7i atomic orbitals

There are 13 7i orbitals. These are labelled 7i_z⁶, 7i_yz⁶, 7i_xz⁶, 7i_xyz⁴, 7i_{(x²–y²)z⁴}, 7i_{y(3x²–y²)(11z³–3zr²)}, 7i_{x(x²–3y²)(11z³–3zr²)}, 7i_{(4xy)(x²–y²)(11z²–r²)}, 7i_{(x⁴–6x²y²+y⁴)(11z²–r²)}, 7i_{(yz)(5x⁴–10x²y²+y⁴)}, 7i_{(xz)(x⁴–10x²y²+5y⁴)}, 7i_{(6yx⁵–20x³y³+6xy⁵)}, and 7i_{x⁶–15x⁴y²+15x²y⁴–y⁶)}.

The 13 7i orbitals. Use the < and > icons to see other views

The 7i orbitals including orbital nodes. Use the < and > icons to see other views

Nodes of the 13 7i orbitals. Use the < and > icons to see other views

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The 7i_z⁶ orbital (top row in the image above) is an abbreviation for 7i_{(231z⁶ - 315z⁴r² + 105z²r⁴–5r⁶)}.

The 7i_yz⁶ orbital (left orbital in next to top row in the above image) is an abbreviation for 7i_{y(33z⁵–30z³r²+5zr⁴)}. The 7i_xz⁶ orbital (right orbital in next to top row in the above image) is an abbreviation for 7i_{x(33z⁵–30z³r²+5zr⁴)}. These two orbitals are related to each other by a 90° rotation about the z-axis.

The 7i_xyz⁴ orbital (left orbital in third row from the top in the above image) is an abbreviation for 7i_{(2xy)(33z⁴–18z²r²+r⁴)}. The 7i_{(x²–y²)z⁴} orbital (right orbital in third row from the top in the above image) is an abbreviation for 7i_{(x²–y²)(33z⁴–18z²r²+r⁴)}. These two orbitals are related to each other by a 45° rotation about the z-axis.

The 7i_{y(3x²–y²)(11z³–3zr²)} orbital is the left orbital in the fourth row from the top in the above image. The 7i_{x(x²–3y²)(11z³–3zr²)} orbital is the right orbital in the fourth row from the top in the above image. These two orbitals are related to each other by a 30° rotation about the z-axis.

The 7i_{(4xy)(x²–y²)(11z²–r²)} orbital is the left orbital in the fifth row from the top in the above image. The 7i_{(x⁴–6x²y²+y⁴)(11z²–r²)} orbital is the right orbital in the 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 7i_{(yz)(5x⁴–10x²y²+y⁴)} orbital is the left orbital in the sixth row from the top in the above image. The 7i_{(xz)(x⁴–10x²y²+5y⁴)} orbital is the right orbital in the sixth row from the top in the above image. These two orbitals are related to each other by a 18° rotation about the z-axis.

The 7i_{(6yx⁵–20x³y³+6xy⁵)} orbital is the left orbital in the sixth row from the top in the above image. The 7i_{x⁶–15x⁴y²+15x²y⁴–y⁶)} orbital is the right orbital in the sixth row from the top in the above image. These two orbitals are related to each other by a 15° rotation about the z-axis.

The 7i orbitals have no spherical nodes but the higher i orbitals (8i, 9i, ...) are more complex since they have one or more spherical nodes.