Download Crystal-Field Theory Ligand-Field or Molecular Orbital Theory

How can we explain bonding between
metals and ligands?
Crystal-Field Theory
Ligand-Field or
Molecular Orbital Theory
October 4, 2010
The Periodic Table
Electronic structure of transition
metals
Filled ns, np shells; chemistry defined by unoccupied nd-orbitals
Number of d-electrons = Z – nearest noble gas e’s – charge
e.g.:
Fe(II) = 26 – 18 – 2 =6
Fe(III) = 26 – 18 – 3 = 5
d2z2-y2-x2
Valence Bond (VB) Theory
developed by Pauling in the 1930s - used in VSEPR
Useful in d-complexes sp3d, sp3d2, sp2d useful in CN = 5 (sp, tbp), 6 (octahedral), and 4 (square plana
Not much used for d- coplexes today, but some of the terminology is essential
Note limitations: M needs 3dx2-y2, 3dz2, 4s, 4px, 4py, 4pz to be unoccupied
applying VB:
3d
4s
4p
Cr+3
d2sp3
[Cr(NH3)6]+3
OK for all d3
Fe3+ d5 LS: ↑↓ ↑↓ ↑
3d
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ OK
d2sp3
Now consider Fe 3+ d5 HS octahedral: d2sp3
↑ ↑ ↑ ↑ ↑
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ sp3d2, but 4d?
d8 octahedral case
3d
4s
4p
4d
Ni+2
high spin sp3d2 again 4d
[Ni(NH3)6]+2
[Ni(L)4]2+
Tetrahedral case: 4L e- pair goes to sp3, OK, paramagnetic
Square planar case: dsp2
↑↓ ↑↓ ↑↓ ↑↓
3d(z2, xy, xz, yz)
↑↓ ↑↓ ↑↓ ↑↓
(dx2-y2)sp2
V
B
VB can rationalize geometry and magnetic properties on a simple level
cannot say anything about electronic spectra (color)
and why some ligands lead to HS and some to LS complexes
why LS d6 complexes are kinetically inert etc..
Need better theory!
Crystal-Field Theory
(gross over-simplification)
d2z2-y2-x2
INTERACTION OF d-ORBITALS with OCTAHEDRAL CRYSTAL FIELD of LIGANDS
Chemistry of TM complexes
controlled by where the
d-electrons are
d-electron energies
controlled by ligand
electrons
charges
charges
10Dq, a.k.a. ∆
Definition: energy splitting between the t2g and eg orbitals
Measurement:
eg
hν
∆E = 10Dq
t2g
[Ti(III)(H2O)6]3+ d-electrons = 22 - 18 – 3 = 1
hν = 20,300 cm-1 = green light (complex = violet)
= 58.04 kcal/mol (on the order of a bond)
∆oct = E= hν
Ti3+ d1
l
Spectrochemical series of ligands
Spectrochemical series of metal ions
Mn2+<Ni2+<Co2+<Fe2+<V2+<Fe3+,Co3+<Mn4+<Mo3+<Rh3+<Ru3+<Pd4+<Ir3+<Pt4+
Strong and weak field
Factors affecting 10 Dq
-Increased charge on metal: draws ligands in more closely; more effect
on d-orbital splitting
-Ligand type: spectrochemical series
-So named because “strong field” ligands have higher energy d-d
transitions (shorter wavelength UV/vis maxima)
I- < Br- < S2- < Cl- < NO3- < OH- ~ RCOO- < H2O ~ RS- < NH3 ~ Im
< 1,2-diaminoethane < bipy < CN-, CO
d2 Case
Electronic configuration is
same for strong or weak field case
d3 Case
