5g atomic orbitals

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

The shapes of the nine 5g orbitals. From left to right: (top row) 5g_z⁴; (next to top row) 5g_z³y and 5g_z³x; (centre row) 5g_z²xy and 5g_{z²(x² - y²)}; (next to bottom row) 5g_zy³ and 5g_zx³, (bottom row) 5g_xy(x²-y²) and 5g_x⁴+y⁴. For each, the purple zones are where the wave functions have positive values and the white zones denote negative values.

The five 5g orbitals. Use the previous and next icons to see other views

The five 5g orbitals including orbital nodes. Use the previous and next icons to see other views

Nodes of the five 5g orbitals. Use the previous and next icons to see other views

The 5g_z⁴ orbital (top row in the image above) is an abbreviation for 5g_{35z⁴ - 30z²r² + 3r⁴}.

The 5g_z³y orbital (left orbital in next to top row in the above image) is an abbreviation for 5g_{yz(7z² - 3r²)}. The 5g_z³x orbital (right orbital in next to top row in the above image) is an abbreviation for 5g_{xz(7z² - 3r²)}. These two orbitals are related to each other by a 90° rotation about the z-axis.

The 5g_z²xy orbital (left orbital in centre row in the above image) is an abbreviation for 5g_{xy(7z² - r²)}. The 5g_{z²(x² - y²)} orbital (right orbital in centre row in the above image) is an abbreviation for 5g_{(x² - y²)(7z² - r²)}. These two orbitals are related to each other by a 45° rotation about the z-axis.

The 5g_zy³ (left orbital in next to bottom row in the above image) is an abbreviation for 5g_{yz(3x² - y²)}. The 5g_zx³ orbital (right orbital in next to bottom row in the above image) is an abbreviation for 5g_{xz(x² - 3y²)}. These two orbitals are related to each other by a 30° rotation about the z-axis.

The 5g_xy(x²-y²) (left orbital in bottom row in the above image) and 5g_(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.