Descriptive Ligand Field Theory - luc.edu

Descriptive Ligand Field Theory

CHEMICAL BONDS recall that (1) the "chemical glue" that "binds" two atoms has its

origin in the electrons shared by and located between those two atoms, and (2) electrons

reside in orbitals. Accordingly, knowledge of orbital locations informs where electrons

reside, and that's where bonds will be found. Consequently, knowledge of TM vs orbital

shapes, locations and names are very important to arguments that follow:

Six-coordinate Complexes in an Oh Field C.N. = 6 and pt. gp. symmetry = Oh

transformation properties of d orbitals in Oh pt. gp. symmetry (a char.table look-up)
d d ez2 and x 2− y2 transform as the g two-dimensional irreducible representation.

dxy , d xz , dyz transform as the t2 g three-dimensional irreducible representation

Consider six ligands positioned at Oh sites as L1
they approach a TM atom/ion to form an
Oh coordination complex, as shown to the right: +z
L2
Now superimpose on this diagram the five
TM L3
d orbitals. Note that orientation of the +x
L6 +y
L5

d dz2 and x 2− y2 pair allows for greater L4

interaction with ligand orbitals , then does

the dxy , d xz , dyz set, which has lobes oriented between incoming ligands. Based on

TM to ligand e-e repulsions, TM vs electrons in the former set will be perturbed more by ligand

electrons and this leads to a differentiation (splitting) of energies for d orbitals in the complex.

(1) Sigma-bonded Oh TM Complexes

Transformation properties of sigma-bonding p-type atomic orbitals for six ligands…

Using methods met and used in Chapter 5, ligand σ -bonding orbitals transform as
Γ a + e + t(σ bonds) = 1g
g 1u The only TM - ligand bonding interaction involves

the eg symmetry orbitals, i.e., eg

d dz2 and x 2 − y2 of the TM.

The TM dxy , d xz , dyz are

non-bonding in this case. The MO t2g
diagram for a sigma bonded Oh TM

complex is shown as Figure 10-5 on

page 321. Isolation of TM d orbitals from this diagram shows the above pattern. The

∆oenergy difference between eg and t2 g TM orbitals in Oh complexes is labeled

and is represented by the arrow in the above diagram. The MAGNITUDE of the
∆oenergy difference
can vary and depends on (a) inherent bonding strength of the

ligand, and (b) charge of the TM ion.

Energy is conserved in the splitting, so the net destabilization of the eg set (two

orbitals) is offset by the stabilization of the t2 g set (three orbitals). Or,

2 x 3 (destabiliz ) + 3x −2 (stabiliz) = 0
5 5

Applying factors of (3 / 5) and ( -2 / 5) to electrons in eg and t2 g sets respectively,

gives the Ligand Field Stabilization Energy. LFSE can be used to show which

particular d n configurations will be more (or less) favored for Oh complex formation.

Refer to text Table 10-5 on page 325, and the following development…

d 1 [as in Ti(III)] LFSE = (3/5)[ 0 ] + (-2/5)[ 1 ] = -2/5

d 2 [as in Ti(II), LFSE = (3/5)[ 0 ] + (-2/5)[ 2 ] = -4/5

V(III) ]

d 3 [as in V(II), LFSE = (3/5)[ 0 ] + (-2/5)[ 3 ] = -6/5

Cr(III) ]

∆oTwo situations arise for d 3 through d 7 depending on the MAGNITUDE of .
∆oWhen energy of
is small, relative to energy required for electron pairing, then a

WEAK FIELD (with respect to ligand bonding strength) or HIGH SPIN (with respect to

number of unpaired electrons) condition prevails and so the maximum number of

unpaired electrons will be present.

∆oWhen energy of is large, relative to energy required for electron pairing, then a

STRONG FIELD or LOW SPIN condition prevails and the t2 g set is filled before the eg .

