Nonadiabatic dynamics play an important role within electron transfer processes, excitation energy transfer events, the linear/nonlinear spectroscopy of molecular open quantum systems, and molecular junction quantum transport. All of the phenomena listed above can involve multiple electronic states, and the transfer rates between such states can be significantly enhanced or suppressed by including the dynamics of the nuclear degrees of freedom. In order to simulate the relevant nonadiabatic dynamics, a precise and computationally feasible electronic structure theory is necessary. Most importantly, the theory has to be simple enough so that analytic gradients and derivative couplings, which are fundamental building blocks for running nonadiabatic dynamics, can be achieved. In the first half of this dissertation, we propose a novel electronic structure theory which is based on HF/CIS or DFT/TDDFT but solves a long-standing issue about the topology of potential energy surfaces near conical intersections as calculated by these popular methods. In the second half of the dissertation, motivated by recent experiments about chiral induced spin selectivity, we turn to systems of a molecule attached to a metal lead(s). We refine the friction tensor formalism (which utilizes a nonequilibrium Green’s function technique) to get the “nuclear” Berry curvature effects which is a result of nonadiabaticity. We demonstrate that even in the presence of electron baths, the nuclear Berry curvature effects can be as important as the friction applied to the nuclear wave packet. We further include spin degrees of freedom to show that, through spin-orbit interactions and nuclear Berry curvature effects, different spin carriers behave differently in a molecular junction, resulting in spin polarization.