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

Question

Every high school learner, in each corner of the world, faces the lesson History of Atom during his courses, just as I did. We learned about s, p, d and f orbitals, though there were no signs of orbitals in molecules.

Then I wondered, are there any other orbitals, simpler or more complex, than the four mentioned? Surprisingly, I learned that there are also usages for orbitals g, h, i and even k and l.

Yes, I use the word "usages". Because I believe, unless something is useful, it will never enter the domain of science. Anyway, I read in Wikipedia (though not much of it I did understand) that these orbitals are used when describing and doing the measurements of molecular orbitals.

Since no element in the periodic table has enough electrons to fill even orbital g (in its base state), in cases of molecular orbitals that have a g defined in themselves, atoms must have been excited. Excitation needs energy, doesn't it? Where does this energy come from? Isn't the formation of new bonds usually exothermic?

Answer 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

Answer 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.

Answer 3

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