In ions, electron configurations differ from their neutral atoms due to the gain or loss of electrons. Cations, which are positively charged due to electron loss, have fewer electrons than their neutral counterparts. This loss typically occurs from the outermost energy level, altering the electron configuration. For example, a sodium cation (Na⁺) has one electron less than a neutral sodium atom, resulting in the electron configuration of neon (Ne). Anions, negatively charged due to electron gain, have additional electrons, which occupy the next available orbital following the Aufbau principle. The change in electron configuration affects an ion's size, reactivity, and how it bonds with other atoms. For instance, ions with a noble gas configuration are typically more stable and less reactive. Understanding these changes is fundamental in predicting the behaviour of ions in chemical reactions and in ionic compounds.

Orbital hybridisation is a concept used to explain the observed shapes of molecules. It involves the mixing of atomic orbitals to form new hybrid orbitals, which can then accommodate bonding and non-bonding electron pairs. The most common types of hybridisation are sp (linear geometry), sp² (trigonal planar geometry), and sp³ (tetrahedral geometry). For example, in methane (CH₄), the carbon atom undergoes sp³ hybridisation, where one 2s and three 2p orbitals mix to form four equivalent sp³ hybrid orbitals. These orbitals then overlap with the 1s orbitals of hydrogen atoms to form C-H bonds, resulting in a tetrahedral shape. Hybridisation theory is crucial in understanding the structure and bonding in covalent compounds. It provides insights into bond angles, molecular shapes, and the physical and chemical properties of molecules

Electron degeneracy in orbitals refers to the situation where two or more orbitals have the same energy level. This is commonly seen in p, d, and f orbitals. For example, in a given energy level, all three p orbitals (px, py, pz) have the same energy, making them degenerate. Electron degeneracy significantly impacts electron arrangement in atoms, as explained by Hund's rule. According to this rule, electrons will fill degenerate orbitals singly, with parallel spins, before pairing up. This arrangement minimises electron-electron repulsion within the atom. In essence, electron degeneracy allows for a more stable distribution of electrons across orbitals with the same energy level, influencing the chemical properties and reactivity of atoms. Understanding degeneracy is crucial in predicting electron configurations, especially in atoms with more complex electron arrangements such as transition metals and lanthanides.

Electron spin is a fundamental property of electrons, representing a form of angular momentum. Each electron has a spin that can be either 'up' (+½) or 'down' (−½). In determining electron configuration, spin is crucial as it leads to the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers. This principle directly influences how electrons are arranged in orbitals. Hund's rule complements this by stating that electrons will occupy degenerate (equal energy) orbitals singly before they pair up. The rule is based on the principle that electrons will minimise repulsion by maximising the number of unpaired electrons with parallel spins in degenerate orbitals. This is because electrons with the same spin are less likely to be found in the same spatial region, reducing electron-electron repulsion. Understanding electron spin and Hund's rule is essential in predicting the electron configurations of atoms, which in turn influences their chemical reactivity and bonding.

The d and f orbitals have more complex shapes compared to the simpler s and p orbitals. The d orbitals, starting from the third energy level (n=3), exhibit a cloverleaf shape and consist of five types: (d{xy}), (d{yz}), (d{xz}), (d{x²-y²}), and (d{z²}). These orbitals can be visualised as four-lobed structures for the first four, and the (d{z²}) orbital appears as a two-lobed structure with a doughnut-shaped region around the nucleus. On the other hand, f orbitals, beginning at the fourth energy level (n=4), are even more complex, with seven different types. These orbitals are crucial because they accommodate more electrons, playing a significant role in the chemical properties and behaviour of transition metals and lanthanides. The d orbitals, in particular, contribute to the formation of metallic bonds, colour, magnetic properties, and catalytic activity in transition metals. Understanding these orbitals is key to comprehending the chemistry of these elements, especially in complex formation and their electronic configurations.