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Orbital Viewer by David Manthey

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Orbital Viewer by David Manthey Orbital Viewer by David Manthey February 1998 Updated September 2004 Orbital Viewer Manual copyright 1998-2004 by David Manthey Orbital Viewer Program copyright 1986-2004 by David Manthey 2 TABLE OF CONTENTS Table of Contents................................................................... 3 Orbital Specification Files (.ORB).......................35 Introduction................................................................................5 Example File ....................................................................... 41 Orbitals.............................................................................................7 File Formats - Output........................................................42 Lighting........................................................................................10 Orbital Specification Files (.ORB).......................42 Stereo Display..........................................................................12 Orbital Viewer Files (.OV) ........................................42 Monoscopic.........................................................................13 Portable Pixel Map Files (.PPM)...........................42 Stereoscope...........................................................................13 TIFF Files (.TIF)...................................................................42 Building a Stereoscope ..........................................13 Bitmap Files (.BMP)........................................................43 Interlaced...............................................................................14 VRML Files (.WRL).........................................................43 Red-Blue ..................................................................................15 AVI Files (.AVI) ..................................................................43 Stereogram............................................................................15 Digistar II Files (.TXT)..................................................44 Overlay....................................................................................15 Orbital Mathematics.........................................................45 Chromadepth ....................................................................16 Introduction.......................................................................45 Camera.......................................................................................... 17 List of Symbols .................................................................45 Cutaway.......................................................................................18 Electron Orbital Wave Function ......................46 Rendering Method..............................................................19 Orbital Function Gradient .....................................49 Point Drawing Mode........................................................20 Imaging Mathematics......................................................52 Polygon Drawing Mode..................................................21 Camera Equations..........................................................52 Raytracing Drawing Mode..........................................24 Raytracing ............................................................................53 Asymptote Drawing Mode.......................................... 29 Grand Table..............................................................................55 Sequences................................................................................... 30 Program History ...................................................................56 Interpolation ..................................................................... 30 Author’s Note.......................................................................... 57 Incremental Position...................................................33 Contact Information................................................... 57 Interpolated Values.......................................................33 Acknowledgements ..................................................... 57 Sequence Output............................................................ 34 References ..................................................................................58 File Formats – Input............................................................35 3 4 INTRODUCTION Orbital Viewer is a program for visualizing atomic and molecular orbitals. Orbitals are the electron probability functions which are computed from Schrödinger’s Equation. The example shown in Figure 1 is a 4f0 orbital (n = 4, l = 3 (f), ml = 0), plotted with a surface of probability where Ψ2 = 10-4. It is illuminated with two light sources to better show its shape. There are two different versions of Orbital Viewer. The first is a graphics program, compatible with Windows 95, Windows NT, and Windows 3.x (with WIN32s installed). This program requires an 80386 processor or better, and is called OV.EXE. The second version is a command line program which can theoretically be run on any machine which has an ANSI C compatible compiler. This program is called ANSIORB.EXE (or something similar, as some computers do not require the .EXE extension 2 -4 to determine file type). Figure 1: 4f0, Ψ =10 Although this manual is focused on OV.EXE (the graphics version), almost all of the options available through the graphics interface are available to the command line version. The principal difference between them is that the graphics version provides an easier way to manipulate and modify an orbital, while the command line version is typically faster and runs on more machines. Both versions can read the same orbital specification file format. This program can display orbitals in three general ways: (1) Probability density: This shows the probability at each point in the orbital based on how intense the colors are, or how many points are present. See Figure 2a. (2) Surface of probability: This is a surface of constant probability. Like an line on a contour map, this displays the location where the probability has a constant value. See Figure 2b. (3) Asymptotes: These are the conic sections, spheres, and other shapes where the probability is zero. See Figure 2c. The phase of the orbital changes at the asymptote. 5 Figure 2a: 4f0, probability density Figure 2b: 4f0, surface of Figure 2c: 4f0, asymptotes plot probability, Ψ2=10-4 Throughout this manual, orbitals have different colors for the positive and negative phases. Phases are taken as defined in Condon and Shortley (see References). In all figures the blue or darker color is the positive phase while the orange color or lighter color is the negative phase. There are also three general types of display: (1) Point density plot: This is a probability density representation of the orbital. Points are randomly selected based on the probability of the orbital. See Figure 3a. This can be combined with a polygon asymptote plot. None of the lighting options apply to this style. (2) Polygon surface plot: This is an approximation of a surface of constant probability, with the vertices of the polygons at the surface. See Figure 3b. This can be combined with a polygon asymptote plot. Opacity is approximated, and shadows and indices of refraction can not be applied to this style. (3) Raytracing: This style supports the most features, including surface, probability, and interior opacity, precise asymptotes, point light sources with shadows, and indices of refraction. See Figure 3c. This is also the most computationally intensive style. Figure 3a: 4f0, point density plot Figure 3b: 4f0, polygon surface Figure 3c: 4f0, raytraced surface plot plot There are many options within each display type. Additionally, lighting can be adjusted, a cutaway can be added (to show the interior of the orbital), and six different forms of stereo displays are supported (to show the orbital in 3D). This manual includes brief examples of the different functions, plus a guide to the input file format, and a section on the equations used to calculate the orbitals. 6 ORBITALS The most important item that can be specified in Orbital Viewer is the atom or molecule which will be drawn. This is specified in the Display / Orbitals menu option. Selecting this displays the dialog shown in Figure 4. Any positive number of atoms can be specified. Each atom is specified by three quantum numbers: n, l, and m. n is the principal quantum number, l is the orbital quantum number, and m is the angular momentum quantum number (sometimes referred to as the magnetic quantum number). m is often written as ml, with the spin quantum number written as ms. The spin quantum number does not effect the shape of the orbital, and, therefore, is not an adjustable parameter. n can be any positive integer. However, due to Figure 4: Orbital Dialog the limits of computer precision, n is restricted to the range of 1 to 30. l can be any value between 0 and n-1, inclusive. m can be any value between –l and +l, inclusive. The actual shape of the orbital is dependant on n-l, l-|m|, and m. The orbital quantum number, l, is often designated as a letter. Letter designations are given to l values from 0 to 20 as follows: {s, p, d, f, g, h, i, k, l, m, n, o, q, r, t, u, v, w, x, y, z}, where s corresponds to l=0, p to l=1, d to l=2, and so forth. The first four of these are due to spectroscopy historical reasons, with s being short for sharp, p for principal, d for diffuse, and f for fine. The remaining letters were assigned in order, skipping those
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