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Chapter 20. Coordination Chemistry (Inorganic Chemistry)

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1. Transition Elements

2. Coordination Ions

3. Crystal Field Theory

1. Transition Elements

⑴ Overview

① Definition: Elements whose outermost (valence) electrons occupy d orbitals; they belong to Groups 3–12 and are also called the d-block elements.

② Essential Memorization Transition Elements: Scandium, Titanium, Vanadium, Chromium, Manganese, Iron, Cobalt, Nickel, Copper, Zinc

③ Coordination bonding occurs mainly in transition metals, which often have many vacant d orbitals.

⑵ Characteristics

① Varied oxidation numbers (exception: Zinc has only one oxidation state)

② Good at forming coordination ions

⑶ Types of d orbitals: Five types in total

Figure 1. Types of d orbitals

Because ℓ = 2, they all have two angular nodes.

2. Coordination Ions

⑴ Coordination Ions: Ions formed by the combination of a metal ion and ligands

Mⁿ⁺: Central metal

xL: Ligand

ML_xⁿ⁺: Coordination ion

① Coordination number = Number of bonds formed by the central metal = Steric number = Number of orbitals participating in hybridization

② Oxidation number of central metal = Charge of coordination compound - Sum of charges of ligands coordinated

○ Oxidation state of central metal determines the number of electrons forming the molecular orbitals of the coordination compound

③ Trace vs. excess amount of ligand

○ If a trace amount of ligand is added, the formation-constant expression can be satisfied even when only a small amount of the metal ion reacts (forms a complex).

○ If an excess amount of ligand is added, the formation-constant expression is satisfied only when the concentration of free metal ions becomes (essentially) zero.

⑵ Formation constant K_f: Equilibrium constant for the formation of coordination ions

① Ionization of complex compounds: Generally, ligands do not ionize in solution (∵ K_f ≫ 1)

② Size comparison: The stronger the bond between the central metal and the ligand, the larger the formation constant

○ Difference in formation constants is mainly due to differences in entropy change

○ Especially related to the situation of common ligands vs. chelates.

○ Chelates have larger formation constants

○ Common ligands ＜ Ethylenediamine (en) ＜ Diethylenetriamine (trien)

○ Chelating ligands are entropy-favored because releasing water molecules (dehydration) increases the number of free molecules.

○ Larger crystal field splitting leads to larger formation constants

○ Exception: Formation constant of OH- for Zn2+ is larger than that of NH3

⑶ Chelate (Chelator): Ligand that binds to multiple sites simultaneously

① Major chelates

○ The 1-fold coordination in the list is included, but is not a chelating ligand

○ 1-fold coordination: H2O, CN-, SCN- (thiocyanate), X- (halogens), NH3, NO2- (nitrite), OH-, etc.

○ 2-fold coordination: Oxalic ion, ethylenediamine (en), ethyleneglycol, acac, CO32-, etc.

○ Oxalic ion: HO2CCO2H

○ Ethylenediamine: H2NCH2CH2NH2

○ Ethyleneglycol: HO(CH2)2OH

○ Acac: (CH3COCHCOCH3)-

○ m -phenylenediamine is not a 2-fold coordination chelate

○ 3-fold coordination: Diethylenetriamine (dien)

○ 6-fold coordination: Ethylenediaminetetraacetic acid (EDTA)

○ EDTA = (HOOCCH2)2NCH2CH2N(CH2COOH)2

○ Complexes coordinated with EDTA have enantiomers

② Chelate effect

○ Definition: When there are two competing reactions to form equivalent bonds, the one involving the chelating ligand occurs more easily

○ In the case of a 1-fold coordination ligand binding to a metal ion in a 6-fold manner, the total number of degrees of freedom is reduced from 7 to 1, leading to an unfavorable entropy change

○ Chelate ion formation reactions are favorable in terms of entropy since they require fewer ligands

○ The formation constant of a chelate is larger than that of a non-chelating ligand

⑷ Hybrid Orbitals

① To understand hybrid orbitals, one must know the orbital arrangement of the central metal ion

○ Note: According to the Aufbau principle, the 4s orbital is filled before the 3d orbital because it is lower in energy. However, once orbitals are formed, the 3d orbital becomes lower in energy than the 4s orbital, and electrons are removed from the 4s orbital at first.

○ Example: The electron configuration of Fe is 1s²2s²2p⁶3s²3p⁶4s²3d⁶, and the electron configuration of Fe²⁺ is 1s²2s²2p⁶3s²3p⁶3d⁶.

○ The reason you must determine the oxidation number of the central metal ion in a problem situation.

③ 4-fold coordination

○ sp3 hybridization: Tetrahedral. [Zn(NH3)4]2+, etc.

