Introduction to Magnetochemistry

Introduction to MagnetochemistryDr. Sumanta Kumar PadhiDepartment of Applied ChemistryISM Dhanbad, Jharkhand826 004, INDIAMagnetism-BackgroundMagnetochemistry is the study of the magnetic properties of materials. By "magnetic properties" we mean not only whether a material will make a good bar magnet, but whether it will be attracted or repelled by a magnet. This includes synthesis, analysis and understanding. This short description is meant to give a basic understanding before you delve into a more complex treatment.Magnetism arises from moving charges, such as an electric current in a coil of wire. In a material which does not have a current present, there are still magnetic interactions. Atoms are made of charged particles (protons and electrons) which are moving constantly.Each spinning electron causes a magnetic field to form around it. In most materials, the magnetic field of one electron is cancelled by an opposite magnetic field produced by the other electron in the pair.The atoms in materials such as iron, cobalt and nickel have unpaired electrons, so they don't cancel the electrons magnetic fields.As a result, each atom of these elements acts like a very small magnet.The processes which create magnetic fields in an atom Nuclear spin. Some nuclei, such as a hydrogen atom, have a net spin, which creates a magnetic field.Electron spin. An electron has two intrinsic spin states (similar to a top spinning) which we call up and down or alpha and beta.Electron orbital motion. There is a magnetic field due to the electron moving around the nucleus.Each of these magnetic fields interact with one another and with external magnetic fields. However, some of these interactions are strong and others are negligible.The magnetic moment of a single atom() is a vector= i F [Am2], circular current i, area FB= eh/4me= 0.9274 10-27Am2(h: Planck constant, me: electron mass) B: Bohr magneton(smallest quantity of a magnetic moment)For one unpaired electron in an atoms = 1.73 B; s = spin only magnetic moment The magnetic moment of an atom has two components a spin component(spin moment ) and an orbital component(orbital moment). Frequently the orbital moment is suppressed (spin-only-magnetism, e.g. coordination compounds of 3d elements)

Magnetismwhen a substance is placed within a magnetic field, H, the field within the substance, B, differs from H by the induced field, 4I, which is proportional to the intensity of magnetization, I.That is; B = H + 4Iwhere B is the magnetic field within the substanceH is the applied magnetic field and I is the intensity of magnetisationThis can also be written asB/H = 1 + 4 I/H, or B/H = 1 + 4 Where B/H is called the magnetic permeability of the material and is the magnetic susceptibility per unit volume, (I/H)The classical theory of magnetism was well developed before quantum mechanics. Lenz's Law (~1834), states that:MagnetismBy definition, in a vacuum is zero, so that B=H.It is usually more convenient to measure mass (gram) susceptibility, g,which is related to the volume susceptibility through the density.g = / where is the density.Finally to get our measured quantity on a basis that can be related to atomic properties, we convert to molar susceptibilitym = g x MW ; (MW = molecular weight of the sample)m = N2 / 3kTwhere N is Avogadro's Number; k is the Boltzmann constant and T the absolute temperatureRewriting this gives the magnetic moment as = 2.828 mT = 2.828(mT)1/26Magnetic States of MatterDiamagnet - A diamagnetic compound has all of it's electron spins paired giving a net spin of zero. Diamagnetic compounds are weakly repelled by a magnet.Paramagnet - A paramagnetic compound will have some electrons with unpaired spins.Paramagnetic compounds are attracted by a magnet. Paramagnetism derives from the spin and orbital angular momenta of electrons. This type of magnetism occurs only in compounds containing unpaired electrons, as the spin and orbital angular momenta is cancelled out when the electrons exist in pairs.

Compounds in which the paramagnetic centers are separated by diamagnetic atoms within the sample are said to be magnetically dilute.

If the diamagnetic atoms are removed from the system then the paramagnetic centres interact with each other. This interaction leads to ferromagnetism (in the case where the neighboring magnetic dipoles are aligned in the same direction) and antiferromagnetism (where the neighboring magnetic dipoles are aligned in alternate directions).7Different types of collective magnetism in a solid due to coupling of magnetic moments

8Curie-und Curie-Weiss law for paramagnetic samples

9Curie-und Curie-Weiss law for paramagnetic samplesCurie: 1/= CT; Curie-Weiss: 1/= C(T-)

10

Curie Constant

Curie-und Curie-Weiss law for paramagnetic samplesCurie: 1/= CT; Curie-Weiss: 1/= C(T-)

13Magnetism in solids (cooperative magnetism)Diamagnetism and paramagnetism are characteristic of compounds with individual atoms which do not interact magnetically (e.g. classical complex compounds)

Ferromagnetism, anti-ferromagnetism and other types of cooperative magnetism originate from an intense magnetical interaction between electron spins of many atoms

14MagnetismDiamagnetismExternal field is weakenedAtoms/ions/molecules with closed shells -10-4 < m < -10-2 cm3/mol (negative sign)

Paramagnetism (van Vleck)External field is strengthenedAtoms/ions/molecules with openshells/unpairedelectrons 10-4 < m < 10-1 cm3/moldiamagnetism(core electrons) + paramagnetism (valence electrons)Pauli-Paramagnetism: special type of magnetism of the conduction electrons in metalsrefers only to the free electrons in the electron gas of a metallic solid)10-6 < m < 10-5 cm3/mol15MagnetismGeneral:1. Diamagnetism: independent of temperature2. Paramagnetism: Curie or Curie-Weiss-law3. Pauli-Paramagnetism: independent of temperature

16Magnetism in transition metalsMany transition metal salts and complexes are paramagnetic due to partially filled d-orbitals.

