Magnetochemistry is concerned with the magnetic properties of chemical compounds. Magnetic properties arise from the spin and orbital angular momentum of the electrons contained in a compound. Compounds are diamagnetic when they contain no unpaired electrons. Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μeff. For first-row transition metals the magnitude of μeff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula. In general, spin–orbit coupling causes μeff to deviate from the spin-only formula. For the heavier transition metals, lanthanides and actinides, spin–orbit coupling cannot be ignored. Exchange interaction can occur in clusters and infinite lattices, resulting in ferromagnetism, antiferromagnetism or ferrimagnetism depending on the relative orientations of the individual spins.
See main article: article and Magnetic susceptibility. The primary measurement in magnetochemistry is magnetic susceptibility. This measures the strength of interaction on placing the substance in a magnetic field. The volume magnetic susceptibility, represented by the symbol
\chiv
\vec{M}=\chiv\vec{H}
\vec{M}
\vec{H}
\chimol=M\chiv/\rho
A variety of methods are available for the measurement of magnetic susceptibility.
See main article: article and Magnetism. When an isolated atom is placed in a magnetic field there is an interaction because each electron in the atom behaves like a magnet, that is, the electron has a magnetic moment. There are two types of interaction.
When the atom is present in a chemical compound its magnetic behaviour is modified by its chemical environment. Measurement of the magnetic moment can give useful chemical information.
In certain crystalline materials individual magnetic moments may be aligned with each other (magnetic moment has both magnitude and direction). This gives rise to ferromagnetism, antiferromagnetism or ferrimagnetism. These are properties of the crystal as a whole, of little bearing on chemical properties.
See main article: article and Diamagnetism. Diamagnetism is a universal property of chemical compounds, because all chemical compounds contain electron pairs. A compound in which there are no unpaired electrons is said to be diamagnetic. The effect is weak because it depends on the magnitude of the induced magnetic moment. It depends on the number of electron pairs and the chemical nature of the atoms to which they belong. This means that the effects are additive, and a table of "diamagnetic contributions", or Pascal's constants, can be put together.[6] [7] [8] With paramagnetic compounds the observed susceptibility can be adjusted by adding to it the so-called diamagnetic correction, which is the diamagnetic susceptibility calculated with the values from the table.[9]
See main article: article and Paramagnetism.
A metal ion with a single unpaired electron, such as Cu2+, in a coordination complex provides the simplest illustration of the mechanism of paramagnetism. The individual metal ions are kept far apart by the ligands, so that there is no magnetic interaction between them. The system is said to be magnetically dilute. The magnetic dipoles of the atoms point in random directions. When a magnetic field is applied, first-order Zeeman splitting occurs. Atoms with spins aligned to the field slightly outnumber the atoms with non-aligned spins. In the first-order Zeeman effect the energy difference between the two states is proportional to the applied field strength. Denoting the energy difference as ΔE, the Boltzmann distribution gives the ratio of the two populations as
e-\Delta
\chi={C\overT}
| C= |
| ||||||||
| 3k |
While some substances obey the Curie law, others obey the Curie-Weiss law.
\chi=
| C | |
| T-Tc |
When the Curie law is obeyed, the product of molar susceptibility and temperature is a constant. The effective magnetic moment, μeff is then defined[12] as
\mueff=constant\sqrt{T\chi}
\mueff=\sqrt{3k\overN
| 2} | |
| \mu | |
| B |
\sqrt{T\chi} ≈ 2.82787\sqrt{T\chi}
Where C has SI units m3 mol−1 K, μeff is
\mueff=\sqrt{3k\overN\mu0
| 2} | |
| \mu | |
| B |
\sqrt{T\chi} ≈ 797.727\sqrt{T\chi}
For substances that obey the Curie law, the effective magnetic moment is independent of temperature. For other substances μeff is temperature dependent, but the dependence is small if the Curie-Weiss law holds and the Curie temperature is low.
Compounds which are expected to be diamagnetic may exhibit this kind of weak paramagnetism. It arises from a second-order Zeeman effect in which additional splitting, proportional to the square of the field strength, occurs. It is difficult to observe as the compound inevitably also interacts with the magnetic field in the diamagnetic sense. Nevertheless, data are available for the permanganate ion.[13] It is easier to observe in compounds of the heavier elements, such as uranyl compounds.
See main article: article and Exchange interaction.
