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

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?

• I strongly disagree with the notion of "unless something is useful, it will never enter the domain of science". There is a branch called Applied Science, where this is true, but for most other science "usefulness" is not a criterion. – Gerhard Dec 20 '14 at 21:04
• Here, by usage I don't mean sth that humans will make a use of it!:) I mean the notion should be able to enter a specific field of theory, no matter how much "applicable" it is. – M.A.R. Dec 20 '14 at 21:07
• I am not sure I follow your train of though entirely... Anyway, a part answer to your question: you can excite your electron quite easily by eg electromagnetic radiation of the right wavelength. I would also assume that when the higher orbitals will be briefly occupied when eg a cation accepts a new electron - but I am no theoretical chemist... – Gerhard Dec 20 '14 at 21:16

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

• can you please give more description of your answer? I repeat the question: Where does the energy of excitation come from? Or is this just my misunderstanding? – M.A.R. Dec 25 '14 at 19:39
• The energy of excitation comes from electromagnetic radiation (light). It could be visible, infrared, ultraviolet, or microwave depending upon the transition. – DavePhD Dec 28 '14 at 7:26

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.

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