The energy-consumption by the chemical and petrochemical industry in the European Union (EU) accounts for about quarter of its energy footprint. Approximately half of this energy goes toward chemical separation, currently dominated by thermally-driven processes such as distillation and absorption and extraction. Based on the recent strategic energy technology plan (SET-plan) focusing on the energy-efficiency and the environment, EU needs to cut down the carbon emissions by 60-80% by 2050. Keeping this in mind, it is crucial to develop energy-effective separation processes. Partial or complete replacement of the thermally-driven separation processes by the membrane-based separation has been estimated to save up to 90% of energy consumption in separation. Two-dimensional (2D) nanoporous materials are emerging membrane platform for molecular separation offering ultrahigh permeance with an attractive molecular selectivity. In general, the 2D membranes can be classified in two categories. The first category is impermeable to molecules (for example, graphene), except when their pores are incorporated by a chemical or a physical etching. Here, the biggest bottleneck has been identifying a suitable pore-structure, and then incorporating similar pore-structure with precision (narrow pore-size-distribution) at a moderate to high density. We are highly interested in understanding a possible pore-structures in graphene that are stable and are attractive for molecular separation. For this, a fundamental understanding of the molecule-pore interaction is crucial. For example, hundreds of different pore-structures (number of missing carbon, zig-zag vs. armchair edge, pore-edge-functionalization) can be envisioned. Here, the most important question is that which lattice structure is the most promising one for a given separation. Since there are a number of promising nanoporous 2D materials and a number of possible pore-structures in graphene, it is highly important to efficiently screen the lattice structure. This thesis will investigate this employing ab-initio density functional theory (DFT) and classical molecular dynamic simulation. One can make a rough estimate by analyzing the size, topology, density, and chemical composition of the nanopore, however, an accurate prediction of the separation performance (permeance and selectivity) can only be made by calculating the entropic and enthalpic changes incurred during adsorption and at the transition state. The second category of 2D material are intrinsically nanoporous two-dimensional structure from the family of inorganic materials (zeolites, metal-organic frameworks, carbon-nitride, etc.), obtained from the exfoliated of their layered precursors. Recently, by screening a database of 2D materials, the group of Prof. Marzari (THEOS), has identified a set of nearly 200 inorganic nanoporous layered materials that seem to be attractive for molecular separations based on a purely geometric survey of materials in the Crystallographic Open Database (COD) and the Inorganic Crystal Structure Database (ICSD). In this thesis, we will study their separation efficiency using DFT and classical molecular dynamic simulation to discover new potentially interesting nanoporous 2D materials. Overall, the thesis will establish to a number of nanoporous 2D structures for energy-efficient molecular separation.