Crystal & Ligand field theory

Topics: Ligand, Inorganic chemistry, Paramagnetism Pages: 59 (7037 words) Published: November 2, 2014
© Drs. XO, PHB, CWR

Crystal & Ligand Field Theory (10.2.1, 10.3)

CHEM 241
Fall 2014
TM − p.1

Ligand field theory (the MO version of crystal field theory) includes two main components:
1. What holds the complexes together:
The set of ligands are held to a metal ion by largely electrostatic forces (although there really is a high degree of covalency). The forces arise from the positive charge on the metal ion and the electric dipoles of the ligands, whose negative ends are associated with the donor atom lone pairs. See Chem 341. 2. What gives the complexes their unique properties - colour and magnetic properties:

This is connected to the effect of the electric field of the ligands on the metal d orbitals and the electrons in them. This effect is a repulsion, so it does not explain the bonding. But, it does explain the d orbital energies in a complex. In what follows, we concentrate on the second component only.

© Drs. XO, PHB, CWR

Octahedral Ligand Field (10.3.1 too detailed)

Any electron in a d orbital is
repelled by the ligand lone pairs
(like charges…) and therefore has
its energy increased relative to what
it would be in the free metal ion.

CHEM 241
Fall 2014
TM − p.2

The ligand lone pairs
(negatively charged)
are located on the
x,y,z coordinate axes.

An electron in a dx2-y2 or dz2
orbital is closer to the ligands
than if it were in a dxy, dxz or dyz
orbital, and so is more repelled
by the lone pairs. These two
metal orbitals (dx2-y2 & dz2)
orbitals are therefore at
higher energy.

eg set (higher E)
orbitals along x,y,z
(aimed at Ls)

t2g set (lower E)
between x,y,z
Figures from: Kotz & Treichel,
Chemistry & Chemical Reactivity,

© Drs. XO, PHB, CWR

CHEM 241
Fall 2014
TM − p.3

Oh Ligand Field – Splitting (10.3.2)


Relative to the free ion, both sets of d orbitals
are at higher energy, but the eg set are higher
by an energy difference ∆o

Figures from: Kotz & Treichel, Chemistry & Chemical Reactivity, Thomson

© Drs. XO, PHB, CWR

Tetrahedral & Square Planar Crystal Fields

CHEM 241
Fall 2014
TM − p.4

(10.3.4 & 10.3.5 are too detailed)
Note: ∆t = 4/9 ∆o and ∆sp = ∆o if all other things
are the same, i.e. same metal ion & same ligands.


This is unlikely in practice.







Figures from: Kotz & Treichel, Chemistry & Chemical Reactivity, Thomson


© Drs. XO, PHB, CWR

CHEM 241
Fall 2014
TM − p.5

Octahedral Electron Configurations (10.3.2)

High spin

If the ligand field is
strong (the value of ∆o
is large), the electrons
will pair in the t2g
orbitals. This is the low
spin (or spin-paired)

Low spin

If the ligand field is weak
(the value of ∆o is
small), the electrons will
fill the t2g and then eg
orbitals with one
electron each orbital
before pairing begins.
This is the high spin (or
spin-free) configuration.

Note. This distinction only matters for configurations d4 to d7 and is due to the balance between unfavorable interelectronic repulsions if they go into the same orbital versus the energy cost of using the eg set.

Figures from: Kotz & Treichel, Chemistry & Chemical Reactivity, Thomson

© Drs. XO, PHB, CWR

Ligand Field Stabilization Energy (10.3.3)
Average energy
(spherical field)

CHEM 241
Fall 2014
TM − p.6

The ligand field
stabilization energy
(LFSE) is the total
energy of the
electrons relative
to the average
shown by the
dotted line.

Octahedral LFSE = (2/5 x # of t2g electrons - 3/5 x # of eg electrons)∆ ∆o
For the d7 configurations shown above, this is:
High spin case: LFSE = (2/5 x 5 - 3/5 x 2)∆
∆o = 4/5∆
Low spin case: LFSE = (2/5 x 6 - 3/5 x 1)∆
∆o = 9/5∆
Note that the quantity is a stabilization, so thermodynamically, the energy is understood have a negative sign if it is not explicitly written.

© Drs. XO, PHB, CWR

So how large is ∆o? (10.4.4)

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