In this thesis, the implementation of the incremental scheme for open-shell systems with unrestricted Hartree-Fock reference wave functions is described. The implemented scheme is tested within robustness and performance with respect to the accuracy in the energy and the computation times. New approaches are discussed to implement a fully automated incremental scheme in combination with the domain-specific basis set approximation. The alpha Domain Partitioning and Template Equalization are presented to handle unrestricted wave functions for the local correlation treatment. Both orbital schemes are analyzed with a test set of structures and reactions. As a further goal, the DSBSenv orbital basis sets and auxiliary basis sets are optimized to be used as environmental basis in the domain-specific basis set approach. The performance with respect to the accuracy and computation times is analyzed with a test set of structures and reactions. In another project, a scheme for the optimization of auxiliary basis sets for uranium is presented. This scheme was used to optimize the MP2Fit auxiliary basis sets for uranium. These auxiliary basis enable density fitting in quantum chemical methods and the application of the incremental scheme for systems containing uranium. Another project was the systematical analysis of the binding energies of four water dodecamers. The incremental scheme in combination with the CCSD(T) and CCSD(T)(F12*) method were used to calculate benchmark energies for these large clusters.