chemistry

Spin states (d electrons)

Spin states (d electrons) is a chemistry topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Spin states (d electrons) rather than just read about it. In short: Spin states when describing transition metal coordination complexes refers to the potential spin configurations of the central metal's d electrons. For several oxidation states, metals can adopt high-spin and low-spin configurations.

Key takeaways

Spin states (d electrons) belongs to chemistry; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Spin states (d electrons) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Spin states (d electrons) from memory before moving on to harder problems.

Reference excerpt

Spin states when describing transition metal coordination complexes refers to the potential spin configurations of the central metal's d electrons. For several oxidation states, metals can adopt high-spin and low-spin configurations. The ambiguity only applies to first row metals, because second- and third-row metals are invariably low-spin. These configurations can be understood through the two major models used to describe coordination complexes; crystal field theory and ligand field theory (a more advanced version based on molecular orbital theory).

High-spin vs. low-spin

Octahedral complexes

The Δ of the d orbitals plays an important role in the electron spin state of a coordination complex. Three factors affect Δ: the period (row in periodic table) of the metal ion, the charge of the metal ion, and the field strength of the complex's ligands as described by the spectrochemical series. Only octahedral complexes of first row transition metals adopt high-spin states. If Δ is large, then the lower energy orbitals are completely filled before population of the higher orbitals according to the Aufbau principle. Complexes such as this are called "low-spin" since filling an orbital matches electrons and reduces the total electron spin. If the separation between the orbitals is small enough then it is easier to put electrons into the higher energy orbitals than it is to put two into the same low-energy orbital, because of the repulsion resulting from matching two electrons in the same orbital. So, one electron is put into each of the five d orbitals before any pairing occurs in accord with Hund's rule resulting in what is known as a "high-spin" complex. Complexes such as this are called "high-spin" since populating the upper orbital avoids matches between electrons with opposite spin.

The charge of the metal center affects Δ. The higher the oxidation state of the metal, the stronger the ligand field. Increased positive charge contracts the ionic radius and an increase in interaction of negatively charged ligands, both of which increase Δ. For a given ligand set, Fe2+ complexes more likely to be high spin than Co3+, as illustrated by their complexes with EDTA. Ligands also affect the magnitude of Δ of the d orbitals according to their field strength as described by the spectrochemical series. Strong-field ligands, such as CN− and CO, increase the Δ and are more likely to be low-spin. Weak-field ligands, such as I− and Br− cause a smaller Δ splitting and are more likely to be high-spin. Some octahedral complexes exhibit spin crossover, where the high and low spin states exist in dynamic equilibrium.

Tetrahedral complexes

The Δ splitting energy for tetrahedral metal complexes (four ligands), Δtet is smaller than that for an octahedral complex. Consequently, tetrahedral complexes are almost always high spin Examples of low spin tetrahedral complexes include Fe(2-norbornyl)4, [Co(4-norbornyl)4]+, and the nitrosyl complex Cr(NO)((N(tms)2)3.

Square planar complexes Many d8 complexes of the first row metals exist in tetrahedral or square planar geometry. In some cases these geometries exist in measurable equilibria. For example, dichlorobis(triphenylphosphine)nickel(II) has been crystallized in both tetrahedral and square planar geometries.

Ligand field theory vs crystal field theory In terms of d-orbital splitting, ligand field theory (LFT) and crystal field theory (CFT) give similar results. CFT is an older, simpler model that treats ligands as point charges. LFT is more chemical, emphasizes covalent bonding and accommodates pi-bonding explicitly.

High-spin and low-spin systems In the case of octahedral complexes, the question of high spin vs low spin first arises for d4, since it has more than the 3 electrons to fill the non-bonding d orbitals according to ligand field theory or the stabilized d orbitals according to crystal field splitting. All complexes of second and third row metals are low-spin.

Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile. Includes Cr2+ (many complexes assigned as Cr(II) are however Cr(III) with reduced ligands), Mn3+. Octahedral low-spin: 2 unpaired electrons, paramagnetic, substitutionally inert. Includes Cr2+, Mn3+. d5

Octahedral high-spin: 5 unpaired electrons, paramagnetic, substitutionally labile. Includes Fe3+, Mn2+. Example: Tris(acetylacetonato)iron(III). Octahedral low-spin: 1 unpaired electron, paramagnetic, substitutionally inert. Includes Fe3+. Example: [Fe(CN)6]3−. d6

Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile. Includes Fe2+, Co3+. Examples: [Fe(H2O)6]2+, [CoF6]3−. Octahedral low-spin: no unpaired electrons, diamagnetic, substitutionally inert. Includes Fe2+, Co3+, Ni4+. Example: [Co(NH3)6]3+. d7

Octahedral high-spin: 3 unpaired electrons, paramagnetic, substitutionally labile. Includes Co2+, Ni3+. Octahedral low-spin:1 unpaired electron, paramagnetic, substitutionally labile. Includes Co2+, Ni3+. Example: [Co(NH3)6]2+. d8 Octahedral high-spin: 2 unpaired electrons, paramagnetic, substitutionally labile. Includes Ni2+. Example: [Ni(NH3)6]2+. Tetrahedral high-spin: 2 unpaired electrons, paramagnetic, substitutionally labile. Includes Ni2+. Example: [NiCl4]2-. Square planar low-spin: no unpaired electrons, diamagnetic, substitutionally inert. Includes Ni2+. Example: [Ni(CN)4]2−.

Ionic radii The spin state of the complex affects an atom's ionic radius. For a given d-electron count, high-spin complexes are larger.

d4 Octahedral high spin: Cr2+, 64.5 pm. Octahedral low spin: Mn3+, 58 pm. d5

Octahedral high spin: Fe3+, the ionic radius is 64.5 pm. Octahedral low spin: Fe3+, the ionic radius is 55 pm. d6 Octahedral high spin: Fe2+, the ionic radius is 78 pm, Co3+ ionic radius 61 pm. Octahedral low spin: Includes Fe2+ ionic radius 62 pm, Co3+ ionic radius 54.5 pm, Ni4+ ionic radius 48 pm. d7 Octahedral high spin: Co2+ ionic radius 74.5 pm, Ni3+ ionic radius 60 pm. Octahedral low spin: Co2+ ionic radius 65 pm, Ni3+ionic radius 56 pm. d8 Octahedral high spin: Ni2+ ionic radius 69 pm. Square planar low-spin: Ni2+ ionic radius 49 pm.

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Illustrations

Worked examples

Example 1 — a first encounter with Spin states (d electrons)

Start with the simplest possible case. Write down what Spin states (d electrons) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Spin states (d electrons) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Spin states (d electrons) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Spin states (d electrons)

In research: Spin states (d electrons) appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Spin states (d electrons) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Spin states (d electrons) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Coordination chemistry, Electron states, so understanding it makes those chapters shorter.
In everyday life: Look for Spin states (d electrons) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Spin states (d electrons) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Spin states (d electrons) means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Spin states (d electrons) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Spin states (d electrons) in simple terms?

Why does Spin states (d electrons) matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Spin states (d electrons)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Spin states (d electrons).