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Atomic orbitals: 4f electron densityThis page addresses the 4f_{xyz}, 4f_{x(z2y2)}, 4f_{y(z2x2)}, and 4f_{z(x2y2)} electron density functions. See below for links to images of the electron densities of the other 4f orbitals. Schematic plot of the 4f_{xyz} electron density function ψ_{4fxyz}. Blue represents negative values for the wave function and red represents positive values. Each of the eight lobes is identical as regards shape but each is orientated in a different direction. The line graph on the left is a plot of values along along the x = y = z line. The surface plot is on the x = y plane, so the line plot is along the diagonal from bottom left to top right of the surface plot. The "surface" of the orbital represents points for which the electron density for that orbital is the same  an isosurface. By choosing different values of electron density, denoted by the bar moving up and down on the line plot or by the moving plane on the surface plot, then the size of the threedimensional plot changes. All values are of necessity not negative since the square of any real number cannot be less than zero. The 4f_{xyz}, 4f_{x(z2y2)}, 4f_{y(z2x2)}, and 4f_{z(x2y2)} are identical in appearance and differ only is direction. The 4f_{x(z2y2)}, 4f_{y(z2x2)}, and 4f_{z(x2y2)} orbitals can be generated from the 4f_{xyz} orbital by 45° rotations about the x, y, and zaxes respectively. This is best seen when viewing all four together. Links to 4f electron density functions  

The Orbitron is a gallery of orbitals on the WWW The Orbitron^{TM}, a gallery of orbitals on the WWW, URL: http://winter.group.shef.ac.uk/orbitron/Copyright 20022015 Prof Mark Winter [The University of Sheffield]. All rights reserved. Document served: Monday 28th September, 2020 