Consider the following diagrams and LFSE's…

WEAK FIELD STRONG FIELD

d 4 [as in Cr(II),

Mn(III) ]

LFSE = (3/5)[ 1 ] + (-2/5)[ 4 ] = -3/5

LFSE = (3/5)[ 0 ] + (-2/5)[ 4 ] = -8/5

∆o ∆o(weak field) < (strong field)

Notice that the d 4 weak field case results in FOUR unpaired electrons, but the strong field

case has only TWO unpaired electrons. So measurements of magnetic moments are used to

identify and distinguish between strong field and weak field ligands.

Convince yourself that the following results would be obtained for d 5 ,d 6 , d 7 cases…

[ WEAK FIELD ] LFSE n [ STRONG FIELD ]LFSE n

d5 0 5 -10/5 1

d 6 -2/5 4 -12/5 0

d 7 -4/5 3 -9/5 1

For 8 and 9 d vse, only weak field cases are possible so they would be as indicated below.

d8 -6/5 2 and d 9 -3/5 1

LFSE are largest for d 6 in a strong field, and zero for d 5 in a weak field. This information can

be used to account for some observations in the accumulated data presented at the beginning

of the hour: Co(III) has the largest hydration energy , and its aqua complex is a d 6 strong

field case. Mn(II) and Fe(III) have lowest hydration energies, and they both are d 5 weak field

cases having LFSE = 0.

Magnetic moments are very informative in identifying ox.sts. and field strengths of complexes.

Consider some information about iron complexes. Octahedral complexes of Fe(II), a d 6 case,
can be strong field/low spin with n =0, or weak field/high spin with n =4. Octahedral

complexes of Fe(III), a d 5 case, can be strong field/low spin with n =1, or weak field/high spin
with n =5. Magnetic moments for the four situations would be

diamagnetic, µ( so) = 4.9, µ( so) = 1.8, µand ( so) = 5.9 B.M. respectively.

(2) Pi-bonded Oh TM Complexes 2p

Carbon Monoxide, a pi-acceptor ligand. 2p
Consider the mo diagram for CO, a ten
electron system.

The HOMO is associated more with
carbon, as is the empty pi* LUMO .

The sigma bond from CO to the TM

involves the HOMO, and is why the 2s

bond is TM - C instead of TM - O. C 2s
Energy of the empty pi* LUMO is
O

similar to that of the TM d vse, and more

importantly, they are symmetry matched, so

bonding between them is possible. In this instance however, the TM furnishes

electrons to the empty pi* LUMO, in a manner known as "back-bonding".

The combination of a sigma bond (donation from C in CO to the TM) and pi-bond (back-
bonding from TM to empty pi* LUMO in CO) makes for exceptionally strong net
bonding. It is the reason for the toxicity of CO which binds so strongly to heme iron in
blood that it can no longer process oxygen. Cyanide anion is isoelectronic with CO and
is also an excellent pi-acceptor ligand. Pi-acceptor ligands are strong field ligands.

Compare CO and CN 1 - to chloride anion, Cl 1 - . Chloride anion has a complete octet
of vse; all of its vs are filled so it cannot accept (pi) electrons from TM. However, it can
donate pi electrons to the TM. But the TM in a complex is already in enough trouble
w/r to electrons and doesn't need any more. Consequently, pi-donor ligands like
chloride anion are weak field ligands; they present too much electron density to the TM.

(3) Relative Bonding Strengths of Ligands - The Spectrochemical Series

∆oWhen the bonding effects ( i.e., values) of series of ligands are compared for

∆osimilar TM's, and then arranged in order of magnitudes of , a qualitative sequence

of ligands results that is called the Spectrochemical Series. A simple example follows:

STRONG FIELD MODERATE FIELD WEAK FIELD
CO CN1 - o-phen
pi-acceptor ligands NO 2 1 - en NH 3 H 2 O F 1 - RCO 2 1 - OH 1 - Cl 1 - Br 1 - I 1 -

sigma donor ligands pi-donor ligands

∆oThe effect of larger values can be demonstrated by the color of coordination

complexes. Consider two complexes of Ni(II), the hexaaqua and hexaammine

complexes. As will become apparent soon, Ni(II), a d 8 system, displays a three-band

absorption spectrum. The hexaaqua complex is green and the hexaammine blue.

