# What are the different kinds of f orbitals?

Apr 1, 2018

$f$ orbitals are very complex and difficult to describe with words.

#### Explanation:

So there is only one kind of $f$ orbitals and that is the $f$ orbital. I suppose you mean the different shapes of the $f$ orbitals.

So the $f$ orbitals have 7 different shapes (since $n = 4$ and $l = 3$ resulting in: $- 3 , - 2 , - 1 , 0 , 1 , 2 , 3$) These structures can be seen in this picture:

With the different dimensions. Hope it helps.

Apr 2, 2018

They are quite complicated, and can often do combinations of $\sigma$, $\pi$, $\delta$, and even $\phi$ bonding.

For an introduction into these kinds of bonds:

$\sigma$ bonds are in every chemical bond. $\pi$ bonds start showing up in double and triple bonds (e.g. ${\text{O}}_{2}$, ${\text{N}}_{2}$, etc), $\delta$ bonds start showing up in quadruple bonds (see link), and $\phi$ bonds aren't seen until a sextuple bond is made (e.g. in ${\text{Mo}}_{2}$ or ${\text{W}}_{2}$).

The $4 f$ orbitals can be separated into three types (here, we use the convention that outer atoms point their $y$ axes inwards and $z$ axes upwards):

1) Two lobes - $\sigma$ bonding only (${m}_{l} = 0$)

• The ${f}_{{z}^{3}}$ (${m}_{l} = 0$) is the only one that only $\sigma$ bonds. It can bond head-on along the $z$ axis.

2) Six lobes - $\sigma$ and $\pi$ bonding, OR $\phi$ bonding only (${m}_{l} = - 3 , + 3 , - 1 , + 1$)

• The ${f}_{y \left(3 {x}^{2} - {y}^{2}\right)}$ (${m}_{l} = - 3$) can $\sigma$ bond along the $x$ axes (for example, with a ${p}_{y}$ orbital) AND $\pi$ bond along the $y$ axes (for example, with a ${p}_{x}$ orbital, or a ${d}_{x y}$ orbital).

It can alternatively form a $\phi$ bond (a six-lobed side-on overlap) along the $x y$ plane (with another ${f}_{y \left(3 {x}^{2} - {y}^{2}\right)}$ orbital in a bimetallic complex).

• The ${f}_{x \left({x}^{2} - 3 {y}^{2}\right)}$ (${m}_{l} = + 3$) can $\sigma$ bond along the $y$ axes (for example, with a ${p}_{y}$ orbital) AND $\pi$ bond along the $x$ axes (for example, with a ${p}_{x}$ orbital, or a ${d}_{x y}$ orbital).

It can alternatively form a $\phi$ bond (a six-lobed side-on overlap) along the $x y$ plane (with another ${f}_{x \left({x}^{2} - 3 {y}^{2}\right)}$ orbital in a bimetallic complex).

• The ${f}_{y {z}^{2}}$ (${m}_{l} = - 1$) can form decent $\sigma$ bonds along the $y$ axes, AND/OR $\pi$ bonds along the $y$ AND $z$ axes.

It can alternatively form a $\phi$ bond (a six-lobed side-on overlap) along the $y z$ plane (with another ${f}_{y {z}^{2}}$ orbital in a bimetallic complex).

• The ${f}_{x {z}^{2}}$ (${m}_{l} = + 1$) can form decent $\sigma$ bonds along the $x$ axes, AND/OR $\pi$ bonds along the $x$ AND $z$ axes.

It can alternatively form a $\phi$ bond (a six-lobed side-on overlap) along the $x z$ plane (with another ${f}_{x {z}^{2}}$ orbital in a bimetallic complex).

3) Eight lobes - $\pi$ bonding OR $\delta$ bonding (${m}_{l} = - 2 , + 2$)

• The ${f}_{z \left({x}^{2} - {y}^{2}\right)}$ (${m}_{l} = - 2$) is for $\pi$ bonding along ANY of the axes, $x , y$, or $z$. The lobes lie above and below each of the axes, but also along them.

It can alternatively form a $\delta$ bond with another ${f}_{z \left({x}^{2} - {y}^{2}\right)}$ orbital in a bimetallic complex.

• The ${f}_{x y z}$ (${m}_{l} = + 2$) is for $\delta$ bonding along ANY of the planes ($x z , y z , x y$) (for example, with ${d}_{x y}$, ${d}_{x z}$, or ${d}_{y z}$ orbitals).

It can alternatively form a $\pi$ bond with another ${f}_{x y z}$ orbital in a bimetallic complex.