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The traditional Gaussian basis sets used in modern quantum chemistry lack anelectron-nuclear cusp, and hence struggle to accurately describe core electronproperties. A recently introduced novel type of basis set, mixedramp-Gaussians, introduce a new primitive function called a ramp function whichaddresses this issue. This paper introduces three new mixed ramp-Gaussian basissets - STO-R, STO-RG and STO-R2G, made from a linear combination of ramp andGaussian primitive functions - which are derived from the single-core-zetaSlater basis sets for the elements Li to Ne. This derivation is done in ananalogous fashion to the famous STO-$n$G basis sets. The STO-RG basis functionsare found to outperform the STO-3G basis functions and STO-R2G outperformsSTO-6G, both in terms of wavefunction fit and other key quantities such as theone-electron energy and the electron-nuclear cusp. The second part of thispaper performs preparatory investigations into how standard all-Gaussian basissets can be converted to ramp-Gaussian basis sets through modifying the corebasis functions. Using a test case of the 6-31G basis set for carbon, wedetermined that the second Gaussian primitive is less important when fitting aramp-Gaussian core basis function directly to an all-Gaussian core basisfunction than when fitting to a Slater basis function. Further, we identifiedthe basis sets that are single-core-zeta and thus should be moststraightforward to convert to mixed ramp-Gaussian basis sets in the future.

Mixed ramp-Gaussian basis sets for core-dependent properties: STO-RG and STO-R2G for Li-Ne