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Abstract
Several projects involving the periodic trends of various small systems were studied using rigorous computational methods. The first project involves comparing the spin-orbit splittings of p-block elements B--I as computed by various four-component methods. Recommendations are given with regards to the best basis set and method to use for computing spin-orbit splittings. In the second project, ground state singlet and triplet states of cyanomethlyene derivatives HBCN-, HCCN, HNCN+, HAlCN-, HSiCN, HPCN+, HGaCN-, HGeCN, and HAsCN+ were studied. Singlet-triplet gaps for these species were computed using a focal point analysis approach and insight is given for the observed trends. In the third project, the isomerization of HXYH to H2XY (X, Y = O, S, Se, Te) was explored. Various means of modelling the relativistic effects of the system are compared. Periodic trends in geometries and isomerization barriers were established and analyzed. Finally, the applicability of quantum mechanical methods as applied to larger system sizes is investigated through the implementation of an open-source adaptive QM/MM software.