6h atomic orbitals

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

The shape of the 6h orbitals. Orbital names are shown beneath the images. For each, the turquoise (cyan) zones are where the values of the 6h wave functions are positive while the white zones denote negative values.

The eleven 6h orbitals. Use the previous and next icons to see other views

The eleven 6h orbitals including nodes. Use the < and > icons to see other views

Nodes of the eleven 6h orbitals. Use the < and > icons to see other views

The 6h_z⁵ orbital (top row in the image above) is an abbreviation for 5h_{z(63z⁴ - 70z²r² + 15r⁴)}.

The 6h_yz⁴ orbital (left orbital in next to top row in the above image) is an abbreviation for 6h_{y(21z⁴–14z²r²+r⁴)}. The 6h_xz⁴ orbital (right orbital in next to top row in the above image) is an abbreviation for 6h_{x(21z⁴–14z²r²+r⁴)}. These two orbitals are related to each other by a 90° rotation about the z-axis.

The 6h_z³xy orbital (left orbital in third row from the top in the above image) is an abbreviation for 6h_{(2xy)(3z³–zr²)}. The 6h_{z³(x²–y²)} orbital (right orbital in third row from the top in the above image) is an abbreviation for 6h_{(x²–y³)(3z³–zr²)}. These two orbitals are related to each other by a 45° rotation about the z-axis.

The 6h_z²y³ (left orbital in fourth row from the top in the above image) is an abbreviation for 6h_{y(3x²–y²)(9z²–r²)}. The 6h_z²x³ orbital (right orbital in fourth row from the top in the above image) is an abbreviation for 6h_{x(x²–3y²)(9z²–r²)}. These two orbitals are related to each other by a 30° rotation about the z-axis.

The 6h_{z(4x³y–4xy³)} orbital is the left orbital in fifth row from the top in the above image). The 6h_{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 6h_yx⁴ (left orbital in bottom row in the above image) is an abbreviation for 6h_{y(5x⁴–10y²x²+y⁴)} and 6h_xy⁴ (right orbital in bottom row in the above image) is an abbreviation for 6h_{x(x⁴–10y²x²+5y⁴)}. They are related to each other by a 18° rotation about the z-axis.

The 6h orbitals do not have spherical nodes but the higher horbitals (7h, 8h, 9h, ...) are more complex since they have spherical nodes.