Exchange interactions occur when the substance is not magnetically dilute and there are interactions between individual magnetic centres. One of the simplest systems to exhibit the result of exchange interactions is crystalline copper(II) acetate, Cu2(OAc)4(H2O)2. As the formula indicates, it contains two copper(II) ions. The Cu2+ ions are held together by four acetate ligands, each of which binds to both copper ions. Each Cu2+ ion has a d9 electronic configuration, and so should have one unpaired electron. If there were a covalent bond between the copper ions, the electrons would pair up and the compound would be diamagnetic. Instead, there is an exchange interaction in which the spins of the unpaired electrons become partially aligned to each other. In fact two states are created, one with spins parallel and the other with spins opposed. The energy difference between the two states is so small their populations vary significantly with temperature. In consequence the magnetic moment varies with temperature in a sigmoidal pattern. The state with spins opposed has lower energy, so the interaction can be classed as antiferromagnetic in this case.[14] It is believed that this is an example of superexchange, mediated by the oxygen and carbon atoms of the acetate ligands.[15] Other dimers and clusters exhibit exchange behaviour.[16]
Exchange interactions can act over infinite chains in one dimension, planes in two dimensions or over a whole crystal in three dimensions. These are examples of long-range magnetic ordering. They give rise to ferromagnetism, antiferromagnetism or ferrimagnetism, depending on the nature and relative orientations of the individual spins.[17]
Compounds at temperatures below the Curie temperature exhibit long-range magnetic order in the form of ferromagnetism. Another critical temperature is the Néel temperature, below which antiferromagnetism occurs. The hexahydrate of nickel chloride, NiCl2·6H2O, has a Néel temperature of 8.3 K. The susceptibility is a maximum at this temperature. Below the Néel temperature the susceptibility decreases and the substance becomes antiferromagnetic.[18]
The effective magnetic moment for a compound containing a transition metal ion with one or more unpaired electrons depends on the total orbital and spin angular momentum of the unpaired electrons,
\vec{L}
\vec{S}
\mueff=\sqrt{\vec{L}(\vec{L}+1)+4\vec{S}(\vec{S}+1)}\muB
Orbital angular momentum is generated when an electron in an orbital of a degenerate set of orbitals is moved to another orbital in the set by rotation. In complexes of low symmetry certain rotations are not possible. In that case the orbital angular momentum is said to be "quenched" and
\vec{L}
| Octahedral | Tetrahedral | ||||
| high-spin | low-spin | ||||
| d1 | e1 | ||||
| d2 | e2 | ||||
| d3 | t2g3 | ||||
| d4 | t2g3eg1 | ||||
| d5 | t2g3eg2 | ||||
| d6 | t2g6 | e3t23 | |||
| d7 | t2g6eg1 | e4t23 | |||
| d8 | t2g6eg2 | ||||
| d9 | t2g6eg3 | ||||
legend: t2g, t2 = (dxy, dxz, dyz). eg, e = (dx2–y2, dz2). When orbital angular momentum is completely quenched,
\vec{L}=0
\mueff=\sqrt{n(n+2)}\muB
| Ion | Number of unpaired electrons | Spin-only moment /μB | observed moment /μB | |
|---|---|---|---|---|
| Ti3+ | 1 | 1.73 | 1.73 | |
| V4+ | 1 | 1.73 | 1.68–1.78 | |
| Cu2+ | 1 | 1.73 | 1.70–2.20 | |
| V3+ | 2 | 2.83 | 2.75–2.85 | |
| Ni2+ | 2 | 2.83 | 2.8–3.5 | |
| V2+ | 3 | 3.87 | 3.80–3.90 | |
| Cr3+ | 3 | 3.87 | 3.70–3.90 | |
| Co2+ | 3 | 3.87 | 4.3–5.0 | |
| Mn4+ | 3 | 3.87 | 3.80–4.0 | |
| Cr2+ | 4 | 4.90 | 4.75–4.90 | |
| Fe2+ | 4 | 4.90 | 5.1–5.7 | |
| Mn2+ | 5 | 5.92 | 5.65–6.10 | |
| Fe3+ | 5 | 5.92 | 5.7–6.0 |
See main article: article and crystal field theory.
According to crystal field theory, the d orbitals of a transition metal ion in an octahedal complex are split into two groups in a crystal field. If the splitting is large enough to overcome the energy needed to place electrons in the same orbital, with opposite spin, a low-spin complex will result.
