A Combination of Various Visualization Methods of Atomic Orbitals and Representations of Their Wave Character

Abstract

This paper reports various kinds of visualization (isosurfaces, pseudo-three-dimensional representations, contour map, and cross sections) on the atomic orbitals of a hydrogen atom using multimedia techniques (animation and still image), and relation to visualization of the wave character by the oscillating circular membrane. These visualizations are very important, because they are suitable methods to understand the character of the atomic orbital wavefunctions. Interactive visualization methods on the wave character of the atomic orbitals of a hydrogen atom were investigated using large capacity and random accessible recording media, i.e., CD-R (Compact Disk Recordable). The wave character of atomic orbitals, such as a node or a nodal surface, was represented by using their classical oscillator in contrast to the atomic orbitals of a hydrogen atom through the interactive operations on a computer.

Visualization of Orbitals (9)–Hydrogen Atomic Orbital as a Standing Wave

“…Vibrations of a circular membrane of a kettledrum are known to be simulated by the use of Bessel functions [5][6][7][8][9][10][11][12][13][14]. The cross section pattern of three-dimensional atomic orbitals obtained from the wave equation of a hydrogen atom is shown to have wave character by comparison with the dynamic standing wave of a two-dimensional circular membrane.…”

Calculation of Potential Energy Concerning "H + Cl₂ → HCl + Cl" and Production of CG Movie for Learner to Acquire Its Image with Structures of Reactants and Reaction Profile

“…Visualization of computer graphics (CG) is a great help to realize not only images of molecules but also images for dynamical reaction mechanism. The visualization has been tried and reported, for example, the interactive movie of hydrogen atom-ic orbital based on the atomic orbital calculation [7,8] and molecular structures of 215 organic compounds in the field of life science based on the molecular mechanics calculation [9,10].…”

An Attempt to Construct an Isosurface Having Symmetry Elements

“…where, r = p x 2 +y 2 +z 2 , is to calculate the function value of χ 1s from r = 0 to +∞ until the value reaches an appropriate constant a, for example, χ 1s = a = 0:001 au ;3=2 (5) and to give a sphere centered on the origin and having radius r that satisfies the equation (5).…”

“…Isosurfaces are displayed by computer graphics, and are used as visualization methods in many fields of chemistry. Orbital wavefunction, probability density, electron density and electrostatic potential have been visualized as isosurfaces [1][2][3][4][5][6][7][8][9][10][11]. The most promising method to draw isosurfaces has been reported as "marching cubes algorithm" [12].…”