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Over the past half century, computational chemistry has evolved from a niche field to a ubiquitous pillar of modern chemical research. Driven by the increased demand for computational chemistry in research settings, the undergraduate curriculum has evolved alongside to ensure that students are well-equipped for modern research. Toward this end, many excellent computational chemistry exercises have been developed that aim to teach students what kinds of questions computational chemistry can answer and how to properly interpret the results. However, there has been far less attention given to the complexities of determining how reliable computational results are and how constraining computational scaling can be. We present an undergraduate lab exercise that uses ab initio methods to predict the combustion energy of methane. The exercise walks students through the process of benchmarking errors on a small system (methane), estimating the computational cost to perform the same analysis on a larger system (propane), and justifying an affordable yet accurate method for a hypothetical study of the larger system. Furthermore, students are introduced to other cost-saving measures like basis set extrapolation and additive corrections. The entire exercise is intentionally designed to require little technical knowledge of computational chemistry and to be flexibly grafted into a standard undergraduate curriculum. In order to ensure accessibility, the exercise utilizes the free open source software Psi4 (available on any operating system) and provides a detailed installation and use guide for completing this lab. This lab will provide students the understanding of how to properly judge, select, and justify different computational models where cost and accuracy compete, a highly desirable set of skills that generalize to any computational science.

Preceding even the Hartree-Fock method, molecular integrals are the very foundation upon which quantum chemical molecular modeling depends. Discussions of molecular integrals are normally found only in advanced and technical texts or articles. The objective of the present article is to provide less experienced readers, or students in a physical/computational chemistry course, a thorough understanding of molecular integrals. Through a series of detailed Handouts, the student/reader can participate in the derivation of molecular integrals, and in turn implement them in computer code. Hartree-Fock theory is discussed in enough detail to motivate the molecular integrals and address such topics as the atomic orbital basis. An introduction to the programming language of choice, Python3, is provided, tailored toward developing the essential skills necessary for implementing molecular integrals. The article is intended to be useful not only to instructors of physical/computational chemistry, but also to any reader who has independently sought a primer on this elusive subject.