The experimentally measured magnetic moment () (and from the equation in the previous page) can provide some important information about the compounds themselves:

1. No of unpaired electrons present2. Distinction between HS and LS octahedral complexes3. Spectral behavior, and4. Structure of the complexes17Sources of ParamagnetismOrbital motion of the electron generates ORBITAL MAG. MOMENT (l)Spin motion of the electron generates SPIN MAG. MOMENT (s)l = orbital angular momentum; s = spin angular momentumFor multi-electron systemsL = l1 + l2 + l3 + .S = s1 + s2 + s3 + l+s = [4S(S+1) + L(L+1)]1/2 ..

For TM-complexes, the magnetic properties arise mainly from the exposed d-orbitals. The d-orbitals are perturbed by ligands. The rotation of electrons about the nucleus is restrictedwhich leads to L = 0s = [4S(S+1)]1/2 ..S = n (1/2) = n/2; n = no of unpaired electronsHences = [4(n/2)(n/2+1)]1/2.. = [n(n+2)]1/2 ..This is called Spin-Only Formulas = 1.73, 2.83, 3.88, 4.90, 5.92 BM for n = 1 to 5, respectively18Diagrammatic representation of spin and orbital contributions to eff

spin contribution electrons are orbital contribution - electronsspinning creating an electric move from one orbital tocurrent and hence a magnetic another creating a current and field hence a magnetic fieldd-orbitalsspinningelectronsThe spin-only formula applies reasonably well to metal ions from the first row of transition metals: (units = B,, Bohr-magnetons)Metal iondn configuration eff(spin only) eff (observed)Ca2+, Sc3+ d000Ti3+d11.731.7-1.8V3+d22.832.8-3.1V2+, Cr3+d33.873.7-3.9Cr2+, Mn3+d44.904.8-4.9Mn2+, Fe3+d55.925.7-6.0Fe2+, Co3+d64.905.0-5.6Co2+d73.874.3-5.2Ni2+d82.832.9-3.9Cu2+d91.731.9-2.1Zn2+, Ga3+d1000Magnetic propertiesExample:What is the magnetic susceptibility of [CoF6]3-, assuming that the spin-only formula will apply:

[CoF6]3- is high spin Co(III). (you should know this). High-spin Co(III) is d6 with four unpaired electrons, so n = 4.

We have eff = n(n + 2)

=4.90 B

egt2genergyhigh spin d6 Co(III)When does orbital angular momentum contribute?There must be an unfilled / half-filled orbital similar in energy tothat of the orbital occupied by the unpaired electrons. If this is so, the electrons can make use of the available orbitals to circulate or move around the center of the complexes and hence generate L and L

Essential Conditions:When does orbital angular momentum contribute?

The orbitals should be degenerate (t2g or eg)The orbitals should be similar in shape and size, so that they are transferable into one another by rotation about the same axis (e.g. dxy is related to dx2-y2 by a rotation of 45o about the z-axis.Orbitals must not contain electrons of identical spin.22When does orbital angular momentum contribute?For an octahedral complexCondition t2g set eg set1 Obeyed Obeyed2 Obeyed Not obeyed3 Since 1 and 2 are satisfied Does not mattercondition 3 dictates whether since condition 2t2g will generate l or not is already not obeyed

These conditions are fulfilled whenever one or two of the three t2g orbitals contain an odd no. of electrons.23Orbital momentum in transitionmetal ions and complexesIn coordination compounds orbital momentum means:Electron can move from one d orbital to another degenerated orbital. However, dxy, dxz, dyz, and dz2, dx2-y2 are no longer degenerate in a complex.In an octahedral complex, e can only move within an open t2g shell (first order orbital momentum => of importance in magnetochemistry)d1, d2, (l.s.)-d4, (l.s.)-d5, etc. have first order orbital momentum(T ground terms)d3, d4 have no first order orbital momentum(A, E ground terms)

24For the first-row d-block metal ions the main contribution to magnetic susceptibility is from electron spin. However, there is also an orbital contribution from the motion of unpaired electrons from one d-orbital to another. This motion constitutes an electric current, and so creates a magnetic field (see next slide). The extent to which the orbital contribution adds to the overall magnetic moment is controlled by the spin-orbit coupling constant, . The overall value of eff is related to (spin-only) by:

eff =(spin-only)(1 - /oct)Spin and Orbital contributions to Magnetic susceptibilityExample: Given that the value of the spin-orbit coupling constant , is -316 cm-1 for Ni2+, and oct is 8500 cm-1, calculate eff for [Ni(H2O)6]2+. (Note: for an A ground state = 4, and for an E ground state = 2).

