Magnetochemie
Conventional Magnets
- Fe, Co, Ni
- CrO2, Fe3O4
- Alloys
spincarriers: atoms
digital
„0“ and „1“
bulk magnet
Magnetochemie
Magnetic 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 remarks
This 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 remarks
Constants and units
χm
molar magnetic suceptibility
[cm3·mol–1]
[emu·mol–1]
[m3·mol–1]
Conversion factor: χm(cgs) × 4π10–6 = χm (SI)
(cgs/emu)
„
(SI)
µ eff / µ B = 2.828 ⋅ χT
3k B
mol
χm = -122.7×10–6 emu/mol
=
2
.
828
(
)
2
3
χm = -1.542×10–9 m3/mol
cm K
Nµ B
---------------------------------------------------------------------------------------------------------N = 6.023×1023 mol–1
µB = 0.92731×10–20 erg/Gauss;
µB = 9.27×10–24 J/T
kB = 1.38×10–23 J/K
K3[Fe(CN)6]
NµB2/(3kB) = 0.125 cm3/(K·mol)
cgs units, N = 6.023×1023 mol–1
µB = 0.92731×10–20 erg/Gauss; 9.27×10–24 J/T
Literature
A. F. Orchard, Magnetochemistry,
Oxford Chemistry Primer, 2007;
Chapter 5
F. E. Mabbs, D.J. Machin,
„Magnetism and Transition Metal
Chemistry“, Chapman and Hall,
London 1973
R. Ribas, Coordination Chemistry,
Wiley-VCH, Chap. 9
Magnetic Properties of Some Iron Compounds
Compound
Fe metal
FeO
FeCl3
y-Fe3O4
[Fe(CN)6]4–
[Fe(CN)6]3–
Fe(Cp)2
Fe(CO)5
Haemoglobin
Magnetism
ferromagnet
antiferromagnet
paramagnet
ferrimagnet
diamagnetic
paramagnetic
diamagnetic
diamagnetic
paramagnetic
Remarks
TC = 1043 K (msat = 2.22 µB)
TN = 716 K
µeff = 5.73 µB
TfN = 856 K
─
µeff = µeff = 2.25 µB (300 K)
─
─
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
µ eff = g e S ( S + 1) µ B
i
S
neff
µ eff
neff =
= g e S ( S + 1)
µB
1
½
1.73
2
1
2.83
3
3/2
3.88
4
2
4.90
5
5/2
5.92
µB = Bohr Magneton = eħ/(2me) =9.27408×10–24 J/T
µeff = effective magnetic moment
neff = effective magnetic moment in units of µB
ge = 2.00232
S = Σsi (Total spin quantum number)
si = spin quantum number (+1/2 or -1/2)
Note: in the OCP text book µeff is represented as meff
Spin-Only-Formula
neff(theor.)
• spin-state of complex and
• number of unpaired electrons can be determined
d3: CrIII, MoIII, MnIV, VII: 3.88 µB
d5: MnII, FeIII:
neff data (~ 300 K) for selected compounds of d3 and d5 ions
d3
CrCl3
[Cr(NH3)6]Br3
[Cr(en)3]Br3
[Cr(bpy)3]Cl3
K3[Cr(CN)6]
K3[Cr(NCS)6].4H2O
K3[Mo(NCS)6].4H2O
(NnBu4)3[Cr(N3)6]
3.90
3.77
3.82
3.81
3.87
3.79
3.70
3.76
K3[Cr(ox)3].3H20
KCr(SO4)2.12H2O
K3[MoCl6]
K2[MnCl6]
[V(en)3]Br2
[V(bpy)3]Cl2
[Mo(bpy)3]Cl3
K4[V(CN)6]
3.62
3.84
3.79
3.84
3.81
3.67
3.66
3.78
d5
MnCl2
MnBr2
(NH4)2Mn(SO4)2.6H2O
[Mn(NH3)6]Cl2
(Et4N)2[MnCl4]
5.79
5.82
5.88
5.92
5.94
FeCl3
(Et4N)[FeCl4]
(NH4)Fe(SO4)2.12H2O
K3[Fe(ox)3].3H2O
5.73
5.88
5.89
5.90
5.92 µB
Ligands and Abbreviations
O
-
N
O
O
Ooxalate
(ox)
rhodanide
N C S-
N
H2N
2,2'-Bipyridin
(bpy)
azide
ethylene diamine
(en)
-
N N+ N-
2+
bidentate ligand
NH2
Cl
H2N
H2N
Chelate ring
NH2
Co
NH2
monodentate
lignd
NMe3
donor atom
Spin-Only-Formula
• spin-state and
• number of unpaired electrons can be determined
this is true also for more exotic compounds
[nBu4]2[Mn(CH3)6]
V(Cp)2, Vanadocene
Mn(Cp)2, Manganocene
3.90 µB → MnIV, d3
3.78 µB → VII, d3
5.86 µB → MnII, d5
d3: CrIII, MoIII, MnIV, VII: 3.88 µB
5.92 µB
d5: MnII, FeIII:
ferrocene
Fe
vandocene
V
2−
CH3
CH3
spectrochemical series:
I- < Br- < S2- < SCN- < Cl- < N3- < F- < OH- < O2- < OH2 <
NCS- < NH3 ~ py < en < bpy < NO2- < CH3- < CN- < CO
Mn
manganocene
H3C Mn CH3
H3C
CH3
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)
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:
5.47 µB
CoCl2
CoCl42─
4.67 µB
expected
3.88 µB → h.s.-CoII has d7 (3 unp. electrons)
general trends:
d6 to d9: larger values than calculated
d1 to d4: smaller values than calculated
only d5 is well behaved
L
L
S
S
This is readily explained
a) by the fact that
λ > 0 for d1-d4 and
λ < 0 for d6-d9
λ = spin-orbit coupling constant
b) Fe3+ (S=5/2), L = ML = Σml = 0
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
µ eff = g e S ( S + 1) µ B
the orbital angular momentum L has also
a magnetic moment associated with it, for free ions with L and S,
µ eff = L( L + 1) + g e 2 S ( S + 1) µ B
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 degenerate
d orbital. However, dxy, dxz, dyz, and dzz, 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)
dxy
dx2-y2 (leer)
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
Terms with T symmetry
exhibit orbital angular momentum
can show spin-orbit coupling
This rule is only applicable in Oh
Symmetry.
