Several theoretical models have been developed to understand the relationship be- tween the electron transmission through organic molecules, the chirality structures, and the electron spin orientation, that explain the high polarization of spin observed in the experiments. Analytical theoretical models contemplate the Hamiltonian associated with the movement of an electron through the molecule, including the contribution of Spin- Orbit (SO) interactions, and orbital overlaps for the kinetic terms. 
In this work, an analytical tight-binding model that includes Slater-Koster elements is derived to represent the contribution of orbital overlap in molecular structures. We in- clude an explicit dependence on the physical variables that describe the molecules (radius, pitch, the distance between atoms, among others.) and one 2p-orbital-base by the site in a general structure to determine general expressions of the Slater-Koster elements in specific coordinate systems. These elements are a quantum representation of the chemical bond between two atoms in a molecule. With the right parametrization of the molecular structure, we tested the behavior of the magnitude of the orbital overlaps with mechanical deformations. Our expressions reproduce the previously obtained analytical results for DNA and nanotubes and can be used to describe other structures, like benzene, oligopep- tides, among others. Finally, we write paths that connect pz orbital in atoms through the Slater-Koster terms, including SO interactions and Stark effect that can be used to generate a list of terms in a Hamiltonian tight-binding model.

Orbital coupling and the dependence of mechanical deformation in molecular structures

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