The Aufbau principle (, from the German Aufbauprinzip, which means "building-up principle"), also called the Aufbau rule, states that in the ground state of an atom or ion, electrons fill subshells of the lowest available energy, then they fill subshells of higher energy. For example, the 1s subshell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible. An example is the configuration for the phosphorus atom, meaning that the 1s subshell has 2 electrons, and so on.
The configuration is often abbreviated by writing only the valence electrons explicitly, while the core electrons are replaced by the symbol for the last previous noble gas in the periodic table, placed in square brackets. For phosphorus, the last previous noble gas is neon, so the configuration is abbreviated to [Ne] 3s2 3p3, where [Ne] signifies the core electrons whose configuration in phosphorus is identical to that of neon.
Electron behavior is elaborated by other principles of atomic physics, such as Hund's rule and the Pauli exclusion principle. Hund's rule asserts that if multiple orbitals of the same energy are available, electrons will occupy different orbitals singly and with the same spin before any are occupied doubly. If double occupation does occur, the Pauli exclusion principle requires that electrons that occupy the same orbital must have different spins (+ and −).
Passing from one element to another of the next higher atomic number, one proton and one electron are added each time to the neutral atom. The maximum number of electrons in any shell is 2n2, where n is the principal quantum number. The maximum number of electrons in a subshell is equal to 2(2 + 1), where the azimuthal quantum number is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively. In the ground state, the electronic configuration can be built up by placing electrons in the lowest available subshell until the total number of electrons added is equal to the atomic number. Thus subshells are filled in the order of increasing energy, using two general rules to help predict electronic configurations: Electrons are assigned to subshells in order of increasing value of n + . For subshells with the same value of n + , electrons are assigned first to the subshell with lower n.
A version of the aufbau principle known as the nuclear shell model is used to predict the configuration of protons and neutrons in an atomic nucleus.
Madelung energy ordering rule
In neutral atoms, the approximate order in which subshells are filled is given by the n + rule, also known as the: Madelung rule (after Erwin Madelung) Janet rule (after Charles Janet) Klechkowsky rule (after Vsevolod Klechkovsky) Wiswesser's rule (after William Wiswesser) aufbau rule or diagonal rule
Here n represents the principal quantum number and the azimuthal quantum number; the values = 0, 1, 2, 3 correspond to the s, p, d, and f subshells, respectively. Subshells with a lower n + value are filled before those with higher n + values. In the many cases of equal n + values, the subshell with a lower n value is filled first. The subshell ordering by this rule is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s, 5g, ... For example, thallium (Z = 81) has the ground-state configuration or in condensed form, [Xe] 6s2 4f14 5d10 6p1.
Other authors write the subshells outside of the noble gas core in order of increasing n, or if equal, increasing n + l, such as Tl (Z = 81) . They do so to emphasize that if this atom is ionized, electrons leave approximately in the order 6p, 6s, 5d, 4f, etc. On a related note, writing configurations in this way emphasizes the outermost electrons and their involvement in chemical bonding.
In general, subshells with the same n + value have similar energies, but the s-orbitals (with = 0) are exceptional: their energy levels are appreciably far from those of their n + group and are closer to those of the next n + group. This is why the periodic table is usually drawn to begin with the s-block elements.
The Madelung energy ordering rule applies only to neutral atoms in their ground state. There are twenty elements (eleven in the d-block and nine in the f-block) for which the Madelung rule predicts an electron configuration that differs from that determined experimentally, although the Madelung-predicted electron configurations are at least close to the ground state even in those cases.