Spin dependent electron transport in chiral molecules, the so-called chirality induced spin selectivity (CISS) effect, have attracted much attention over the past few years. Experimentally the spin polarization has been detected, and there is a theoretical consensus on the necessity of both spin-orbit coupling and geometrical helicity in order to get a non-vanishing spin polarization. Several model Hamiltonians has been proposed to describe the CISSS effect, and while they can yield spin polarization agreeing with the experimentally observed magnitudes, they are relying on unrealistic values of the spin orbit interaction parameters. In recent years the importance of electron correlation has been emphasized. Thus, this thesis presents the general theory on how to treat the CISS effect as a many body problem, taking electron correlation into account. The Hamiltonian modelling is described and one approach on how to treat the helical structure of the molecule and the spin-orbit coupling is presented. Building on this thesis, further studies will hopefully lead to a first principle understanding of the CISS effect.

The spin dynamics within a chiral and achiral molecule was investigated. It was investigated through a diminishing periodic potential, depicting the molecules being dropped onto a substrate. Born-Oppenheimers approximation and a tight-binding model was used to describe the molecules. Moreover, Schrödingers equation was defined for the problem and an iterative approach was used to solve it. The results indicated an induced spin selectivity for the chiral molecule, which varied over time. In contrast, the achiral molecule exhibited weaker spin selectivity. This difference might lie in how the spin couples to the linear momentum in the different structures.