This thesis demonstrates how various computational chemistry methodologies and statistical approaches can assist in material discovery. Two directly related areas are membranes for protein separation and lithium-ion battery electrolytes for energy storage. Within the protein separation project, coarse-grained Brownian dynamics simulations are conducted to study the separation of two similarly sized proteins: villin headpiece and amyloid beta. The preferred membrane pore size and hydrophobicity are determined through calculating separation factors. The simulation also explains the preferred pore size through understanding the protein structural changes both inside and outside the membrane pores. In addition, a simple model based on the net hydropathy of a protein is developed and tested to estimate the separation factor trends of two additional protein pairs: bovine serum albumin and hemoglobin as well as lysozyme and cytochrome c. This work shows the benefits of simulation in material discovery: it presents fast methodologies to guide the experimental membrane design and to provide molecular details to explain the conclusions.  In the second project of this thesis, lithium-ion battery electrolytes are studied. While lithium-ion batteries have shown success in portable devices, there is still significant room for improvement in terms of safety, manufacturing cost, and durability. Molecular dynamics simulations, optimization algorithms, and quantitative structure property relationships are conducted to improve the predictive behaviors of electrolyte properties, which then could be used to design better liquid electrolytes. This work uses a "scaling method" that scales current molecular dynamics simulation parameters to improve the model estimation accuracy. Then an automated framework with Latin Hypercube Sampling and global optimization algorithms is developed to systematically find the scales. The automated framework, combining molecular dynamics simulations and optimization algorithms, provides a simple and systematic way to increase the prediction accuracy and could be extended to completely different systems. Different from this framework, a quantitative structure property relationship model that relates the properties with molecules' structural and molecular information is developed. The model is proven to be able to predict properties in a fast manner given sufficient training data. This project shows that exploring and utilizing statistical approaches can improve the predictive behaviors of existing simulation models. Overall, diverse topics could be studied through different computational methods serving as predictive tools. In addition, the future outlook of computational chemistry methodologies and their challenges are discussed in detail.