row atoms being comparable to the LDA approximation. The pseudo-potential is easy to implement in both real and Fourier space, and its dual space Gaussian form ensures optimal efficiency. The paper also discusses the accuracy of the pseudo-potential in molecular calculations and compares it with other methods. The results show that the pseudo-potential provides high accuracy for molecules with first row atoms and is significantly more accurate than standard Gaussian basis sets. The pseudo-potential is also compared with Gaussian94 results for some difficult molecules, showing good agreement. The paper concludes that the proposed pseudo-potential is highly accurate and efficient for electronic structure calculations.