Terms with T symmetry
exhibit L = 1,
HSO = -AλLS
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
Octahedral symmetry
n
ground t2gnegm
term
ligand field
term
quenching
1
2
3
4
2D
5
6S
6
5D
7
4F
8
9
3F
2T
2g
3T
1g
4A
2g
5E
g
3T
1g
6A
1g
2T
2g
5T
2g
1A
1g
4T
1g
2E
g
3A
2g
2E
g
No
No
Yes
Yes
No
Yes
No
No
Yes
No
Yes
Yes
Yes
3F
4F
5D
2D
t2g1
t2g2
t2g3
t2g3eg1
t2g4
t2g3eg2
t2g5
t2g4eg2
t2g6
t2g5eg2
t2g6eg1
t2g6eg2
t2g6eg3
These ions
actually
have L = 1
and thus a
„residual“
contribution
(not full
contribution)
to the
spin moment
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
Orbital momentum
octahedral (3A2g)
tetrahedral (3T1)
trigonal bipyramidal
square pyramidal
square planar
2.9
3.2
3.2
3.2
0
– 3.4 µB
– 4.0 µB
– 3.8 µB or
– 3.4 µB or
CN
NC
Ni
CN
Ni
Cl
NC
0
0
2−
Cl
2−
quenched
not quenched
CoII, tetr. 4.4-4.8
CoII, oct., 4.8-5.3
Cl
4A
2
4T
1g
Cl
−
2+
N
N
H 2N
H2N
N
H
Ni
NH2
N
H2
N
H2
Ni
Cl
NH2
tetr. [NiX4]2- (X = Cl, Br, I)
tetr. [Ni(SPh)4]2─
[Ni(PPh3)2Br2] 3.27 µB
Spin equilibria
NiII(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
diars
Examples (all are low-spin):
d4
[Cr(bpy)3]2+ , [Cr(CN)6]4–, [Mn(CN)6]3–
t2g4
S=1
d5 [Fe(CN)6]3–, [Fe(en)3]3+, [Mn(CN)6]4–
t2g5
S = 1/2
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
3.20 µB
2.25 µB
2.40 µB
1.84 µB
2.18 µB
the deviations from the ideal values are again attributable to orbital
contributions to the magnetic moment
High-spin → low-spin transitions, spincrossover
Become feasible for d4 to d7 in octahedral case, if ∆o(h.s.) ~ ∆o(l.s.)
• h.s.->l.s transitions can be affected by
variation of temperature or pressure
• At lower temperature the l.s-form
always dominates
• l.s. and h.s. form can be present in
an equilibrium (in solution as well as
in solid state)
Prominet examples:
Fe, d5: [Fe(S2CNR)3]
High-spin → low-spin transitions
S
S
N
S
S-
S
Fe
S
S
S
Fe, d5: [Fe(S2CNR)3]
High T
Low T
χ(50%L.S./50%H.S.) = χ(L.S.) + χ(H.S.)
µeff → 4.7 µB (h.s., S = 5/2)
µeff → 2.25 µB (l.s., S = ½)
Spin-equilibria are rare.
Abrupt spincrossover more often
encountered
High-spin and low-spin tetrahedral complexes
d3
d6
d5
d4
M
n
h.s.
l.s.
h.s.
l.s.
h.s.
l.s.
h.s.
l.s.
3
1
4
0
5
1
4
2
d3: K3FeVO4
3.71 µB S = 3/2 (e)2(t2)1 high-spin
ReIV(o-tolyl)4 1.31 µB S = ½ (e)3(t2)0 low-spin
MnIV(1-nor)4 3.78 µB S = 3/2 (e)2(t2)1 high-spin
d4: [CoV(1-nor)4]+
[FeIV(1-nor)4]+
[MnIII(1-nor)4]-
S = 0 (e)4(t2)0 low-spin
S = 0 (e)4(t2)0 low-spin
S = 2 (e)2(t2)2 high-spin
MR4-complexes with 4d and 5d elements and sterically demanding ligands
are low-spin
1-nor
High-spin → low-spin transitions
N
N
N
N
N
Fe
NCS
NCS
N
Phenanthrolin (phen)
cis-[FeII(NCS)2(phen)2]
Fe, d6: [FeII(bpy)2(NCS)2]
High T
Low T
µeff → 5.2 µB (h.s., S = 4/2)
µeff → 2.25 µB (l.s., S = 0)
High-spin and low-spin tetrahedral complexes
d3
d6
d5
d4
M
n
h.s.
l.s.
h.s.
l.s.
h.s.
l.s.
h.s.
l.s.
3
1
4
0
5
1
4
2
d5: [NEt4][FeCl4]
[NEt4][Fe(SPh)4]
CoIV(1-nor)4
5.88 µB S = 5/2 (e)2(t2)3 high-spin
5.73 µB S = 5/2 (e)2(t2)3 high-spin
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
1-nor
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 bonds
or 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 deviations
from 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 L
are parallel; and any orbital contribution increases µeff beyond the spin-only
value
• All octahedral complexes of 4d and 5d elements are low-spin