○ dsp2 hybridization: Square planar. [Ni(CN)4]2-, [Pt(NH3)4]2+, mostly d8 complexes

④ 6-fold coordination

○ sp3d2 (d2sp3) hybridization: Octahedral. XeF4, [Co(NH3)6]3+, [PtCl6]2-, etc.

○ Assuming the principal quantum number of the s and p orbitals is n:

○ d²sp³: when the complex uses the (n-1)-th d orbital electrons.

○ sp³d²: when the complex uses the n-th d orbital electrons.

⑸ Isomerism: Compounds with the same chemical formula but different atomic arrangements

① Structural Isomerism: Compounds with different bonds between atoms

○ Linkage Isomerism: Isomers with different metal-ligand bonds

○ Ionization Isomerism: Isomers that form different ions in solution

② Stereoisomerism: Compounds where atoms are bonded in the same way but have different spatial arrangements

○ Type 1. Geometric Isomerism: cis/trans isomers, fac/mer isomers, etc.

○ Type 1-1. cis/trans Isomerism: If two substituents are on the same side, it’s cis; if on opposite sides, it’s trans

○ Type 1-2. fac/mer Isomerism

○ fac Isomerism: When three substituents are mutually orthogonal

○ fac comes from ‘facial’, and it refers to three substituents lying in a single plane

○ mer Isomerism: When a pair of substituents are opposite each other

○ mer comes from ‘meridional’, and it refers to a pair of substituents forming a meridian

○ Type 2. Optical Isomerism (Enantiomerism)

○ Example 1. FeCl₃(H₂O)₃ (ferric chloride) has fac/mer isomerism. There’s a symmetry plane within the molecule, so there’s no optical isomers

Figure 2. Stereoisomers of FeCl₃(H₂O)₃

○ Example 2. [CoBr₄Cl₂]^3- has two stereoisomers: there is no optical isomers

Figure 3. Stereoisomers of [CoBr₄Cl₂]^3-

○ Example 3. [Co(bipy)Br₂Cl₂]^- has four stereoisomers where a pair of optical isomers exists.

Figure 4. Stereoisomers of [Co(bipy)Br₂Cl₂]^-

○ Example 4. Co(en)₂Cl₂⁺ has two cis-Co(en)₂Cl₂⁺ and one trans-Co(en)₂Cl₂⁺ that are mirror images of each other

Figure 5. Stereoisomerism of Co(en)₂Cl₂⁺

○ Example 5. Co(en)2BrCl+ has two cis-Co(en)2BrCl+ and one trans-Co(en)2BrCl+ that are mirror images of each other

○ Stereochemistry and the cross product of vectors

Figure 6. Stereoisomerism of Co(en)₂BrCl⁺

○ Example 6. [Co(en)₃]³⁺ with symmetric ligands attached in sets of 3 has mirror image isomers: There are a total of 2 stereoisomers

○ Λ form: left-handed (levorotatory), (−)

○ Δ form: right-handed (dextrorotatory), (+)

Figure 7. Stereoisomerism of [Co(en)₃]³⁺

○ Example 7. [Co((R)-pn)₃]³⁺ has four types of isomers: Λ-fac, Δ-fac, Λ-mer, Δ-mer

Figure 8. Stereoisomerism of [Co((R)-pn)₃]³⁺

○ Example 8. [Fe(gly)₃]^3- with a chelating ligand gly at 2 positions (N-terminal and O-terminal) has four types of stereoisomers as in Example 7

③ Experimental determination of stereochemical arrangement: Use CD (circular dichroism spectroscopy) and ORD (optical rotary dispersion).

○ Characteristics of CD/ORD

Table 1. Characteristics of CD/ORD

○ Cotton effect: In the UV spectral region, peaks are observed in both the ORD spectrum and the CD spectrum.

○ Info 1. Sign (±): CD (+), ORD (long-wavelength maximum)

○ Info 2. Magnitude: CD peak value; ORD peak and valley amplitude

○ Info 3. Position: CD peak wavelength = ORD inflection point

○ Application 1. Determining dextrorotation vs. levorotation

○ In stereochemistry, dextrorotation is denoted (+) and levorotation is denoted (−).

○ If CD shows a positive peak → (+) orientation; if it shows a negative peak → (−) orientation.

○ If the maximum in the ORD curve occurs at wavelengths longer than the inflection point → (+) orientation; otherwise → (−) orientation.

