# 5*g* atomic orbitals

For any atom, there are nine 5*g* orbitals. The higher *g*-orbitals (6*g* and 7*g*) are more complex since they have spherical nodes.

**The shapes of the nine 5 g orbitals.** From left to right:
(top row) 5

*g*

_{z4}; (next to top row) 5

*g*

_{z3y}and 5

*g*

_{z3x}; (centre row) 5

*g*

_{z2xy}and 5

*g*

_{z2(x2 - y2)}; (next to bottom row) 5

*g*

_{zy3}and 5

*g*

_{zx3}, (bottom row) 5

*g*

_{xy(x2-y2)}and 5

*g*

_{x4+y4}. For each, the purple zones are where the wave functions have positive values and the white zones denote negative values.

The 5*g*_{z4} orbital (top row in the image above) is an abbreviation for 5*g*_{35z4 - 30z2r2 + 3r4}.

The 5*g*_{z3y} orbital (left orbital in next to top row in the above image) is an abbreviation for 5*g*_{yz(7z2 - 3r2)}. The 5*g*_{z3x} orbital (right orbital in next to top row in the above image) is an abbreviation for 5*g*_{xz(7z2 - 3r2)}. These two orbitals are related to each other by a 90° rotation about the *z*-axis.

The 5*g*_{z2xy} orbital (left orbital in centre row in the above image) is an abbreviation for 5*g*_{xy(7z2 - r2)}. The 5*g*_{z2(x2 - y2)} orbital (right orbital in centre row in the above image) is an abbreviation for 5*g*_{(x2 - y2)(7z2 - r2)}. These two orbitals are related to each other by a 45° rotation about the *z*-axis.

The 5*g*_{zy3} (left orbital in next to bottom row in the above image) is an abbreviation for 5*g*_{yz(3x2 - y2)}. The 5*g*_{zx3} orbital (right orbital in next to bottom row in the above image) is an abbreviation for 5*g*_{xz(x2 - 3y2)}. These two orbitals are related to each other by a 30° rotation about the *z*-axis.

The 5*g*_{xy(x2-y2)} (left orbital in bottom row in the above image) and 5*g*_{(x4+y4)} (right orbital in bottom row in the above image) are related to each other by a 22.5° rotation about the *z*-axis.

The Orbitron

^{TM}, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/

Copyright 2002-2023 Prof. Mark Winter [The University of Sheffield]. All rights reserved.