Designing new materials is very important and necessary for catching new development opportunities, like 3D printing, the internet of things (IoT), cyber-physical system, nanotechnology, biotechnology, clean energy, and overcoming the existing challenges, like air pollutions, water pollutions, climate change, shortages of food and clean water in the current world. The first step to designing novel materials is to fully understand the mechanisms of chemical processes and materials properties by computing free energy landscapes. This dissertation explores computational free energy calculations in different simulation scales, including lattice models, atomistic models, coarse-grained models, quantum models, via different molecular simulation methods, including Monte Carlo simulations, classical molecular dynamics simulations, and first principle molecular dynamics simulations to illustrate the inside mechanisms. We calculate the elastic constants of liquid crystals in both the lattice model (qualitative results) and the atomistic model (quantitative results) via mapping the elastic free energy landscapes. Next, we explore the confirmation free energy in gold clusters via first principle molecular dynamics simulations. Finally, we bridge machine learning methods and free energy calculations in studying the adhesive free energy between polymers and surfaces.