Electron Configurations

Aufbau Principle
The Aufbau principle (from the German Aufbau meaning "building up, construction": also Aufbau rule or building-up principle) is used to determine the electron configuration of an atom, molecule or ion. The principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons. As they are added, they assume their most stable conditions (electron orbitals) with respect to the nucleus and those electrons already there.


According to the principle, electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g. 1s before 2s). The order in which these orbitals are filled is given by the n+l rule (also known as the Madelung rule after Erwin Madelung, or the Klechkowski rule in some countries), where orbitals with a lower n+l value are filled before those with higher n+l values. The rule is based on the total number of nodes in the atomic orbital, n+l, which is related to the energy.^[1] In the case of equal n+l values, the orbital with a lower n value is filled first. The fact that most of the ground state configurations of neutral atoms fill orbitals following this n+l,n pattern was obtained experimentally, by reference to the spectr

oscopic characteristics of the elements.^[2]

The number of electrons that can occupy each orbital is limited by the Pauli exclusion principle. If multiple orbitals of the same energy are available, Hund's rule says that unoccupied orbitals will be filled before occupied orbitals are reused (by electrons having different spins).

A version of the Aufbau principle can also be used to predict the configuration of protons and neutrons in an atomic nucleus.

It should be noted that the Madelung energy ordering rule applies only to neutral atoms in their ground state, and even in that case, there are several elements for which it predicts configurations that differ from those determined experimentally.^[3] Copper and chromium are common examples of this property. Elemental copper should have nine electrons in the 3d orbital. But, its electronic configuration is [Ar].3d¹⁰.4s¹ instead of [Ar].3d⁹.4s² as would be expected by the Madelung rule. By filling the 3d orbital, copper can be in a lower energy state. Similarly, chromium takes the electronic configuration of [Ar].3d⁵.4s¹ instead of [Ar].3d⁴4s². In this case, chromium has a half-full 3d shell.

History

The principle takes its name from the German, Aufbauprinzip, "building-up principle", rather than being named for a scientist. In fact, it was formulated by Niels Bohr and Wolfgang Pauli.
The Aufbau Principle states that:

The orbitals of lower energy are filled in first with the electrons and only then the orbitals of high energy are filled.

It was an early application of quantum mechanics to the properties of electrons, and explained chemical properties in physical terms. Each added electron is subject to the electric field created by the positive charge of atomic nucleus and the negative charge of other electrons that are bound to the nucleus. Although in hydrogen there is no energy difference between orbitals with the same principal quantum number n, this is not true for the outer electrons of other atoms. Classically, orbitals with the highest angular momentum are 'circular orbits' outside the inner electrons, but orbits with low angular momentum (s- and p-orbitals) have high orbital eccentricity, get closer to the nucleus and feel on average a less strongly screened nuclear charge. That explains why 4s-orbitals are filled before even 3d-orbitals.

Hund's Rule
In atomic physics, Hund's rules refer to a set of rules used to determine which is the term symbol that corresponds to the ground state of a multi-electron atom. They were proposed by Friedrich Hund. In chemistry, rule one is especially important and is often referred to as simply Hund's Rule.
The three rules are:

1. For a given electron configuration, the term with maximum multiplicity has the lowest energy. Since multiplicity is equal to , this is also the term with maximum . S is the spin angular momentum.
2. For a given multiplicity, the term with the largest value of has the lowest energy, where L is the orbital angular momentum.
3. For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of lies lowest in energy. If the outermost shell is more than half-filled, the level with highest value of is lowest in energy. J is the total angular momentum, J = S + L.

These rules specify in a simple way how the usual energy interactions dictate the ground state term. The rules assume that the repulsion between the outer electrons is very much greater than the spin-orbit interaction which is in turn stronger than any other remaining interactions. This is referred to as the LS coupling regime.
Full shells and subshells do not contribute to the quantum numbers for total S, the total spin angular momentum and for L, the total orbital angular momentum. It can be shown that for full orbitals and suborbitals both the residual electrostatic term (repulsion between electrons) and the spin-orbit interaction can only shift all the energy levels together. Thus when determining the ordering of energy levels in general only the outer valence electrons need to be considered.

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