Electronic configuration is
same for strong or weak field case
d4 Weak Field – High Spin (HS)
Case
∆o < Ep, pairing energy
S=2
4
d
Strong Field – Low Spin
Case
∆o > Ep, pairing energy
S=1
Electron pairing
Ions with equal and greater than d4 electronic configuration in octahedral (Oh)
coordination can have low and high spin forms depending on value of ∆o (10Dq)
octahedral
Fe3+ (d5)
Low spin
eg
∆o=10 Dq
t2g
P = spin pairing energy
High spin
eg
∆o =10 Dq
t2g
smaller than ∆o: S = ½
spin pairing energy larger
than ∆o: S = 5/2
LS: ∆o > P
HS: ∆o < P
Unpaired (non-integer) spin: paramagnetic
- detectable by magnetic measurement or sometimes by EPR
Crystal-field Stabilization Energy (CFSE)
CFSE = x(-4Dq) + y(+6Dq)
or since
∆o = 10 Dq
CFSE = x(-0.4∆o) +
y(+0.6∆o)
where
x = number of electrons in t2g (lower levels)
y = number of electrons in eg (upper levels)
Crystal-Field Stabilization Energy, CFSE
or
Ligand-Field Stabilization Energy, LFSE
d1
d2
= -0.8 ∆o
Low Spin
LFSE = -0.4∆o
High Spin
CFSE = x(-0.4 ∆o) + y(0.6 ∆o)
d3
= -1.2 ∆o
High Spin
Low Spin
d4
LFSE = -0.6 ∆o
-1.6 ∆o + P
d5
0
-2 ∆o + 2P
Pairing Energy, P
Two terms contribute to P:
1. loss of exchange energy
p3
— — — or — — —
E 2 E 1 > E2
E1
total exchange energy = Σ N ( N − 1) K
2
N = number of e- with parallel spin
K = exchange energy (characteristic of atom or ion) e.g., ∆E = E2-E1
2. coulombic repulsion between paired e-
Crystal-Field Stabilization Energy, CFSE or LFSE
CFSE = x(-0.4∆o) + y(+0.6 ∆o)
High Spin
High Spin
Low Spin
d6
Low Spin
d7
LFSE =
-0.4 ∆o + P -2.4 ∆o + 2P
d8
LFSE =
d10
d9
-1.2 ∆o
-0.8 ∆o
-0.6 ∆o
0
Note: largest CFSE-LFSE for LS, d6
-1.8 ∆o + P
r
Relationship between d-orbitals of TM surrounded by
tetrahedral coordination of ligands
Octahedral vs Tetrahedral Splitting Pattern of d-Orbitals
∆tet = 4/9; ∆tet ≅ 1/2 ∆o
tetrahedral
octahedral
∆O > ∆T thus no strong field vs. weak field cases for
tetrahedral complexes; note absence of subscript g in tetrahedral (t and e)
Color of tetrahedral complexes different
Octahedral HS
tetrahedral
S=½
1 unpaired e-
Co(II) d7
S = 3/2
3 unpaired e-
Total spin quantum #:
S ≡ Σ si
N
Σ = Summing over N electrons with
si spin quantum # on each elelctron
si = ±1/2
Jahn-Teller
Effect:
Cu2+ d9
J-T theorem: any nonlinear molecule in a degenerate
electronic state will be unstable and will undergo a
distortion to a system of lower symmetry and lower
energy thereby removing the degeneracy
J-T active ions:
Strong JT: HS-d4, d9 [LS d7]– eg orbitals
Weak JT: d1, d2, LS-d4, LS-d5, HS d7 – t2g
J-T does not predict if
distortion is:
elongation along z (as
shown)
or
elongation along x-y,
lowering dx2-y2
Would you expect JT in Td d4 and d9?
