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Three-Dimensional Representation of Surface Spherical Harmonics and Their Squares Using Normal Projections: Some Comments on the Functions - Preparing for an Undergraduate Exercise

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Rudolf Kiralj

Rudjer Boskovic Institute, P.O.B. 1016, Zagreb, Bijenicka 54 HR-10 001, CROATIA

J. Chem. Educ., 1998, 75 (3), p 332

DOI: 10.1021/ed075p332

Publication Date (Web): March 1, 1998

Section:

History, Education, and Documentation

Abstract

Surface spherical harmonics and their squares occur in quantum chemistry as angular wavefunctions and angular probability densities, respectively. These functions can be found in a large variety of physico-chemical problems dealing with spherical symmetry or spherical surfaces. Thus there is a great need for exact graphical representation of the harmonics. At the undergraduate level, the definition, interpretation or graphical representation of the harmonics found in various literature can be inaccurate or source of confusion. This article focus on some important concepts as the result of a literature survey regarding the definition of surface spherical harmonics and spherical coordinates, the classification of spherical harmonics, and the occurence of the surface spherical harmonics and their squares in various fields. Knowing these concepts, undergraduates are prepared to make their own exercises - three-dimensional drawings of surface spherical harmonics and their squares based on normal projections and mechanical hand-drawing. By this, students can overcome their visualization difficulties about the functions, learn more about their nature as well as the principles of graphical representation.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Physical Chemistry

Keywords (Subject):

Quantum Chemistry

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