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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
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
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