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Atomic orbitals: 5f (general set)
For any atom, there are seven 5f orbitals. The f-orbitals are unusual in that there are two sets of orbitals in common use. Those shown here are the general set. The other set is known as the cubic set and might be more appropriate to use if the atom is in a cubic environment. Three of the orbitals are common to both sets. These are are the 5fxyz, 5fz3, and 5fz(x2-y2) orbitals.
Follow the links towards the base of the page for information about individual orbitals.
The shape of the seven 5f orbitals (general set). From left to right: (top row) 5fz3, (next to top row) 5fxz2, 5fyz2, (next to bottom row) 5fy(3x2-y2), 5fx(x2-3y2), (bottom row) 5fxyz, and 5fz(x2-y2). For each, the blue zones are where the wave functions have negative values and the silver zones denote positive values.
In the general set of 5f orbitals, there are four distinct shapes, each of which possess a number of planar and conical nodes. each of the 5f orbitals possesses one radial node.
The 5fxyz and 5fz(x2-y2) (bottom row in the image above) each have eight lobes and are related to each other by a 45° rotation about the z-axis. Each orbital has three nodal planes, which for the 5fxyz are the xy, xz, and yz planes.
The 5fy(3x2-y2) and 5fx(x2-3y2) orbitals (next to bottom row in the image above) are related to each other by a 90° rotation about the z-axis. Each orbital has six lobes separated by three nodal planes lying at 60° to each other.
The 5fxz2 and 5fyz2 orbitals (next to top row in the image above) are related to each other by a 90° rotation about the z-axis. At first sight, they are similar in shape to the 5fy(3x2-y2) and 5fx(x2-3y2) orbitals but they are not. While these orbitals contain six lobes, the nodal planes are not at 60° to each other and two of the six lobes are "bean-shaped". Look closely! In the case of the 5fxz2 orbital these two bean-shaped lobes lie on the x-axis while in the 5fyz2 case they lie along the y-axis. These differences may be appreciated better by examining the electron density plots for the 5fxz2 and 5fx(x2-3y2) orbitals.
The 5fz3 orbital (top row in the image above) has a planar node in the xy plane and two conical nodes orientated along the z-axis.
Links to 5f wave functions
Links to 5f electron density functions
Links to 5f electron "dot-density" functions
The Orbitron is a gallery of orbitals on the WWWThe OrbitronTM, a gallery of orbitals on the WWW, URL: http://winter.group.shef.ac.uk/orbitron/
Copyright 2002-2015 Prof Mark Winter [The University of Sheffield]. All rights reserved.
Document served: Sunday 16th February, 2020