Magnetochemistry
Magnetochemistry is concerned with the magnetic properties of
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 is defined by the relationship
where, is the
units), and is the magnetic field strength, also measured in amperes per meter. Susceptibility is a dimensionless quantity. For chemical applications the molar magnetic susceptibility (χmol) is the preferred quantity. It is measured in m3·mol−1 (SI) or cm3·mol−1 (CGS) and is defined aswhere ρ is the density in kg·m−3 (SI) or g·cm−3 (CGS) and M is molar mass in kg·mol−1 (SI) or g·mol−1 (CGS).
A variety of methods are available for the measurement of magnetic susceptibility.
- With the
- The torsion balancewhich uses a sample in a fixed position and a variable secondary magnet to bring the magnets back to their initial position. It, too, is calibrated against HgCo(NCS)4.
- With a Faraday balance the sample is placed in a magnetic field of constant gradient, and weighed on a torsion balance. This method can yield information on magnetic anisotropy.[3]
- SQUID is a very sensitive magnetometer.
- For substances in solution NMR may be used to measure susceptibility.[4][5]
Types of magnetic behaviour
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.
- Diamagnetism. When placed in a magnetic field the atom becomes magnetically polarized, that is, it develops an induced magnetic moment. The force of the interaction tends to push the atom out of the magnetic field. By convention diamagnetic susceptibility is given a negative sign. Very frequently diamagnetic atoms have no unpaired electrons ie each electron is paired with another electron in the same atomic orbital. The moments of the two electrons cancel each other out, so the atom has no net magnetic moment. However, for the ion Eu3+ which has six unpaired electrons, the orbital angular momentum cancels out the electron angular momentum, and this ion is diamagnetic at zero Kelvin.
- Paramagnetism. At least one electron is not paired with another. The atom has a permanent magnetic moment. When placed into a magnetic field, the atom is attracted into the field. By convention paramagnetic susceptibility is given a positive sign.
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.
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]
Paramagnetism
Mechanism and temperature dependence
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
This is known as the
where N is the Avogadro constant, g is the Landé g-factor, and μB is the Bohr magneton. In this treatment it has been assumed that the electronic ground state is not degenerate, that the magnetic susceptibility is due only to electron spin and that only the ground state is thermally populated.
While some substances obey the Curie law, others obey the
Tc is the
Effective magnetic moment
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
Where C has CGS units cm3 mol−1 K, μeff is
Where C has SI units m3 mol−1 K, μeff is
The quantity μeff is effectively dimensionless, but is often stated as in units of Bohr magneton (μB).[12]
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.
Temperature independent paramagnetism
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.
Exchange interactions
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
Complexes of transition metal ions
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, and , respectively. "Total" in this context means "
Spin-only formula
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 is smaller than might be expected (partial quenching), or zero (complete quenching). There is complete quenching in the following cases. Note that an electron in a degenerate pair of dx2–y2 or dz2 orbitals cannot rotate into the other orbital because of symmetry.[20]
Quenched orbital angular momentum dn 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, and the paramagnetism can be attributed to electron spin alone. The total spin angular momentum is simply half the number of unpaired electrons and the spin-only formula results.
where n is the number of unpaired electrons. The spin-only formula is a good first approximation for high-spin complexes of first-row transition metals.[21]
Ion Number of
unpaired
electronsSpin-only
moment /μBobserved
moment /μBTi3+ 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
The small deviations from the spin-only formula may result from the neglect of orbital angular momentum or of spin–orbit coupling. For example, tetrahedral d3, d4, d8 and d9 complexes tend to show larger deviations from the spin-only formula than octahedral complexes of the same ion, because "quenching" of the orbital contribution is less effective in the tetrahedral case.[22]
Low-spin complexes
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.
High and low -spin octahedral complexes d-count 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+
With one unpaired electron μeff values range from 1.8 to 2.5 μB and with two unpaired electrons the range is 3.18 to 3.3 μB. Note that low-spin complexes of Fe2+ and Co3+ are diamagnetic. Another group of complexes that are diamagnetic are
Spin cross-over
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]
2nd and 3rd row transition metals
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
μeffkT/ζ=0
μeffBehaviour 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
Lanthanides and actinides
and the calculated magnetic moment is given by
Magnetic properties of trivalent lanthanide compounds[25] lanthanide Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 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
In actinides spin–orbit coupling is strong and the coupling approximates to j j coupling.
This means that it is difficult to calculate the effective moment. For example, uranium(IV), f2, in the complex [UCl6]2− has a measured effective moment of 2.2 μB, which includes a contribution from temperature-independent paramagnetism.[26]
Main group elements and organic compounds
Very few compounds of
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.
Applications
The
For many years the nature of
- 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
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
See also
- Magnetic mineralogy
- Magnetoelectrochemistry
- Magnetic ionic liquid
- Spin ice
- Spin glass
- Superdiamagnetism, Superparamagnetism, Superferromagnetism
- Single-molecule magnetism
References
- ^ Earnshaw, p. 89
- ^ Magnetic Susceptibility Balances
- ISBN 978-0-470-16680-2.
- .
- ^ Orchard, p. 15. Earnshshaw, p. 97
- ^ Figgis&Lewis, p. 403
- ^ Carlin, p. 3
- .
- ^ Figgis&Lewis, p. 417
- ^ Figgis&Lewis, p. 419
- ^ Orchard, p. 48
- ^ .
- ^ Orchard, p. 53
- ^ ISBN 978-1-891389-02-3. Retrieved 22 February 2011.
- ^ Figgis&Lewis, p. 435. Orchard, p. 67
- ^ Carlin, sections 5.5–5.7
- ^ Carlin, chapters 6 and 7, pp. 112–225
- ^ Carin, p. 264
- ^ Figgis&Lewis, p. 420
- ^ Figgis&Lewis, pp. 424, 432
- ^ Figgis&Lewis, p. 406
- ^ Figgis&Lewis, Section 3, "Orbital contribution"
- ^ Orchard, p. 125. Carlin, p. 270
- ^ Figgis&Lewis, pp. 443–451
- ^ Greenwood&Earnshaw p. 1243
- ^ Orchard, p. 106
- ISBN 0-471-57234-9.
- ^ Atkins, P. W.; Symons, M. C. R. (1967). The structure of inorganic radicals; an application of electron spin resonance to the study of molecular structure. Elsevier.
- ISBN 0-12-092352-1.
- ISBN 3540422471.
- PMID 11749483.)
{{cite journal}}
: CS1 maint: multiple names: authors list (link - ^ Greenwood&Earnshaw, pp. 1099–1011
- ^ Greenwood&Earnshaw, p. 240
Bibliography
- Carlin, R.L. (1986). Magnetochemistry. ISBN 978-3-540-15816-5.
- Earnshaw, Alan (1968). Introduction to Magnetochemistry. Academic Press.
- Figgis, B.N.; Lewis, J. (1960). "The Magnetochemistry of Complex Compounds". In Lewis. J. and Wilkins. R.G. (ed.). Modern Coordination Chemistry. New York: Wiley.
- ISBN 978-0-08-037941-8.
- ISBN 0-19-879278-6.
- Selwood, P.W. (1943). Magnetochemistry. Interscience PublishersInc.
- Vulfson, Sergey (1998). Molecular Magnetochemistry. ISBN 90-5699-535-9.