A hybrid approach is described, which combines stochastic classical molecular dynamics and first principles Density Functional theory to model the atomic and electronic structure of large molecular and solid-state systems. The stochastic molecular dynamics using Generalized Simulated Annealing (GSA) is based on the nonextensive statistical mechanics and thermodynamics. Examples are given of applications in linear-chain polymers, structural ceramics, impurities in metals, and pharmacological molecule-protein interactions.