We can not solve the Schroedinger equation exactly so assumptions must be made.
Usual assumption: the hydrogenic obitals are adequate and electrons occupy them in some fashion.
The occupation of electrons in orbitals is called the electron configuration – this is one way to describe the electronic properties of atoms.
Two guiding principals used to account for electron configurations:
Aufbau Principle: electrons occupy orbitals in such a manner to give the lowest possible total energy
Pauli Exclusion Principle: each electron in an atom is described by a unique set of quantum numbers (n, l, ml, ms) - i.e., two electrons per hydrogenic orbital
Periodic Table: based on electron configurations and can be used to predict them but not absolute (electron configurations are experimental quantities)
Aids in finding correct electron configurations from the Periodic Table:
Half-filled phenomenon: when d or f electrons are the valence shell, if a shift of 1 electron (occasionally 2 but this is not predictive) from an s orbital to the d or f orbital leads to a filled or half filled d or f orbital, this will stabilize the electron configuration.
Anions: add electrons to the neutral atom and follow above rules.
Cations: electrons are always removed from the orbitals of neutral atoms with the largest principal quantum number (n); the remaining electrons fill the orbitals with the lowest n consistent with the Pauli Principle
Another way to indicate electron configurations
A term symbol gives the required information about the angular momentum quantum numbers l, ml, and ms
For Ground States of atoms:
1) Only consider unfilled subshells; filled shells do not contribute
2) Fill the valence electrons into the unfilled subshell such that the highest total spin is attained using the highest possible ml values (this is Hund's Rule)
3) L =
4) S =
5) The term symbol is written as 2S+1L
2S+1 is called the total spin multiplicity or degeneracy and is written as a number
L is the total orbital angular momentum and is written as a letter: