Magnetochemie

Conventional Magnets

spincarriers: atoms

- Fe, Co, Ni- CrO2, Fe3O4- Alloys

digital„0“ and „1“

bulk magnet

MagnetochemieMagnetic properties of the d-block elements

I. Magnetism of Octahedral transition metal complexes

• Spin-only Paramagnetism

• High-spin / Low-spin Complexes (Octahedral)

II. Orbital contribution to the magnetic moment

There are many coordination compounds, with unpaired d-electrons (these are paramagnetic)

[CuCl4]2– (d9)[Co(NH3)4(SO4)]+ (d7)

Plastocyanin(Cu2+, d9)[Co(NH3)5(H2O)]3+ (d6)

[NiCl4]2– (d8)

[VO(H2O)5]SO4 (d1) [CrCl3] (d3)

General remarksThis lecture deals only with paramagnetic coordination compounds.

Complicated mathematics will be avoided, where possible!

TMn+ ions have pure d-electron configurations (recall: s electrons are lost first,as the diffuse s-orbitals are destablized in complexes)

Cr2+: d4

Fe3+: d5

Ni2+: d8

metal organic compounds have also dn

Fe2+, Cr(CO)6, Cr(η6-C6H6)2 d6

Fe3+, V(CO)6, V(η6-C6H6)2 d5

General remarksConstants and units

χm molar magnetic suceptibility [cm3·mol–1] (cgs/emu)[emu·mol–1] „[m3·mol–1] (SI)

Conversion factor: χm(cgs) × 4π10–6 = χm (SI)

K3[Fe(CN)6] χm = -122.7×10–6 emu/molχm = -1.542×10–9 m3/mol

----------------------------------------------------------------------------------------------------------N = 6.023×1023 mol–1

µB = 0.92731×10–20 erg/Gauss; µB = 9.27×10–24 J/TkB = 1.38×10–23 J/K

NµB2/(3kB) = 0.125 cm3/(K·mol)

)(828.2332 Kcm

molN

k

B

B =µ

cgs units, N = 6.023×1023 mol–1

µB = 0.92731×10–20 erg/Gauss; 9.27×10–24 J/T

TBeff χµµ ⋅= 828.2/

Literature

A. F. Orchard, Magnetochemistry,Oxford Chemistry Primer, 2007; Chapter 5

F. E. Mabbs, D.J. Machin,„Magnetism and Transition MetalChemistry“, Chapman and Hall,London 1973

R. Ribas, Coordination Chemistry,Wiley-VCH, Chap. 9

Magnetic Properties of Some Iron Compounds

Compound Magnetism RemarksFe metal ferromagnet TC = 1043 K (msat = 2.22 µB)FeO antiferromagnet TN = 716 KFeCl3 paramagnet µeff = 5.73 µB

y-Fe3O4 ferrimagnet TfN = 856 K[Fe(CN)6]4– diamagnetic ─[Fe(CN)6]3– paramagnetic µeff = µeff = 2.25 µB (300 K)Fe(Cp)2 diamagnetic ─Fe(CO)5 diamagnetic ─Haemoglobin paramagnetic µeff ~ 4.95 µB

1. Spin-Only-Paramagnetism

Effective magnetic moment, µeff, of 3d metal complexes can be estimated

to a first approximation with the spin-only formula

Beeff SSg µµ )1( +=

)1( +== SSgn eB

effeff µ

µ

µB = Bohr Magneton = eħ/(2me) =9.27408×10–24 J/Tµeff = effective magnetic momentneff = effective magnetic moment in units of µBge = 2.00232S = Σsi (Total spin quantum number)si = spin quantum number (+1/2 or -1/2)

i S neff

1 ½ 1.73

2 1 2.83

3 3/2 3.884 2 4.905 5/2 5.92

Note: in the OCP text book µeff is represented as meff

Spin-Only-Formula• spin-state of complex and• number of unpaired electrons can be determined

d3: CrIII, MoIII, MnIV, VII: 3.88 µB

d5: MnII, FeIII: 5.92 µB

neff(theor.)

neff data (~ 300 K) for selected compounds of d3 and d5 ions

d3

CrCl3 3.90 K3[Cr(ox)3].3H20 3.62[Cr(NH3)6]Br3 3.77 KCr(SO4)2.12H2O 3.84[Cr(en)3]Br3 3.82 K3[MoCl6] 3.79[Cr(bpy)3]Cl3 3.81 K2[MnCl6] 3.84K3[Cr(CN)6] 3.87 [V(en)3]Br2 3.81K3[Cr(NCS)6].4H2O 3.79 [V(bpy)3]Cl2 3.67K3[Mo(NCS)6].4H2O 3.70 [Mo(bpy)3]Cl3 3.66(NnBu4)3[Cr(N3)6] 3.76 K4[V(CN)6] 3.78

d5

MnCl2 5.79 FeCl3 5.73MnBr2 5.82 (Et4N)[FeCl4] 5.88(NH4)2Mn(SO4)2.6H2O 5.88 (NH4)Fe(SO4)2.12H2O 5.89[Mn(NH3)6]Cl2 5.92 K3[Fe(ox)3].3H2O 5.90(Et4N)2[MnCl4] 5.94

Ligands and Abbreviations

N

N

2,2'-Bipyridin(bpy)

ethylene diamine

H2NNH2

Co NMe3H2NCl

H2N

NH2

NH2

2+

donor atomChelate ring

bidentate ligandmonodentate lignd

rhodanide

S-CN

azide

N-N+-N

oxalate

OO-

O-O

(ox)

(en)

Spin-Only-Formula• spin-state and• number of unpaired electrons can be determined

d3: CrIII, MoIII, MnIV, VII: 3.88 µB

d5: MnII, FeIII: 5.92 µB

this is true also for more exotic compounds

[nBu4]2[Mn(CH3)6] 3.90 µB → MnIV, d3

V(Cp)2, Vanadocene 3.78 µB → VII, d3

Mn(Cp)2, Manganocene 5.86 µB → MnII, d5

Spin-Only Formula only valid for the following conditions:• room temperature (295 K)• for 3d TM ions (i.e. K2[ReIVCl6] = 3.25 µB (expected = 3.88 µB)• for mononuclear complexes (polynulcear complexes may show

cooperative phenomena (antiferro- or ferromagnetic interactions))• for totally quenched orbital momentum (= TM ions with E or A ground terms)

ferrocene

Fe

vandocene

V

manganocene

Mn Mn CH3H3C

CH3

H3C

CH3

CH3

2−

I- < Br- < S2- < SCN- < Cl- < N3- < F- < OH- < O2

- < OH2 < NCS- < NH3 ~ py < en < bpy < NO2

- < CH3- < CN- < CO

spectrochemical series:

Orbital contributions to the magnetic moment• do explain the deviations from the spin-only values• the orbital contribution to the magnetic moment is not totally quenched

Two prominent examples:CoCl2 5.47 µBCoCl42─ 4.67 µBexpected 3.88 µB → h.s.-CoII has d7 (3 unp. electrons)

general trends:d6 to d9: larger values than calculatedd1 to d4: smaller values than calculatedonly d5 is well behaved

This is readily explained

a) by the fact thatλ > 0 for d1-d4 andλ < 0 for d6-d9

λ = spin-orbit coupling constant

b) Fe3+ (S=5/2), L = ML = Σml = 0

L

S

L

S

Spin-orbit coupling can cause temperature dependent magnetic moments (Ti3+, d1)

Orbital contribution to the magnetic moment

Orbital contribution to the magnetic moment

Spin-only formula

Beeff SSg µµ )1( +=

the orbital angular momentum L has alsoa magnetic moment associated with it, for free ions with L and S,

Beeff SSgLL µµ )1()1( 2 +++=

orbit spin

Orbital momentum in transition metal ions and complexes

In coordination compounds orbital momentum means:electron can move from one d orbital to another degenerated orbital. However, dxy, dxz, dyz, and dzz, dx2-y2 are no longerdegenerate in a complex.

In an octahedral complex, e– can only move within anopen 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)

Terms with T symmetryexhibit orbital angular momentum

can show spin-orbit couplingThis rule is only applicable in Oh

Symmetry.

Terms with T symmetryexhibit L = 1, HSO = -AλLS

EJ = -1/2Aλ[J(J+1)-L(L+1)-S(S+1)For (t2g)n less than half occupied: λ positive

more than half occupied: λ negative

dx2-y2

dxy

(leer)

Quenching of the orbital contribution, T-term and A, E-term ions

Quenching of the orbital contribution, to the magnetic moment, due to ligand field

n ground t2gneg

m ligand field quenchingterm term

1 2D t2g1 2T2g No

2 3F t2g2 3T1g No

3 4F t2g3 4A2g Yes

4 5D t2g3eg

1 5Eg Yest2g

4 3T1g No5 6S t2g

3eg2 6A1g Yes

t2g5 2T2g No

6 5D t2g4eg

2 5T2g Not2g

6 1A1g Yes7 4F t2g

5eg2 4T1g No

t2g6eg

1 2Eg Yes8 3F t2g

6eg2 3A2g Yes

9 2D t2g6eg

3 2Eg Yes

These ionsactually

have L = 1

and thus a„residual“

contribution(not full

contribution)to the

spin moment

Octahedral symmetry

Typical Ions: Ti3+ (d1), V3+ (d2), l.s-Mn3+ (d4), l.s.-Fe3+ (d5, i.e. K3[Fe(CN)6])h.s-Fe2+ (d6), h.s.-Co(2+)

Magnetic moment depends also on C.N.Nickel(II), d8

octahedral (3A2g) 2.9 – 3.4 µBtetrahedral (3T1) 3.2 – 4.0 µBtrigonal bipyramidal 3.2 – 3.8 µB or 0square pyramidal 3.2 – 3.4 µB or 0square planar 0