These colors are observed b/c the energies they represent are not absorbed, as

shown in the following diagram of the visible range of energies…

Visible region of the
electromagnetic
spectrum

[ Ni ( H 2 O ) 6 ] 2 +
complex, absorbs
energies (in black)
and appears green
in color.

[ Ni ( NH 3 ) 6 ] 2 +
complex, absorbs
energies (in black)
and appears blue
in color.

In both spectra the color is due to the three-band absorption system of the nickel(II) ion
However, ammonia is a stronger field ligand than water so the 3 bands absorb at higher
energies. This shifts the transparent "window" between the center and right absorption
bands to higher energies and imparts a blue color to the ammine complex.

Water is classified as a ligand of moderate/weak donating ability, so it would be
anticipated that aqua complexes are WEAK FIELD / HIGH SPIN cases. Indeed that is
found to be the case , except for one FROTM ion. Only one TM cation forms a strong

field complex with water as ligand, and that is Co(III), a d 6 system. Recall that d 6
strong field has the highest LFSE . Complexes of d 6 strong field are diamagnetic.

Four-coordinate Complexes in a Square-Planar Field C.N. = 4 and pt. gp. symmetry = D4h

transformation properties of d orbitals in D4h pt. gp. symmetry (a char.table look-up)
d az2 transforms as the 1g irreducible representation
d bx 2− y2 transforms as the 1g irreducible representation.
dxy transforms as the b2g irreducible representation, and
d xz , d yz transform as the eg two-dimensional irreducible representation

Consider four ligands in a square-planar +z

arrangement approaching on the ± x and L4 L3
± y daxes. Clearly the x 2− y2 would be
TM L2
most directly in-line with the ligands and
+y
has the highest energy. Remaining d
+x L1
orbitals would be affected in the following

order dxy then dz2 and lastly the d xz , d yz pair. This leads to the splitting pattern

as shown to the right. The numbers indicate the b1g
ordering of entering electrons into this pattern.

Ni(II), a d 8 system, forms square-planar complexes. 7,8 b2g

Introducing 8 electrons into the sq-planar pattern 5,6 a1g
results in a diamagnetic condition. This feature
allows identification and differentiation of sq-planar

Ni(II) complexes from Oh Ni(II) complexes because e1,3 2,4 g
the Oh compounds will be paramagnetic with

µ( so) =2.83 B.M.

All available information is used when characterizing coordination compounds, including

chemical analysis, magnetic moments, conductances, and (from the next chapter)

absorption spectra. So while it may be possible to differentiate sq-planar Ni(II) with four

donor atoms, from Oh Ni(II) with six donor atoms by chemical analysis alone, all

information available is collected and applied to the problem. Differences in magnetic

moments for sq-planar and Oh Ni(II) offers additional reliable information for making

the determination.

Four-coordinate Complexes in a Tetrahedral Field C.N. = 4 and pt. gp. symmetry = Td

transformation properties of d orbitals in Td pt. gp. symmetry (a char.table look-up)
d d ez2 and x 2− y2 transform as the two-dimensional irreducible representation.

dxy , d xz , dyz transform as the t2 three-dimensional irreducible representation

Note in Td symmetry there are no g or u subscripts. This is b/c in Td symmetry there is no

inversion center.

In a Td symmetry field, the splitting pattern t2
e
for the five d orbitals is as shown to the right.

Note that it is the inverse of the Oh splitting
pattern.

The energy difference between the two levels is labeled ∆t and is represented by the arrow

in the diagram. Because there are only four donor atoms the Td field is less than an Oh field.

In fact it can be shown that ∆t ≈ 4 ∆o . Consequently, Td complexes are always
9

WEAK FIELD / HIGH SPIN cases.

Ni(II) also forms Td complexes as well as Oh and sq-planar complexes, and even five-
coordinate complexes. Its coordination depends very much on the ligand itself. One of the fun
parts of coordination chemistry is in the designing and subsequent preparation of specific
ligand types to cause formation of a complex having a particular geometrical arrangement.

Chemical analysis and magnetic moment determinations often allows differentiation between
six-coordinate and four-coordinate complexes, and in the latter case, between tetrahedral and
square-planar geometries.