SQUARE PLANAR COMLEXES
elongation of M-L along z
second and third row d8 complexes are
square planar. E.g., Pd (II), Pt(II), Rh(I), Ir(I)
Square-planar Splitting Pattern of dOrbitals
Ni2+, d8
[Ni(CN)4]-2
Square planar Ni2+ complex is diamagnetic
S=0
Chapter 21 (20), self study on pg. 646 (564)
d8 complexes:[NiCl4]2- paramagnetic, S=1; and
Ni(CN)4]2- diamagnetic
tetrahedral
Squareplanar
-
---
--
--
Thermodynamic Aspects of LFSE
Lattice Energies of MCl2 compounds
M2+: Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Same for MF2, MF3 and [MF6]3- complexes
Ni
Cu
Zn
Deviation from d0, d5 and d10 is due to thermochemical LFSE
Agreement between e.g.: [Ni(H2O)6]2+, LFSE (thermochemical), 120 kJ/mol and LFSE
(spectroscopic), 126 kJ/mol (1.2∆oct deter. From spectra of [Ni(H2O)6]2+, ∆oct 8500 cm-1)
Must remember that LFSE is <10% of the total in
reaction energies
M2+ (aq) + H2O (l) → [M(H2O)6]2+ (aq)
Ni2+
Octahedral vs Tetrahedral coordination
Fig. 20.26 suggests that for d0, d5, and d10 there should be no preference for
octahedral or tetrahedral coordination; there is a large preference for octahedral
for d3 and HS d8
Case of spinels: MgAl2O6 mineral spinel; Mg2+ in Td while Al3+ in Oh site many analogous
“normal” spinel compounds with A2+(M3+)2O6 -LFSE can favor the formation of so-called
inverse spinels: e.g. normal: Fe(II)[(Cr(III)]2O4
LFSE [Cr(III) d3 1.2 ∆oct] > LFSE Fe(II) d6 (HS, -0.4 ∆oct)
Fe3+(Fe2+, Fe3+)O4 LFSE = 0 for Fe3+ (d5), but Fe2+ (d6) provides -0.4∆oct
What about Mn3O4, Co3O4
Review Chapter MO Theory: Chapter 2 Shriver and Atkins
Molecular Orbital Theory of Octahedral Complexes-[ML6]n+
See Oh character Table on Appendix 3
s
A1g or a1g totally symmetric irred. Rep
px, py, pz
T1u or t1u
dxy, dxz, dyz
T2g or t2g
dx2-y2, dz2
Eg or eg
X2+y2+z2
2z2-x2-y2, x2-y2
xy, xz, yz
x, y, z,
Molecular Orbital Theory – Octahedral complexes
X2+y2+z2
2z2-x2-y2, x2-y2
xy, xz, yz
x, y, z,
16S
[Ne] 3s23p4
M – L σ - bonding in a [ML6]n+ complex
M-L only σ bonding Bonding
Model
Example:[ Mo(CO)6]
Mo: 5s1 4d5 – 6e6CO: 12 eTotal of 18 e- fill into MOs:
[CoF6]3- High
Spin (HS)
a1g2, t1u6, eg4, t2g6 Low Spin (LS)
Co3+ : d6 – 6e6F-:
6x2 -
12e-
Total: 18 ea1g2, t1u6, eg4, t2g4 eg*2
so far not so different
from CFT as far as
t2g & eg
orbital splitting, filling
in [ML6]n+
Considering M-L π Bonding
difference between CFT and LFT
dπ-pπ
dπ -dπ
dπ-pπ*
dπ-σ*
Consider t2g set of ligand π-orbitals for Oh complex along x and z directions
interacting with dxz M orbital
z
px and pz LGO π-interaction wirh dxz
bonding and antibonding
x
Effect of π bonding with π-donating ligands: e.g., F-, Br-, Cl-, I-
electrons from π-donor L
fill t2g π orbitals
electrons from M fill t2g*
hence
∆O < no π-bonding
M – L π-bonding with π*-accapter ligands
e.g., R3N, CN-, CO
M – L π-bonding with π*-acceptor ligands:
e.g., R3N, CN-, CO
d-block metal organometallic
complexes and related complexes
tend to obey the effective atomic number
rule, or 18-electron rule
6 L provide 12 σ-bonding, a1g2, t1u6, eg4,
e- from M fill t2g
For π-acceptor ligands,
d electrons from M occupy t2g
since occupation of eg* is detrimental
to M-L bond formation (∆O is large!), π-acceptor
ligands are not favored for d7, d8, d9, d10
A low oxidation state organometallic complex
contains π-acceptor Ls and the M center tends
to acquire 18 e- in its valence shell (the 18-electron rule)
and filling the valence orbitals: a1g2, t1u6, eg4, t2g6 LS
π-donor ligands
π-acceptor ligands
Conclusions
For complexes with σ-donor, π-donor and π-acceptor ligands:
•∆o decreases with π-bonding donor ligands
•Increased π donation stabilizes the t2g orbitals, and destabilizes t2g* , decreasing ∆o
•π-acceptor ligands stabilize t2g level, and increase ∆o
•∆o is relatively large for π-acceptor ligands, thus they tend to be low spin
Observed spectrochemical series is explained:
I-, Br-, π-donating ligands are weak field (small ∆o)
CO, NO, CN- π-acceptor ligands, are strong field (large ∆o)