Application of CFT

 

APPLICATIONS OF CRYSTAL FIELD THEORY

Crystal field theory was developed by Hans Bethe(1929) and Van Vleck(1935). This theory (CFT) largely replaced Valence Bond Theory for interpreting the chemistry of coordination compounds.

Main assumptions in CFT,

·         According to CFT, the interactions between the central metal ion and its ligands are

purely electrostatic (ionic).

·         The ligands are treated as point Charges.

·         If the ligand is anionic : ion-ion interaction. If the ligand is neutral : ion-dipole interaction

·         The electrons on metal occupy those d-orbitals farthest away from the direction of approach of ligands.

Three p - orbitals

Five d - orbitals

In octahedral field:

dxy, dxz, dyz ▬ t_2g set

dz², dx²-y² ▬ e_g set

Applications of CFT are,

1.      Ionic Radii: In a transition series, for a given oxidation state, the ionic radius decreases steadily on going from left to right (dotted line). For weak field ligand, ionic radius increases with t_2g³e_g¹ configuration as the electron in the e_g level experience repulsion with the ligands. For strong field ligand, ionic radius increases with t_2g⁶e_g¹ configuration.

Ionic radii of M²⁺ in MCl₂

Fig: Plot of ionic radii vs number of  d-electrons present in bivalent metal ions.

1.      Lattice energy: Lattice energy of an ionic crystal is defined as the amount of energy released when one mole of the ionic crystal is formed by the combination of the constituent gaseous cations and gaseous anions of the ionic crystal. Thus the lattice energy of MX₂ ionic crystal is the energy released in the reaction.

M₂(g)+2X^-(g) à MX₂(s) + Energy released(lattice energy)

Across the transition series lattice energy increases continuously as  the ionic radii of the metals decrease. Deviations from expected line can be attributed to CFSE. Ca^2+, Mn²⁺ and Zn²⁺ have d⁰, d⁵ and d¹⁰ which have a common CFSE is 0 lie on a curve that is nearly a straight line i.e. they follow the expected line. Other metal ions deviate from the expected line due to extra CFSE. CFSE increases from d¹ to d³ and decreases again to d⁵, then rises to d⁸.

MF₂ of first row transition metals

Fig: Plot of lattice energy vs number of d-electrons of bivalent metal fluorides of the 1^st transition series.

1.      Enthalpy of Hydration/Formation: The enthalpy of hydration is closely related to the enthalpy formation of hexaaqua complex. The variation of enthalpy of M²⁺ ions M²⁺(g) + 6 H₂O(l) =[M(OH₂)₆]²⁺(aq).

 Stronger electrostatic attraction energy between ions and water dipoles increases hydration enthalpy (ΔH). ΔH is proportional to the charge but inversely proportional  to the radius of the ion. ΔH should increase continuously across transition series due to decrease in ionic radii. But, experimental ΔH values show characteristic double-humped shaped curve which can be account for by variation of  CFSE with d orbital configuration.

The trend for hydration enthalpies corresponds with the one for the ionic radii

M²⁺(g) + 6 H₂O(l) = [M(H₂O)₆]²⁺(aq)

H₂O = weak field ligand

Fig: Plot of heat of hydration of M²⁺ ions vs number of d electrons present in M²⁺ ions.

1.     Crystal structure of spinals: The mixed oxides of divalent and trivalent metal ions are called spinals. Spinals are of two types,(a)normal spinal and (b)inverse spinal.

Normal Spinal: These are represented by the general formula AB₂O₄ (i.e.A²⁺B³⁺ B³⁺).where A is a divalent cations like Mg, Cr, Mn, Fe, Co, Ni, Cu, Zn, Cd. B is a trivalent cation like Al, In, Ti, V, Cr, Mn, Fe, Co. In this spinals all the A²⁺ cations occupy the tetrahedral holes and all B³⁺ occupy octahedral holes. If M³⁺ ion has a higher CFSE in an octahedral field compared to M2+ ion, normal spinel will result. Example:FeCr₂O₄ ,Mn₃O₄ ,Co₃O4 etc.

Mn₃ O₄ (oxygen weak field ligand)

Mn²⁺ ; d⁵ = t_2g³e_g²; no CFSE

Mn³⁺; d⁴ = t_2g³e_g¹; 0.6 Δo

Structure is Normal Spinel.