| Number of unpaired electrons | examples | |||
| high-spin | low-spin | |||
|---|---|---|---|---|
| d4 | 4 | 2 | Cr2+, Mn3+ | |
| d5 | 5 | 1 | Mn2+, Fe3+ | |
| d6 | 4 | 0 | Fe2+, Co3+ | |
| d7 | 3 | 1 | Co2+ | |
When the energy difference between the high-spin and low-spin states is comparable to kT (k is the Boltzmann constant and T the temperature) an equilibrium is established between the spin states, involving what have been called "electronic isomers". Tris-dithiocarbamato iron(III), Fe(S2CNR2)3, is a well-documented example. The effective moment varies from a typical d5 low-spin value of 2.25 μB at 80 K to more than 4 μB above 300 K.[23]
Crystal field splitting is larger for complexes of the heavier transition metals than for the transition metals discussed above. A consequence of this is that low-spin complexes are much more common. Spin–orbit coupling constants, ζ, are also larger and cannot be ignored, even in elementary treatments. The magnetic behaviour has been summarized, as below, together with an extensive table of data.[24]
| d-count | kT/ζ=0.1 μeff | kT/ζ=0 μeff | Behaviour with large spin–orbit coupling constant, ζnd | |
|---|---|---|---|---|
| d1 | 0.63 | 0 | μeff varies with T1/2 | |
| d2 | 1.55 | 1.22 | μeff varies with T, approximately | |
| d3 | 3.88 | 3.88 | Independent of temperature | |
| d4 | 2.64 | 0 | μeff varies with T1/2 | |
| d5 | 1.95 | 1.73 | μeff varies with T, approximately |
Russell-Saunders coupling, LS coupling, applies to the lanthanide ions, crystal field effects can be ignored, but spin–orbit coupling is not negligible. Consequently, spin and orbital angular momenta have to be combined
\vec{L}=\sumi\vec{l}i
\vec{S}=\sumi\vec{s}i
\vec{J}=\vec{L}+\vec{S}
\mueff=g\sqrt{\vec{J}(\vec{J}+1)};g={3\over2}+
| \vec{S | |
| (\vec{S}+1)-\vec{L}(\vec{L}+1)}{2 |
\vec{J}(\vec{J}+1)}
| Number of unpaired électrons | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | |
| calculated moment /μB | 2.54 | 3.58 | 3.62 | 2.68 | 0.85 | 0 | 7.94 | 9.72 | 10.65 | 10.6 | 9.58 | 7.56 | 4.54 | 0 | |
| observed moment /μB | 2.3–2.5 | 3.4–3.6 | 3.5–3.6 | 1.4–1.7 | 3.3–3.5 | 7.9–8.0 | 9.5–9.8 | 10.4–10.6 | 10.4–10.7 | 9.4–9.6 | 7.1–7.5 | 4.3–4.9 | 0 |
\vec{J}=\sumi\vec{j}i=\sumi(\vec{l}i+\vec{s}i)
Very few compounds of main group elements are paramagnetic. Notable examples include: oxygen, O2; nitric oxide, NO; nitrogen dioxide, NO2 and chlorine dioxide, ClO2. In organic chemistry, compounds with an unpaired electron are said to be free radicals. Free radicals, with some exceptions, are short-lived because one free radical will react rapidly with another, so their magnetic properties are difficult to study. However, if the radicals are well separated from each other in a dilute solution in a solid matrix, at low temperature, they can be studied by electron paramagnetic resonance (EPR). Such radicals are generated by irradiation. Extensive EPR studies have revealed much about electron delocalization in free radicals. The simulated spectrum of the CH3• radical shows hyperfine splitting due to the interaction of the electron with the 3 equivalent hydrogen nuclei, each of which has a spin of 1/2.[27] [28]
Spin labels are long-lived free radicals which can be inserted into organic molecules so that they can be studied by EPR.[29] For example, the nitroxide MTSL, a functionalized derivative of TEtra Methyl Piperidine Oxide, TEMPO, is used in site-directed spin labeling.
The gadolinium ion, Gd3+, has the f7 electronic configuration, with all spins parallel. Compounds of the Gd3+ ion are the most suitable for use as a contrast agent for MRI scans.[30] The magnetic moments of gadolinium compounds are larger than those of any transition metal ion. Gadolinium ispreferred to other lanthanide ions, some of which have larger effective moments, due to its having a non-degenerate electronic ground state.[31] For many years the nature of oxyhemoglobin, Hb-O2, was highly controversial. It was found experimentally to be diamagnetic. Deoxy-hemoglobin is generally accepted to be a complex of iron in the +2 oxidation state, that is a d6 system with a high-spin magnetic moment near to the spin-only value of 4.9 μB. It was proposed that the iron is oxidized and the oxygen reduced to superoxide.
Fe(II)Hb (high-spin) + O2 [Fe(III)Hb]O2−Pairing up of electrons from Fe3+ and O2− was then proposed to occur via an exchange mechanism. It has now been shown that in fact the iron(II) changes from high-spin to low-spin when an oxygen molecule donates a pair of electrons to the iron. Whereas in deoxy-hemoglobin the iron atom lies above the plane of the heme, in the low-spin complex the effective ionic radius is reduced and the iron atom lies in the heme plane.[32]
Fe(II)Hb + O2 [Fe(II)Hb]O2 (low-spin)This information has an important bearing on research to find artificial oxygen carriers.
Compounds of gallium(II) were unknown until quite recently. As the atomic number of gallium is an odd number (31), Ga2+ should have an unpaired electron. It was assumed that it would act as a free radical and have a very short lifetime. The non-existence of Ga(II) compounds was part of the so-called inert-pair effect. When salts of the anion with empirical formula such as [GaCl<sub>3</sub>]− were synthesized they were found to be diamagnetic. This implied the formation of a Ga-Ga bond and a dimeric formula, [Ga<sub>2</sub>Cl<sub>6</sub>]2−.[33]