Chemistry - What is the usage of orbitals more complex than f orbitals?

Solution 1:

Surprisingly, I learned that there are also usages for orbitals g,h,i and even j.

Actually, the letter "j" is not used, so it is s, p, d, f, g, h, i, k, l, etc.

The higher angular momentum orbitals do enter the domain of science, due to excited states of atoms. Transitions to and from excited states are observable through atomic spectroscopy.

For example there is the article Microwave spectroscopy of Al I atoms in Rydberg states: D and G terms

Solution 2:

One use of orbitals beyond f is in computational chemistry to construct basis sets. It's important to remember that orbitals are entirely a mathmatical construct that chemists and physicists have found useful in conceptualizing chemical properties and so we can use the idea of orbitals outside of their normal context of framing the periodic table. To develop a nearly complete basis set for certain elements, one can use a large collection of orbitals of different angular momentum. As an older example, Nesbet, Barr, and Davidson attempted to compute the energy of a neon atom using a basis set that included up to i orbitals.

As an interesting side note, I found a nice visualization of the orbitals (really the spherical harmonics, but its essentially synonymous in this case) up to n on Sylvain Paris's MIT page.

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Solution 3:

The letters beyond $f$ can also appear in higher orbital angular momentum states, as, $^1G$ in a low spin $d^2$ complex.