Molecular Modeling with the Monte Carlo Method

Understanding how molecules interact and behave in physical systems is fundamental to modern chemistry and physics, yet analytical solutions quickly become impossible. Computational molecular modeling using the Monte Carlo method offers a powerful, probabilistic approach to simulate and analyze these complex thermodynamic systems. This text-only course guides you through the core principles of molecular simulation, taking you from foundational statistical mechanics to writing your own simulation code. You will learn how to model simple physical states—specifically ideal gases and hard-sphere systems—and extract meaningful thermodynamic properties. What you'll learn: Understand the core mathematical concepts behind Monte Carlo simulations and probability theory; Model the behavior of an ideal gas using probabilistic algorithms; Implement the Metropolis algorithm to simulate hard-sphere molecular interactions; Write clean, efficient simulation code using modern scientific computing practices; Calculate and analyze key thermodynamic properties like pressure, energy, and radial distribution functions; Apply vectorization techniques to optimize computational performance. The course begins with essential definitions of statistical ensembles and probability before moving step-by-step into coding simulations. You will progress from simple non-interacting particles to colliding hard-sphere systems, analyzing simulation data at each stage. This course is designed for beginners in computational science, physics, or chemistry. No prior experience with molecular modeling is required, though basic familiarity with programming concepts is helpful. Start reading today to build your own molecular simulations from the ground up.