7h atomic orbitals

There are eleven 7h orbitals. These are labelled 7h_z⁵, 7h_yz⁴, 7h_xz⁴, 7h_z³xy, 7h_{z³(x²–y²)}, 7h_z²y³, 7h_z²x³, 7h_{z(4x³y–4xy³)}, 7h_{z(x⁴–6x²y²+y⁴)}, 7h_yx⁴, and 7h_xy⁴.

The shape of the 7h orbitals. Orbital names are shown beneath the images. For each, the turquoise (cyan) zones are where the values of the 7h wave functions are positive while the white zones denote negative values.

The eleven 7horbitals. Use the previous and next icons to see other views

The 7horbitals including orbital nodes. Use the previous and next icons to see other views

Nodes of the eleven horbitals. Use the previous and next icons to see other views

The 7h_z⁵ orbital (top row in the image above) is an abbreviation for 5h_{z(63z⁴ - 70z²r² + 15r⁴)}.

The 7h_yz⁴ orbital (left orbital in next to top row in the above image) is an abbreviation for 7h_{y(21z⁴–14z²r²+r⁴)}. The 7h_xz⁴ orbital (right orbital in next to top row in the above image) is an abbreviation for 7h_{x(21z⁴–14z²r²+r⁴)}. These two orbitals are related to each other by a 90° rotation about the z-axis.

The 7h_z³xy orbital (left orbital in third row from the top in the above image) is an abbreviation for 7h_{(2xy)(3z³–zr²)}. The 7h_{z³(x²–y²)} orbital (right orbital in third row from the top in the above image) is an abbreviation for 7h_{(x²–y³)(3z³–zr²)}. These two orbitals are related to each other by a 45° rotation about the z-axis.

The 7h_z²y³ (left orbital in fourth row from the top in the above image) is an abbreviation for 7h_{y(3x²–y²)(9z²–r²)}. The 7h_z²x³ orbital (right orbital in fourth row from the top in the above image) is an abbreviation for 7h_{x(x²–3y²)(9z²–r²)}. These two orbitals are related to each other by a 30° rotation about the z-axis.

The 7h_{z(4x³y–4xy³)} orbital is the left orbital in fifth row from the top in the above image). The 7h_{z(x⁴–6x²y²+y⁴)} orbital is the right orbital in fifth row from the top in the above image. These two orbitals are related to each other by a 22.5° rotation about the z-axis.

The 7h_yx⁴ (left orbital in bottom row in the above image) is an abbreviation for 7h_{y(5x⁴–10y²x²+y⁴)} and 7h_xy⁴ (right orbital in bottom row in the above image) is an abbreviation for 7h_{x(x⁴–10y²x²+5y⁴)}. They are related to each other by a 18° rotation about the z-axis.

The 7h orbitals each have one spherical nodes but the higher horbitals (8h, 9h, ...) are more complex since they have additional spherical nodes while lower orbitals (7h have none.