Crystal Field Theor1

Crystal Field Theory:•This theory (CFT) largely replaced VB Theory for interpreting the chemistry of coordination compounds.

CFT-Assumptions:•The interactions between the metal ion and the ligands are purely electrostatic (ionic). •The ligands are regarded as point charges •If the ligand is negatively charged: ion-ion interaction. interaction. If the ligand is neutral : ion-dipole interaction interaction •The electrons on the metal are under repulsive from those on the ligands •The electrons on metal occupy those d-orbitals farthest away from the direction of approach of ligands

Octahedral Comp C omp lexes In an octah octahedral edral comp complex lex,, there are six ligands attached to the central transition metal. metal. The d-orbital splits into two different levels. The The bottom three energy levels levels are named dxy, dxz, and dyz (collectively referred to as t2g). The two upper energy energy levels are named dx2−y2, and dz2 (collectively referred to as eg).

Figure: Splitting of the degenerate d-orbitals (without a ligand field) due to an octahedral ligand field

∆  ) the energy levels of  e  ). The distance that the electrons have to  e g are higher (0.6 ∆  o while  t 2g is lower (0.4 ∆ o

move from t 2g to e g and it dictates the energy that the complex will absorb from white light, which will  determine the color  the color . Whether the complex is paramagnetic is paramagnetic or diamagnetic  will  will be determined by the spin

trahedral

state. If there are unpaired electrons, the complex is paramagnetic;

Complexes In a tetrahedral complex, there are four ligands attached attached to the central metal. The d orbitals also split into two different energy levels. The top three consist of the dxy, dxz, and dyz orbitals. The bottom two consist of the dx2−y2 and dz2 orbitals. The reason for this is due to poor orbital overlap between the metal and the ligand orbitals. The orbitals are directed on the axes, while the ligands are not.

Figure 5: (a) Tetraheral ligand field surrounding a central transition metal (blue sphere). (b) Splitting of the degenerate d-orbitals (without a ligand field) due to an octahedral ligand field (left diagram) and the tetrahedral field (right diagram).

The difference in the splitting energy is tetrahedral splitting constant ( Δt), which less than ( Δo) for the same ligands: Δt=0.44Δo(1)

Consequentially, Δ t is typically smaller than the spin pairing energy, so tetrahedral complexes are usually high spin .

Square Planar Comp lexes In a square planar, there are four ligands as well. However, the difference is that the electrons of the ligands are only attracted to the xy plane. Any orbital in the xy plane has a higher energy level. There are four different energy levels for the square planar (from the highest energy level to the lowest energy level): d x -y , dxy, dz , and both d xz and dyz. 2

2

2

Figure 6: Splitting of the degenerate d-orbitals (without a ligand field) due to an square planar ligand field.

The splitting energy (from highest orbital to lowest orbital) is  Δ sp and tends to be larger then  Δ o Δsp=1.74Δo(2)

Moreover, Δ sp is also larger than the pairing energy, so the square planar complexes are usually low spin complexes.

Example 1 For the complex ion [Fe(Cl) 6]3- determine the number of d electrons for Fe, sketch the d-orbital energy levels and the distribution of d electrons amo them, list the number of lone electrons, and label whether the complex is paramagnetic or diamagnetic. SOLUTION  

Step 1: Determine the oxidation state of Fe. Here it is Fe 3+. Based on its electron configuration, Fe 3+ has 5 d-electrons. Step 2: Determine the geometry of the ion. Here it is an octahedral which means the energy splitting should look like:



Step 3: Determine whether the ligand induces is a strong or weak field spin by looking at the spectrochemical series. Cl- is a weak fie ligand (i.e., it induces high spin complexes). Therefore, electrons fill all orbitals before being paired.



Step four: Count the number of lone electrons. Here, there are 5 electrons. Step five: The five unpaired electrons means this complex ion is  paramagnetic (and strongly so).

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Example 2 A   tetrahedral complex absorbs at 545 nm. What is the respective octahedral crystal field splitting ( Δo)? What is the color of the complex? SOLUTION Δt=hcλ  Δt=(6.626×10−34J⋅s)(3×108m/s)545×10−9m=3.65×10−19J

However, the   tetrahedral splitting (Δt) is ~4/9 that of the   octahedral splitting (Δo). Δt=0.44Δo Δo=Δt0.44=3.65×10−19J0.44=8.30×10−18J

This is the energy needed to promote  one electron in  one complex. Often the crystal field splitting is given per mole, which requires this number to b multiplied by Avogadro's Number (6.022×1023). This complex appears red, since it absorbs in the complementary green color (determined via the color wh eel).

if all electrons are paired, the complex is diamagnetic.

Problems For each of the following, sketch the d-orbital energy levels and the distribution of d electrons among them, state the geometry, list the number of d-electrons, list the number of lone electrons, and label whether they are paramagnetic or dimagnetic: 1.

[Ti(H2O)6]2+

2.

[NiCl4]2-

3.

[CoF6]3- (also state whether this is low or high spin)

4.

[Co(NH3)6]3+ (also state whether this is low or high spin)

5.

True or False: Square Planer complex compounds are usually low spin.

 Answ er s 1. octahedral, 2, 2, paramagnetic

2. tetrahedral, 8, 2, paramagnetic (see Octahedral vs. Tetrahedral Geometries)

3. octahedral, 6, 4, paramagnetic, high spin

4. octahedral, 6, 0, diamagnetic, low spin

6.

True

For an octahedral complex CFSE = −0.4 x n(t2g) + 0.6 x n(eg) ∆o Where, n(t2g) and n(eg) are the no. of electrons occupying the respective levels If CFSE is very large, pairing occurs (i.e. CFSE > P) If CFSE is rather small, no pairing occurs (i.e P > CFSE)

∆o

is dependent on

•Nature of the ligands •The charge on the metal ion •Whether the metal is a 3d, 4d, or 5d element

Spectrochemical Series I− < Br− < S2− < SCN−