Electron Configuration

Electron configuration is the distribution of electrons among orbitals in an atom, ion, or molecule. It specifies orbital or subshell occupation rather than the paths of individual particles. Configurations describe both lowest-energy and excited electronic arrangements. They are fundamental to understanding chemical behavior, although a configuration alone does not completely specify an electronic state: several states can arise from the same orbital occupations. (old.goldbook.iupac.org)

Quantum basis and orbital organization

In quantum mechanics, an atomic orbital is a one-electron wavefunction, not a classical orbit around the nucleus. Its squared magnitude describes the spatial probability density associated with that electron. Atomic orbitals are obtained from the Schrödinger equation, exactly for idealized one-electron systems and approximately for many-electron atoms. (openstax.org)

Three quantum numbers organize atomic orbitals. The principal quantum number $n=1,2,3,\ldots$ identifies a shell. The orbital angular momentum quantum number $l=0,1,\ldots,n-1$ distinguishes subshells within that shell. Values $l=0,1,2,3$ are denoted by the letters $s,p,d,f$, respectively. The magnetic quantum number $m_l$, ranging from $-l$ to $+l$, distinguishes the $2l+1$ orbitals belonging to a subshell. (physics.nist.gov)

The electron also has intrinsic spin angular momentum, with spin projection $m_s=+\tfrac12$ or $-\tfrac12$. Consequently, the $s,p,d,f$ subshells contain one, three, five, and seven spatial orbitals and can accommodate at most two, six, ten, and fourteen electrons. Summing the capacities of a shell’s subshells gives the maximum shell population $2n^2$. This is a capacity limit, not a requirement that a shell fill completely before another begins. (physics.nist.gov)

Notation

An atomic configuration is written as a sequence of subshell labels with superscripts giving their electron populations. Thus $2p^4$ means four electrons distributed across the three orbitals of the $2p$ subshell, not four electrons in one orbital. Closed subshells contain their maximum allowed populations; partially occupied subshells are called open. (physics.nist.gov)

For a neutral atom, the superscripts sum to its atomic number. Sodium, with eleven electrons, has the configuration

Noble-gas shorthand replaces a filled inner configuration with the corresponding element symbol in brackets, giving sodium as $[\mathrm{Ne}]\,3s^1$. Orbital diagrams provide additional information by representing individual orbitals as boxes or lines and electrons as arrows indicating spin projection. (openstax.org)

Occupation principles

Three principles guide the construction of common atomic configurations:

• Pauli exclusion principle. No two electrons in an atom can share all four quantum numbers. Each spatial orbital therefore holds at most two electrons, with opposite spin projections. This restriction applies to excited as well as lowest-energy arrangements. (physics.nist.gov)
• Aufbau principle. In the orbital-filling description, electrons occupy lower-energy orbitals before higher-energy ones. It is a useful construction rule, rather than a universally fixed ordering of subshell labels. (goldbook.iupac.org)
• Hund’s rules. For atomic states in the usual Russell–Saunders coupling regime, the greatest spin multiplicity generally gives the lowest energy. Its familiar orbital-diagram expression is that degenerate orbitals are occupied singly with parallel spins before pairing. The other Hund rules distinguish states according to total orbital and total angular momentum. (goldbook.iupac.org)

For example, nitrogen has $1s^2\,2s^2\,2p^3$, with one electron in each $2p$ orbital in its lowest-energy arrangement. Oxygen has $1s^2\,2s^2\,2p^4$, requiring one paired orbital and two singly occupied orbitals. (openstax.org)

Energy ordering and exceptions

For hydrogen and other one-electron species, the nonrelativistic orbital energy depends on $n$, so subshells with the same $n$ are degenerate. In many-electron atoms, electron–electron interactions remove this simple degeneracy, and subshell energies also depend on $l$. The familiar filling sequence begins $1s,2s,2p,3s,3p,4s,3d$, but actual configurations must account for the interacting atom as a whole. (openstax.org)

Experimental ground-state configurations include chromium as $[\mathrm{Ar}]\,3d^5\,4s^1$ and copper as $[\mathrm{Ar}]\,3d^{10}\,4s^1$, rather than the simplest sequence-based predictions $3d^4\,4s^2$ and $3d^9\,4s^2$. Such cases show why tabulated atomic configurations cannot always be inferred from an elementary filling diagram. (nist.gov)

Formation of positive ions likewise is not always the reverse of a fixed filling sequence. Neutral iron is $[\mathrm{Ar}]\,3d^6\,4s^2$, whereas singly ionized iron is $[\mathrm{Ar}]\,3d^6\,4s^1$. Neutral copper and its singly charged ion are $[\mathrm{Ar}]\,3d^{10}\,4s^1$ and $[\mathrm{Ar}]\,3d^{10}$, respectively. (nist.gov)

Chemical periodicity and electronic states

Recurring outer configurations help explain the structure of the periodic table. Lithium and sodium, for example, each have one outer $s$ electron beyond a closed core. These valence electrons play a central role in chemical reactions, whereas inner electrons form the core. Similar outer occupations contribute to recurring chemical properties among related elements. (openstax.org)

In molecular orbital theory, configurations instead specify occupations of molecular orbitals. One molecular configuration can produce different spin and angular-momentum states; IUPAC’s oxygen-molecule example illustrates this distinction between configuration and state. (old.goldbook.iupac.org)

A many-electron state may also require more than one configuration for an adequate description. Configuration interaction combines many-electron wavefunctions constructed from different configurations to improve the representation of the electronic state. A configuration label therefore often identifies a useful component of a quantum description, rather than the complete wavefunction. (goldbook.iupac.org)