Slater–Pauling rule

Slater–Pauling rule The Slater–Pauling rule is a guideline used in transition metal chemistry to predict the magnetic moment of a coordination compound. This rule relates the number of unpaired electrons in a metal ion to its magnetic properties. The rule was developed by John C. Slater and Linus Pauling.

Definition and statement

The Slater–Pauling rule states that for a given coordination geometry, the number of unpaired electrons in a transition metal ion can be estimated by assuming that all electrons are paired in ligand orbitals, with the exception of those in the d orbitals of the metal ion. For an octahedral complex, the rule can be expressed as: $\mu = \sqrt{n(n+2)}$, where $\mu$ is the magnetic moment and $n$ is the number of unpaired electrons.

Historical context and development

The Slater–Pauling rule was developed in the 1930s by John C. Slater and Linus Pauling, two prominent physicists and chemists. At that time, there was a growing interest in understanding the electronic structure of transition metal compounds. Slater and Pauling built upon the crystal field theory developed by Siegfried Heitler, Walter London, and Hans Bethe to create a simple and useful rule for predicting magnetic properties.

Physical interpretation and derivation

The Slater–Pauling rule is based on the crystal field splitting of d orbitals in a transition metal ion. In an octahedral complex, the five d orbitals split into two sets: $t_{2g}$ and $e_g$. The $t_{2g}$ orbitals have a lower energy than the $e_g$ orbitals. According to the Hund's rule, electrons occupy the $t_{2g}$ orbitals with one electron per orbital before pairing up. The Slater–Pauling rule takes into account this electron configuration and provides a simple way to estimate the number of unpaired electrons.

Applications and examples

The Slater–Pauling rule has been widely used to predict the magnetic properties of transition metal compounds, such as ferromagnetism and antiferromagnetism. For example, it can be used to predict the magnetic moment of iron(III) compounds, such as iron(III) chloride (FeCl3). The rule is also useful in understanding the electronic structure of metal complexes and coordination compounds.

Limitations and exceptions

The Slater–Pauling rule has several limitations and exceptions. For example, it assumes a high-spin state, which is not always the case. In some cases, the low-spin state may be more stable, leading to a different number of unpaired electrons. Additionally, the rule does not take into account spin-orbit coupling and other relativistic effects.

Relationship to other rules and models

The Slater–Pauling rule is related to other rules and models in transition metal chemistry, such as the Hund's rule and the crystal field theory. It is also connected to more advanced models, such as ligand field theory and density functional theory. These models provide a more detailed understanding of the electronic structure of transition metal compounds and can be used to refine the predictions of the Slater–Pauling rule.

Category:Chemical rules