Spin states (d electrons) - AbsoluteAstronomy.com

Spin states when describing transition metal

Transition metal

The term transition metal has two possible meanings:*The IUPAC definition states that a transition metal is "an element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell." Group 12 elements are not transition metals in this definition.*Some...

coordination complexes refers to the potential spin configurations of the metal centers d electrons. In many molecules these spin states vary between high-spin and low-spin configurations. These configurations can be understood through the two major models used to describe coordination complexes; ligand field theory

Ligand field theory

Ligand field theory describes the bonding, orbital arrangement, and other characteristics of coordination complexes. It represents an application of molecular orbital theory to transition metal complexes. A transition metal ion has nine valence atomic orbitals, five d, one s, and three p orbitals...

, which is an application of molecular orbital theory

Molecular orbital theory

In chemistry, molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule...

to transition metals, and crystal field theory

Crystal field theory

Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes,...

, which has roots in VSEPR theory

VSEPR theory

Valence shell electron pair repulsion theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It is also named Gillespie–Nyholm theory after its two main developers...

Octahedral complexes

The Δ splitting of the d-orbitals

Atomic orbital

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

plays an important role in the electron spin state of a coordination complex. There are three factors that affect the Δ: the period of the metal center, the charge of the metal center, and the field strength of the complex's ligands as described by the spectrochemical series

Spectrochemical series

A spectrochemical series is a list of ligands ordered on ligand strength and a list of metal ions based on oxidation number, group and its identity...

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In order for low spin splitting to occur, the energy cost of placing an electron into an already singly occupied orbital must be less than the cost of placing the additional electron into an e_g orbital at an energy cost of Δ. If the energy required to pair two electrons is greater than the energy cost of placing an electron in an e_g, Δ, high spin splitting occurs.

If the separation between the orbitals is large, then the lower energy orbitals are completely filled before population of the higher orbitals according to the Aufbau principle

Aufbau principle

The Aufbau principle is used to determine the electron configuration of an atom, molecule or ion. The principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons...

. 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.

Within a transition metal group moving down the series corresponds with in an increase in Δ. The observed result is larger Δ splitting for complexes in octahedral geometries based around transition metal centers of the second or third row, periods 5 and 6 respectively. This Δ splitting is generally large enough that these complexes do not exist as high-spin state. This is true even when the metal center is coordinated to weak field ligands. It is only octahedral coordination complexes which are centered around first row transition metals that fluctuate between high and low-spin states.

The charge of the metal center plays a role in the ligand field and the Δ splitting. For example, Fe²⁺ and Co³⁺ are both d⁶; however, the higher charge of Co³⁺ creates a stronger ligand field than Fe²⁺. All other things being equal, Fe²⁺ is more likely to be high spin than Co³⁺.

Ligands also affect the magnitude of Δ splitting of the d-orbitals

Atomic orbital

according to their field strength as described by the spectrochemical series

Spectrochemical series

A spectrochemical series is a list of ligands ordered on ligand strength and a list of metal ions based on oxidation number, group and its identity...

. Strong-field ligands, such as CN⁻ and CO, increase the Δ splitting 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.

Tetrahedral complexes

The Δ splitting energy for tetrahedral metal complexes (four ligands), Δ_tet is smaller than that for an octahedral complex. Therefore, it is rare to have a Δ_tet large enough to cause electrons to pair before filling high orbitals. Thus, tetrahedral complexes are usually high-spin. "There are no known ligands powerful enough to produce the strong-field case in a tetrahedral complex" (Transition metals and Coordination Chemistry:The Crystal field Model by Steven S. Zumdahl. Chemical Principles)

Square planar complexes

Most spin state transitions are between the same geometry, namely octahedral. However, in the case of d⁸ complexes is a shift in geometry between spin states. There is no possible difference between the high and low-spin states in the d⁸ octahedral complexes, however d⁸ complexes are able to shift from paramagnetic tetrahedral geometry to a diamagnetic low-spin square planar geometry.

Ligand field theory vs Crystal field theory

The rationale for why the spin states exist according to ligand field theory

Ligand field theory

is essentially the same as the crystal field theory

Crystal field theory

explanation. However the explanation of why the orbitals split is different accordingly with each model and requires translation.

High-spin and low-spin systems

The first d electron count

D electron count

The d electron count is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes...

(special version of electron configuration

Electron configuration

In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure...

) with the possibility of holding a high spin or low spin state is octahedral 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. The spin state of the complex also affects an atom's ionic radius

Ionic radius

Ionic radius, rion, is the radius of an atom's ion. Although neither atoms nor ions have sharp boundaries, it is important to treat them as if they are hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice...

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d⁴:Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile. Includes Cr²⁺ ionic radius

Ionic radius

80 pm

Picometre