This dissertation describes a tight-binding technique that treats the dynamics of electrons and ions simultaneously. The main features are a generalized Hellmann- Feynman theorem, a standard, time-dependent, self-consistent-field description and the interaction picture. The time-dependence is incorporated by using Peierls Substitution. We also apply the velocity-Verlet algorithm to predict the motion of the ions. We first test the validity of this semi-empirical tight-binding approach on several smaller systems including ethylene, 2-butene, and stilbene. The cis-trans isomerization is modeled and in each case the results agree well with those obtained from other computational and empirical methods. Next, we use the tight-binding model to simulate the photoisomerization of the retinal molecule from its cis to trans form. The results are comparable to those obtained from experiments. The vibrational frequencies for retinal obtained using the force-constant techniques in this model agree well with those obtained from Fourier transform methods and a standard software. The cis-trans isomerization takes 217.91 fs to complete with a field strength of 1.0 gauss.cm, which is comparable to 200 fs reported from experiments. The isomerization depends on the strength of the vector potential, the time-step of the simulation and also the wavelength of the light. Using different parameters the isomerization takes place in 1-2 ps which is within the range reported from experimentation. The present semi-empirical technique provides an excellent compromise between computationally-prohibitive first principles methods and approximate empirical methods to model the motion of electrons and ions in a large molecule like retinal.
