Summary

 

This diagram was created with Mathematica.

(*Source code written in Mathematica 6.0 by Steve Byrnes, March 2011. This source code is public domain.*)
(*Shows schematic electron wavefunctions for 1s orbital of hydrogen atom, and 1s bonding and
antibonding orbitals of hydrogen molecule. Plotted as a 1D slice of a 3D system.
All graphs are schematic: I'm not actually solving the Schrodinger equation, but hopefully it looks like I did. *)

ClearAll["Global`*"]

(***Oscillation frequencies, in units of oscillations per cycle of the animated gif***)

sfreq = 4;
bondfreq = 3;
antibondfreq = 5;

(***Wavefunction normalization coefficients***)

scoef = 0.893;
bondcoef = 0.618;
antibondcoef = 0.646;

(***Define wavefunctions***)

s[x_, t_] := scoef * Exp[-(x - 1.25)^2]*Exp[-2*Pi*I*sfreq*t];
bond[x_, t_] := bondcoef * (Exp[-x^2] + Exp[-(x - 2.5)^2]) * Exp[-2*Pi*I*bondfreq*t];
antibond[x_, t_] := antibondcoef * (Exp[-x^2] - Exp[-(x - 2.5)^2]) * Exp[-2*Pi*I*antibondfreq*t];

(***Make individual graphs***)

SetOptions[Plot, {Ticks -> None, PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Pink]}, 
   Axes -> {True, False}, PlotRange -> {{-2.5, 5}, {-1, 1}}, 
   AspectRatio -> 1.1}, Frame -> True, FrameTicks -> None];
SetOptions[ListPlot, {Ticks -> None, PlotStyle -> Directive[Red, AbsolutePointSize[10]]}, Axes -> {True, False}];
OneProton = ListPlot[{{1.25, 0}}];
TwoProtons = ListPlot[{{0, 0}, {2.5, 0}}];
SWaves[t_] := Plot[{Re[s[x, t]], Im[s[x, t]]}, {x, -2.5, 5}];
BondWaves[t_] := Plot[{Re[bond[x, t]], Im[bond[x, t]]}, {x, -2.5, 5}];
AntibondWaves[t_] := Plot[{Re[antibond[x, t]], Im[antibond[x, t]]}, {x, -2.5, 5}];
SPlot[t_] := Show[SWaves[t], OneProton];
BondPlot[t_] := Show[BondWaves[t], TwoProtons];
AntibondPlot[t_] := Show[AntibondWaves[t], TwoProtons];

(***Draw all graphs together, arranged in the shape of a molecular orbital diagram***)

TotalPlot[t_] := 
 Graphics[{White, Rectangle[{0, 0}, {1.5, 1}], 
   Inset[SPlot[t], ImageScaled[{0, 0.5}], ImageScaled[{0, 0.5}], .45],
   Inset[SPlot[t], ImageScaled[{1, 0.5}], ImageScaled[{1, 0.5}], .45], 
   Inset[BondPlot[t], ImageScaled[{0.5, 0}], ImageScaled[{0.5, 0}], .45],
   Inset[AntibondPlot[t], ImageScaled[{0.5, 1}], ImageScaled[{0.5, 1}], .45]}, ImageSize -> 300]

(***Export animation***)
   
output = Table[TotalPlot[t], {t, 0, 90/91, 1/91}];
SetDirectory["C:\\Users\\Steve\\Desktop"]
Export["test.gif", output]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.

The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse