Part A:Cathode wear is the limiting factor in the lifetime of electrolytic cells in aluminium production. One important reason for wear in carbon cathode materials is the penetration and diffusion of sodium from the melt, through the cathode materials. A long-term goal is to use quantum chemistry methods to investigate this phenomena on an atomic scale. In order to investigate large systems, density functional theory (DFT) must be applied. A comparison of results from calculations on a small model system using various density functionals to results from high level ab initio calculations shows that TPSS is the best suited functional for sodium-graphite interactions. Using this functional, a larger system consisting of two coronene molecules and a sodium atomhas been investigated and and diffusion coeffcients have been calculated based on harmonic transition state theory. Results show that calculated diffusion coeffcients match experimental observations well, but also confirm that the model system considered is not large enough to describe bulk graphite.Part B:Halogenated alkanes is a group of molecules that has received much attention, both in experiments and theoretical investigations. Here we focus on the 1,2-dihaloethanes. The restricted rotation around the C-C bond leads to a mixture of two rotamers, anti and gauche. Experiments and previous theoretical results show which conformer is lowest in energy depends on the subsituted halogen, gauche is the preferred conformer for fluoro-subsituted molecules, while anti is lowest in energy for the other halogens. This is attributed to steric repulsion. In order to further inestitgate this phenomena, the geometries of 1,2-difluoroethane and 1,2-dichloroethane are optimizedat the CCSD(T)/cc-pVDZ level. By replacing one or both of the carbon atoms by silicon, the corresponding halo(halomethyl)silane and 1,2-dihalodisilanes are formed. These molecules are also investigated using the same methods. Strutural parameters and conformational energies are compared to experimental observations and theoreticalresults from literature. Results from calculations correspond well with experiments (for the molecules where experimental values are available) and with previous calculations (in the case of silane analogues). As predicted, the accuracy of the calculations increase when including electron correlation (MP2 and CCSD(T)) compared to the results from HF.Part C:A computational method using wave functions constructed as a linear combination of non-orthonogal Slater determinants is proposed in an article by Koch and Dalgaard in 2003. Removing the requirement of orthogonality leads to a much more flexible wave function and more electron correlation can be recovered by using fewer determinants. The method is implemented in Dalton. Test calculations for systems where FCI results are available shows the method has favourable performance compared to MP2 and CCSD(T).