Incoming links: Electron configuration
Allow us to determine with good approximation in a multi-electron atom which electron configuration have more energy. It is a bit like the Aufbau principle, but at a finer resolution.
Note that this is not trivial since there is no explicit solution to the Schrödinger equation for multi-electron atoms like there is for hydrogen.
For example, consider carbon which has electron configuration 1s2 2s2 2p2.
If we were to populate the 3 p-orbitals with two electrons with spins either up or down, which has more energy? E.g. of the following two:
m_L -1 0 1
u_ u_ __
u_ __ u_
__ ud __Quantum numbers appear directly in the Schrödinger equation solution for the hydrogen atom.
However, it very cool that they are actually discovered before the Schrödinger equation, and are present in the Bohr model (principal quantum number) and the Bohr-Sommerfeld model (azimuthal quantum number and magnetic quantum number) of the atom. This must be because they observed direct effects of those numbers in some experiments. TODO which experiments.
E.g. The Quantum Story by Jim Baggott (2011) page 34 mentions:This refers to forbidden mechanism. TODO concrete example, ideally the first one to be noticed. How can you notice this if the energy depends only on the principal quantum number?
As the various lines in the spectrum were identified with different quantum jumps between different orbits, it was soon discovered that not all the possible jumps were appearing. Some lines were missing. For some reason certain jumps were forbidden. An elaborate scheme of ‘selection rules’ was established by Bohr and Sommerfeld to account for those jumps that were allowed and those that were forbidden.
Quantum Numbers, Atomic Orbitals, and Electron configurations by Professor Dave Explains (2015)
Source. He does not say the key words "Eigenvalues of the Schrödinger equation" (Which solve it), but the summary of results is good enough.This notation is so confusing! People often don't manage to explain the intuition behind it, why this is an useful notation. When you see Indian university entry exam level memorization classes about this, it makes you want to cry.
The key reason why term symbols matter are Hund's rules, which allow us to predict with some accuracy which electron configurations of those states has more energy than the other.
web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf puts it well: electron configuration notation is not specific enough, as each such notation e.g. 1s2 2s2 2p2 contains several options of spins and z angular momentum. And those affect energy.
This is why those symbols are often used when talking about energy differences: they specify more precisely which levels you are talking about.
Basically, each term symbol appears to represent a group of possible electron configurations with a given quantum angular momentum.
We first fix the energy level by saying at which orbital each electron can be (hyperfine structure is ignored). It doesn't even have to be the ground state: we can make some electrons excited at will.
The best thing to learn this is likely to draw out all the possible configurations explicitly, and then understand what is the term symbol for each possible configuration, see e.g. term symbols for carbon ground state.
It also confusing how uppercase letters S, P and D are used, when they do not refer to orbitals s, p and d, but rather to states which have the same angular momentum as individual electrons in those states.
It is also very confusing how extremelly close it looks to spectroscopic notation!
The form of the term symbol is:
The can be understood directly as the degeneracy, how many configurations we have in that state.
Bibliography:
- chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Electronic_Spectroscopy/Spin-orbit_Coupling/Atomic_Term_Symbols
- chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/08%3A_Multielectron_Atoms/8.08%3A_Term_Symbols_Gives_a_Detailed_Description_of_an_Electron_Configuration The PDF origin: web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf
- chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Inorganic_Coordination_Chemistry_(Landskron)/08%3A_Coordination_Chemistry_III_-_Electronic_Spectra/8.01%3A_Quantum_Numbers_of_Multielectron_Atoms
- physics.stackexchange.com/questions/8567/how-do-electron-configuration-microstates-map-to-term-symbols How do electron configuration microstates map to term symbols?