The hydrogen atom is the first real chemical system solved by instructors and/or students in undergraduate quantum chemistry. Despite the simplicity of the Laplacian for H in the xyz Cartesian coordinates, it must be converted into the rθφ spherical polar coordinates before the Schrödinger equation can be solved. This conversion can be formidably tedious for most students and instructors, and thus is often taught in a hand-waving manner or skipped completely; so is the process of solving the Schrödinger equation of H, especially if students are not familiar with partial differential equations. Even after students take quantum chemistry, solving the Schrödinger equation for H often remains a mystery. To demystify these derivations, hands-on exercises were designed for students to derive two-dimensional (2D) quantum chemistry for the H atom. After the reduction of the dimensionality, students are expected to express the 2D Laplacian in polar coordinates and then solve the Schrödinger equation all by themselves. The solved electronic structure of the 2D H atom reveals a quantum confinement effect caused by the reduced dimensionality. Motivated students can also study the ground and excited states of H2 in a 2D world. In sum, these exercises help reinforce students’ understanding of quantum chemistry of real atoms and molecules in three dimensions; they also challenge students to derive quantum chemistry for a fictitious 2D world and to critically evaluate the validity of their derivations.

Let students develop quantum chemistry for a two-dimensional world

255th National Meeting (2018)

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