Spin transition

Last updated February 23, 2019

The spin transition is an example of transition between two electronic states in molecular chemistry. The ability of an electron to transit from a stable to another stable (or metastable) electronic state in a reversible and detectable fashion, makes these molecular systems appealing in the field of molecular electronics.

The electron is a subatomic particle, symbol e⁻
or β⁻
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. As it is a fermion, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

Metastability stable state of a dynamical system other than the systems state of least energy

In physics, metastability is a stable state of a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived as they are prevented from rearranging to their preferred ground state by barriers in the potential energy.

Molecular electronics is the study and application of molecular building blocks for the fabrication of electronic components. It is an interdisciplinary area that spans physics, chemistry, and materials science. The unifying feature is use of molecular building blocks to fabricate electronic components. Due to the prospect of size reduction in electronics offered by molecular-level control of properties, molecular electronics has generated much excitement. It provides a potential means to extend Moore's Law beyond the foreseen limits of small-scale conventional silicon integrated circuits.

In octahedral surroundings

When a transition metal ion of configuration $d^{n}$ , $n=4$ to $7$ , is in octahedral surroundings, its ground state may be low spin (LS) or high spin (HS), depending to a first approximation on the magnitude of the $\Delta$ energy gap between $e_{g}$ and $t_{2g}$ metal orbitals relative to the mean spin pairing energy $P$ (see Crystal field theory). More precisely, for $\Delta >>P$ , the ground state arises from the configuration where the $d$ electrons occupy first the $t_{2g}$ orbitals of lower energy, and if there are more than six electrons, the $e_{g}$ orbitals of higher energy. The ground state is then LS. On the other hand, for $\Delta <<P$ , Hund's rule is obeyed. The HS ground state has got the same multiplicity as the free metal ion. If the values of $P$ and $\Delta$ are comparable, a LS↔HS transition may occur.

In chemistry, the term transition metal has three possible meanings:

The ground state of a quantum-mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In the quantum field theory, the ground state is usually called the vacuum state or the vacuum.

In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes.

$d^{n}$ configurations

Between all the possible $d^{n}$ configurations of the metal ion, $d^{5}$ and $d^{6}$ are by far the most important. The spin transition phenomenon, in fact, was first observed in 1930 for tris (dithiocarbamato) iron(III) compounds. On the other hand, the iron(II) spin transition complexes were the most extensively studied: among these two of them may be considered as archetypes of spin transition systems, namely Fe(NCS)₂(bipy)₂ and Fe(NCS)₂(phen)₂ (bipy = 2,2'-bypiridine and phen = 1,10-phenanthroline).

Iron(II) complexes

We discuss the mechanism of the spin transition by focusing on the specific case of iron(II) complexes. At the molecular scale the spin transition corresponds to an interionic electron transfer with spin flip of the transferred electrons. For an iron(II) compound this transfer involves two electrons and the spin variations is $\Delta S=2$ . The occupancy of the $e_{g}$ orbitals is higher in the HS state than in the LS state and these orbitals are more antibonding than the $t_{2g}$ . It follows that the average metal-ligand bond length is longer in the HS state than in the LS state. This difference is in the range 1.4–2.4 pm for iron(II) compounds.

Electron transfer (ET) occurs when an electron relocates from an atom or molecule to another such chemical entity. ET is a mechanistic description of a redox reaction, wherein the oxidation state of reactant and product changes.

Ligand molecule or functional group that binds or can bind to the central atom in a coordination complex

In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal–ligand bonding can range from covalent to ionic. Furthermore, the metal–ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known to involve Lewis acidic "ligands".

To induce a spin transition

The most common way to induce a spin transition is to change the temperature of the system: the transition will be then characterized by a $\rho _{H}=f(T)$ , where $\rho _{H}$ is the molar fraction of molecules in high-spin state. Several techniques are currently used to obtain such curves. The simplest method consists of measuring the temperature dependence of molar susceptibility. Any other technique that provides different responses according to whether the state is LS or HS may also be used to determine $\rho _{H}$ . Among these techniques, Mössbauer spectroscopy has been particularly useful in the case of iron compounds, showing two well resolved quadrupole doublets. One of these is associated with LS molecules, the other with HS molecules: the high-spin molar fraction then may be deduced from the relative intensities of the doublets.

Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer in 1958, consists in the nearly recoil-free, resonant absorption and emission of gamma rays in solids.

Types of transition

Various types of transition have been observed. This may be abrupt, occurring within a few kelvins range, or smooth, occurring within a large temperature range. It could also be incomplete both at low temperature and at high temperature, even if the latter is more often observed. Moreover, the $\rho _{H}=f(T)$ curves may be strictly identical in the cooling or heating modes, or exhibit a hysteresis: in this case the system could assume two different electronic states in a certain range of temperature. Finally the transition may occur in two steps.

The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is the base unit of temperature in the International System of Units (SI).

Hysteresis dependence of the state of a system on its history

Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect.

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