Ni CNNCCN

NC

2−

Ni

Cl

ClCl

Cl

2−

N

NiH2NNH

NH2

NH2Ni

N

NH2NH2

H2N

Cl

2+ −

Orbital momentum

quenchednot quenched

CoII, tetr. 4.4-4.8 4A2CoII, oct., 4.8-5.3 4T1g

tetr. [NiX4]2- (X = Cl, Br, I) tetr. [Ni(SPh)4]2─[Ni(PPh3)2Br2] 3.27 µB

Spin equilibriaNiII(tetr.) ↔ NiII(sq.pl) (in solution)

High-spin and low-spin complexes

possible for d4-d7 electronic configurations (in octahedral complexes)possible for d3-d6 electronic configurations (in tetrahedral complexes)

AsPh2

AsPh2

Examples (all are low-spin):

d4 [Cr(bpy)3]2+ , [Cr(CN)6]4–, [Mn(CN)6]3– t2g4 S = 1

3.20 µB

d5 [Fe(CN)6]3–, [Fe(en)3]3+, [Mn(CN)6]4– t2g5 S = 1/2

2.25 µB 2.40 µB 2.18 µB

d6 [Fe(CN)6]4–, [Co(NH3)6]3+, [Cr(CO)6] t2g6 S = 0

d7 [Co(diars)3]2+, [Co(NO2)6]4–, [NiF6]3– t2g6eg1 S = ½

1.84 µB

the deviations from the ideal values are again attributable to orbital contributions to the magnetic moment

diars

High-spin → low-spin transitions, spincrossoverBecome feasible for d4 to d7 in octahedral case, if ∆o(h.s.) ~ ∆o(l.s.)

• h.s.->l.s transitions can be affected byvariation of temperature or pressure

• At lower temperature the l.s-formalways dominates

• l.s. and h.s. form can be present inan equilibrium (in solution as well asin solid state)

Prominet examples:

Fe, d5: [Fe(S2CNR)3]

High-spin → low-spin transitions

Fe, d5: [Fe(S2CNR)3]

High T µeff → 4.7 µB (h.s., S = 5/2) Low T µeff → 2.25 µB (l.s., S = ½)

S S-

N Fe SS

S

S

S

S

Spin-equilibria are rare.Abrupt spincrossover more oftenencounteredχ(50%L.S./50%H.S.) = χ(L.S.) + χ(H.S.)

High-spin and low-spin tetrahedral complexes

h.s. l.s.

n 3 1

h.s. l.s.

4 0

h.s. l.s.

5 1

d3 d4 d5 d6

h.s. l.s.

4 2

M 1-nor

d3: K3FeVO4 3.71 µB S = 3/2 (e)2(t2)1 high-spinReIV(o-tolyl)4 1.31 µB S = ½ (e)3(t2)0 low-spinMnIV(1-nor)4 3.78 µB S = 3/2 (e)2(t2)1 high-spin

d4: [CoV(1-nor)4]+ S = 0 (e)4(t2)0 low-spin[FeIV(1-nor)4]+ S = 0 (e)4(t2)0 low-spin[MnIII(1-nor)4]- S = 2 (e)2(t2)2 high-spin

MR4-complexes with 4d and 5d elements and sterically demanding ligandsare low-spin

High-spin → low-spin transitions

Fe NCSN

NCS

N

N

NN

N

cis-[FeII(NCS)2(phen)2]

Phenanthrolin (phen)

Fe, d6: [FeII(bpy)2(NCS)2]

High T µeff → 5.2 µB (h.s., S = 4/2) Low T µeff → 2.25 µB (l.s., S = 0)

High-spin and low-spin tetrahedral complexes

h.s. l.s.

n 3 1

h.s. l.s.

4 0

h.s. l.s.

5 1

d3 d4 d5 d6

h.s. l.s.

4 2

M 1-nor

d5: [NEt4][FeCl4] 5.88 µB S = 5/2 (e)2(t2)3 high-spin[NEt4][Fe(SPh)4] 5.73 µB S = 5/2 (e)2(t2)3 high-spinCoIV(1-nor)4 1.89 µB S = 1/2 (e)4(t2)1 low-spin

d6: [CoIII(1-nor)4]– 3.18 µB S = 1 (e)4(t2)2 low-spin

General observations:• low-spin tetrahedral complexes are rare (∆t = –4/9 ∆o)• a tetrahedral complex with low-spin configuration requires:

strong ligand field, a high-metal oxidation state, sterically demanding ligands(particularly for bigger 4d 5d elements) to prevent the formation of M-M bondsor adoption of coordination number 6

High-spin and low-spin complexes

• l.s.-d4, l.s.-d5, and l.s.-d7 display positive and commonly large deviationsfrom the spin only expectation (for the first transition series)Explanation: (t2g)n configurations behave magnetically like (p)n configs;when more than half-filled subshell (as is the case in d4-d7); S and Lare parallel; and any orbital contribution increases µeff beyond the spin-onlyvalue• All octahedral complexes of 4d and 5d elements are low-spin