High-spin Ni2+ = d8 = A ground state, so = 4. n = 2, so (spin only) = (2(2+2))0.5 = 2.83 B

eff = (spin only)(1 - (-316 cm-1 x (4/8500 cm-1))) =2.83 B x 1.149

=3.25 B

Spin and Orbital contributions to Magnetic susceptibilityThe value of is negligible for very light atoms, but increases with increasing atomic weight, so that for heavier d-block elements, and for f-block elements, the orbital contribution is considerable. For 2nd and 3rd row d-block elements, is an order of magnitude larger than for the first-row analogues. Most 2nd and 3rd row d-block elements are low-spin and therefore are diamagnetic or have only one or two unpaired electrons, but even so, the value of eff is much lower than expected from the spin-only formula. (Note: the only high-spin complex from the 2nd and 3rd row d-block elements is [PdF6]4- and PdF2).

Spin and Orbital contributions to Magnetic susceptibility

Spin and Orbital contributions to Magnetic susceptibility

ExampleOhTdFree ionNiII (d8)S = 1, L = 3L+S = [4S(S+1)+L(L+1)]1/2 = 4.47 B.M.Orbital Contribution = 0The magnetic moment is close to spin only valueMagnetic moment is higher than the spin-only value as there is positive orbital contributionMagnetic Properties of lanthanides4f electrons are too far inside 4fn5s25p6 (compared to the d electrons in transition metals)Thus 4f normally unaffected by surrounding ligandsHence, the magnetic moments of Ln3+ ions are generally well-described from the coupling of spin and orbital angular momenta ~ Russell-Saunders Coupling to give J vectorSpin orbit coupling constants are large (ca. 1000 cm-1)Ligand field effects are very small (ca. 100 cm-1) only ground J-state is populated spin-orbit coupling >> ligand field splittingmagnetism is essentially independent of environmentMagnetic Properties of lanthanidesMagnetic moment of a J-state is expressed by:

J = L+S, L+S-1,L-SFor the calculation of g value, we use minimum value of J for the configurations up to half-filled; i.e. J = LS for f0-f7 configurationsmaximum value of J for configurations more than half-filled; i.e. J = L+S for f8-f14 configurations For f0, f7, and f14, L = 0, hence J becomes S

Magnetic Exchange (coupling of unpaired electrons): There are three types: 1.Anti-ferromagnetic interactions: This will occur if the spins of unpaired electrons from an antiparallel arrangement in a magnetic field. (-J, coupling constant)

Spins are aligned in an antiparallel arrangement.

In this case the effective magnetic moment is expected to be lower than what spin-only magnetism would predict. The spins cancel.

TN

Magnetic Exchange (coupling of unpaired electrons): 2.Ferromagnetic interactions (less common): This occurs is the spins of the Unpaired electrons (upe) on neighbouring metal atoms align in the same direction. (+J coupling)

In this case, we expect eff to be higher than spin only magnetism would predict.

Magnetic Exchange (coupling of unpaired electrons): 3.Ferrimagnetic interactions (note the spelling with an i and not an o) Similar to anti-ferromagnetic interaction but with different metals

In this case, different metals with different number of upe.

Spin Crossover (SCO)Spin Crossover(SCO), sometimes referred to asspin transitionorspin equilibriumbehavior, is a phenomenon that occurs in some metal complexes wherein the spin state of the complex changes due to external stimuli such as a variation of temperature, pressure, light irradiation or an influence of a magnetic field.With regard to a ligand field andligand field theory, the change in spin state is a transition from a low spin (LS) ground state electron configuration to a high spin (HS) ground state electron configuration of the metals d atomic orbitals (AOs), or vice versa. The magnitude of the ligand field splitting along with the pairing energy of the complex determines whether it will have a LS or HS electron configuration. A LS state occurs because the ligand field splitting () is greater than the pairing energy of the complex (which is an unfavorable process).Conversely, a HS state occurs with weaker ligand fields and smaller orbital splitting. In this case the energy required to populate the higher levels is substantially less than the pairing energy and the electrons fill the orbitals according to Hunds Rule by populating the higher energy orbitals before pairing with electrons in the lower lying orbitals. An example of a metal ion that can exist in either a LS or HS state is Fe3+in an octahedral ligand field. Depending on the ligands that are coordinated to this complex the Fe3+can attain a LS or a HS stateSpin Crossover (SCO)Spin crossover refers to the transitions between high to low, or low to high, spin states. This phenomenon is commonly observed with some first row transition metal complexes with a d4 d7electron configuration in an octahedral ligand geometry.

Spin Crossover (SCO)

Octahedral complexes with between 4 and 7 d electrons can be either high-spin or low-spin depending on the size of When the ligand field splitting has an intermediate value such that the two states have similar energies, then the two states can coexist in measurable amounts at equilibrium. Many "crossover" systems of this type have been studied, particularly for iron complexes.In the d6case of Fe(phen)2(NCS)2, the crossover involves going from S=2 to S=0. At the higher temperature the ground state is5T2gwhile at low temperatures it changes to1A1g. The changeover is found at about 174K.