This thesis presents a new theoretical formalism which incorporates dynamical effects in atomistic electronic structure and related calculations. This research, fundamental by nature, brings about a deeper understanding of the dynamical processes in a range of materials. This establishes technologically important correlation with experimentally measured macroscopic properties and materials characterization. This method—the first of its kind—is a natural and long overdue extension of customary adiabatically separated time-independent electronic structure methods. It accounts explicitly for atomic motion due to thermal and zero-point vibration. The approach developed requires no direct treatment of time dependence in the quantum mechanical calculations, making the method widely applicable utilizing currently available electronic structure and ab-initio molecular dynamics software. The formalism is extensively applied and demonstrated for the linear optical response of bulk gallium arsenide and electronic structure of the C(111) 2 x 1 surface. Both cases are complimented by comparison of key observables to experimental data which may be used to judge the quality of the results. The results are found to be in good agreement with experimental data, with most exceptions being readily explainable and well understood.