# 7*i* atomic orbitals

There are 13 7*i* orbitals. These are labelled
7*i*_{z6}, 7*i*_{yz6}, 7*i*_{xz6}, 7*i*_{xyz4}, 7*i*_{(x2–y2)z4}, 7*i*_{y(3x2–y2)(11z3–3zr2)}, 7*i*_{x(x2–3y2)(11z3–3zr2)}, 7*i*_{(4xy)(x2–y2)(11z2–r2)}, 7*i*_{(x4–6x2y2+y4)(11z2–r2)}, 7*i*_{(yz)(5x4–10x2y2+y4)}, 7*i*_{(xz)(x4–10x2y2+5y4)}, 7*i*_{(6yx5–20x3y3+6xy5)}, and 7*i*_{x6–15x4y2+15x2y4–y6)}.

**The shape of the 7 i orbitals.** Orbital names are shown beneath the images. For each, the orange zones are where the values of the 7

*i*wave functions are positive while the white zones denote negative values.

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

The 7*i*_{yz6} orbital (left orbital in next to top row in the above image) is an abbreviation for 7*i*_{y(33z5–30z3r2+5zr4)}. The 7*i*_{xz6} orbital (right orbital in next to top row in the above image) is an abbreviation for 7*i*_{x(33z5–30z3r2+5zr4)}. These two orbitals are related to each other by a 90° rotation about the *z*-axis.

The 7*i*_{xyz4} orbital (left orbital in third row from the top in the above image) is an abbreviation for 7*i*_{(2xy)(33z4–18z2r2+r4)}. The 7*i*_{(x2–y2)z4} orbital (right orbital in third row from the top in the above image) is an abbreviation for 7*i*_{(x2–y2)(33z4–18z2r2+r4)}. These two orbitals are related to each other by a 45° rotation about the *z*-axis.

The 7*i*_{y(3x2–y2)(11z3–3zr2)} orbital is the left orbital in the fourth row from the top in the above image. The 7*i*_{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 7*i*_{(4xy)(x2–y2)(11z2–r2)} orbital is the left orbital in the fifth row from the top in the above image. The 7*i*_{(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 7*i*_{(yz)(5x4–10x2y2+y4)} orbital is the left orbital in the sixth row from the top in the above image. The 7*i*_{(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 7*i*_{(6yx5–20x3y3+6xy5)} orbital is the left orbital in the sixth row from the top in the above image. The 7*i*_{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 7*i* orbitals have no spherical nodes but the higher *i* orbitals (8*i*, 9*i*, ...) are more complex since they have one or more spherical nodes.

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.