Inverted Spinals: These are represented by the formula, B(AB)O₄ (i.e.B²⁺A³⁺B³⁺O₄). In these spinals all the bivalent cations and half of trivalent cations are in octahedral holes. The remaining half of the trivalent cations are in tetrahedral holes. If M²⁺ ion has a higher CFSE in an octahedral field compared to M³⁺ ion, inverse spinel will result. Examples:NiAl₂O₄ ,Fe₃O₄ , etc.

Fe₃O₄ (oxygen is weak field ligand)

Fe2+; d6 = t_2g⁴ e_g² ; 0.4 Δo

Fe³⁺ ; d5 = t_2g³ e_g² ; no CFSE

Structure is Inverse Spinel.

1.     Distortion in octahedral and tetrahedral complexes (Jahn Teller Distortion): It describes the geometrical distortion of molecules and ions that is associated with certain electron configurations. The Jahn–Teller theorem essentially states that any nonlinear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion which removes that degeneracy, because the distortion lowers the overall energy of the species.

Some examples of Jahn-Teller distorted complexes are,

CuBr2                                                  4 Br at 240pm 2 Br at 318pm

CuCl2.2H2O                           2 O at 193pm 2 Cl at 228pm 2 Cl at 295pm

CsCuCl3                                 4 Cl at 230pm 2 Cl at 265pm

CuF2                                       4 F at 193pm 2 F at 227pm

CuSO4.4NH3.H2O                4 N at 205pm 1 O at 259pm 1 O at 337pm

K2CuF4                                  4 F at 191pm 2 F at 237pm

CrF2                                        4 F at 200pm 2 F at 243pm

KCrF3                                     4 F at 214pm 2 F at 200pm

MnF3                                      2 F at 209pm 2 F at 191pm 2 F at 179pm

 

 Octahedral Field:

t2g (dxy, dxz, dyz )

eg (dz², dx²-y²)—shaded

Example:

 For d⁵ system,

 CFSE=-20Dq or -2 Δo  t2g⁵ eg⁰ (low spin). Hence in this case John Teller Distortion can occur.

                       0 Dq or 0 Δo   t2g³ eg² (high spin).Here John Teller Distortion does not occur.

Octahedral transition-metal ions with d¹, d², d³,d⁴,d⁵, d⁶, d⁷,d⁸, d⁹,and d¹⁰ configurations can be described by the following diagrams .

 Tetrahedral Complexes:

D t < D o

D t = 4/9 D o

All tetrahedral complexes are high-spin since the CFSE is normally smaller than the paring energy. Hence low spin configurations are rarely observed. Usually, if a very strong field 

1.      Colour of transition metal complexes: Although visible light appears "white", it is made up of a series of colors. White light consists of three primary colors (red, yellow and blue). These primary colors can be mixed to make three secondary colors (orange, green and violet).

An color wheel is a useful way show to these relationships. If we add the colors on opposite sides of the wheel together, white light is obtained. We only detect colors when one or more of the wavelengths in the visible spectrum have been absorbed, and thus removed, by interaction with some chemical species .When the wavelengths of one or more colors is absorbed, it is the colors on the opposite side of the color wheel that are transmitted. 

Transition Metal Complexes:When light passes through a solution containing transition metal complexes, we see those wavelengths of light that are transmitted. The solutions of most octahedral Cu(II) complexes are blue. The visible spectrum for an aqueous solution of Cu(II), [Cu(H₂O₆]²⁺, shows that the absorption band spans the red-orange-yellow portion of the spectrum and green, blue and violet are transmitted.

The absorption band corresponds to the energy required to excite an electron from the t_2g level to the e_g level.

 

the energy possessed by a light wave is inversely proportional to its wavelength. The Cu(II) solution transmits relatively high energy waves and absorbs the low energy wavelengths. This indicates that the band gap between the two levels is relatively small for this ion in aqueous solution.
d-Orbital Splitting:The magnitude of the splitting of the d-orbitals in a transition metal complex depends on three things;the geometry of the complex ,the oxidation state of the metal,the nature of the ligands.
A comparison of the visible absorption maxima for a number of cobalt (III) complexes shows the effects of ligands on the d-orbital band gap.

1.      Magnetic properties of transition metal complexes:

Types of Magnetism:

1.      Diamagnetism: This arises due to paired electrons. When all the electrons in a molecule are paired, it is called a diamagnetic compound. This compound will be slightly repelled by the external magnetic field.

2.      Paramagnetism: This is due to unpaired electrons in a compound. The compound will be moderately attracted by the external magnetic field. The dipoles will not be aligned uniformly but at random in the absence of external field.

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