○ Application 2. Cotton effects by functional group

Table 2. Cotton effects by functional group

3. Crystal Field Theory (CFT)

⑴ Definition: Theory that explains the color and magnetic properties of coordination ions through changes in the energy of d orbitals of the central metal ion forming coordination complexes

⑵ Crystal field splitting

① Definition: When the nonbonding electron pairs of ligands repel the d orbital electrons of the central metal ion, the energy levels of the d orbitals rise significantly. Depending on the distance between d orbitals and ligands, various energy differences emerge, causing the d orbitals to split

② The larger the repulsion, the more unstable it is, resulting in higher energy levels

⑶ Crystal field splitting according to structure

① Overview

○ The splitting of the crystal field affects the d orbital electron arrangement.

○ The d orbitals are important in determining paramagnetic / diamagnetic properties, so a good understanding of the crystal field splitting based on structure is necessary.

② Assumptions

○ Metal-ligand bonding is considered as complete ionic bonding.

○ The greater the overlap between ligands and orbitals, the higher the energy level of the d orbitals as the repulsion strength increases.

③ Octahedral Structure

○ Ligands approach from the x, y, and z axes.

○ The ligand’s negative charge repels more strongly with the d_z² and d_x²-y² orbitals, where the probability of finding electrons is highest along the axial directions.

○ Comparison: d z2 = dx2-y2 > dxy = dyz = dxz (memorize)

○ Jahn-Teller effect: In CrF2 crystals, the 6 Cr-F bonding pairs around Cr consist of 2 long and 4 short bonds.

Figure 9. Crystal Field Theory for Octahedral Structures

④ Tetrahedral Structure

○ Ligands approach the space between the x, y, and z axes.

○ The ligand’s negative charge repels more strongly with the d_xy, d_yz, and d_xz orbitals.

○ Comparison: d xy = dyz = dxz > dz2 = dx2-y2 (memorize)

Figure 10. Crystal Field Theory for Tetrahedral Structures

⑤ Square Planar Structure

○ Example: Cisplatin (cis-Pt(NH3)2Cl2)

○ Ligands approach from the x and y axes.

○ The ligand’s negative charge repels most strongly with the d_x²-y² orbital, which has a high electron density along the x and y axes.

○ Comparison: d x2-y2 > dxy > dz2 > dxz = dyz (memorize)

○ Note that dxz and dyz have lower energy levels than dz2.

Figure 11. Crystal Field Theory for Square Planar Structures

⑥ Linear Structure

○ Example: I3-

○ Repulsion increases as ligands approach along the z-axis, causing higher energy levels.

○ Comparison: dz2 > dxz = dyz > dxy = dx2-y2

○ (Note) dxz and dyz are always paired.

Figure 12. d-orbital energy splitting of the central metal ion (M) in an ML₂ complex with a linear geometry.

㈎: d_z², ㈏: d_yz, ㈐: d_x²-y²

⑷ Magnitude of Crystal Field Splitting

① Principles

○ The stronger the central metal-ligand bond, the greater the aggregation of ligand electrons towards the central metal, leading to increased crystal field splitting.

○ Larger crystal field splitting leads to increased formation constants.

○ As the crystal-field splitting becomes larger, the central metal ion becomes less likely to be reduced, so its oxidizing strength becomes weaker.

② Factor 1: Ligand Field Theory (LFT)

○ Different ligands cause different degrees of bonding with the central metal, resulting in varying crystal field splitting sizes.

○ Difference from Crystal Field Theory

○ Crystal Field Theory understands metal-ligand interaction as electrostatic forces.

○ Ligand Field Theory considers metal-ligand interaction as covalent bonding.

○ Crystal Field Theory assumes constant d orbital energy levels based on ligand type.

○ Ligand Field Theory assumes variable d orbital energy levels based on ligand type.

○ Comparison

CO, CN- > NO2- > ONO- > en > NH3 > SCN- ＞ H2O > OH- > F- > Cl- > Br- > I-

○ For halide anions, as the period decreases their ionic radius becomes smaller, increasing electron–electron repulsion, so the crystal-field splitting becomes larger.

○ First four (C, N, E, N) are essential to memorize.

○ Strong-field ligands, weak-field ligands

○ Exception: In the case of Zn2+ as the central metal, the formation constant of OH- is greater than NH3.

③ Factor 2: Central Metal Charge

○ Greater central metal charge leads to stronger attraction of electrons to the nucleus, resulting in increased repulsion and crystal field splitting.

○ Greater oxidation number of the central metal leads to larger crystal field splitting → shorter absorption wavelength.

○ Exception: CuCl2 is blue, while CuCl is white due to full occupancy of d orbitals reflecting all light.

④ Factor 3: Hybrid Orbital Structure

○ Octahedral structures have more electron repulsion than tetrahedral structures, leading to larger crystal field splitting.

○ Ligand Field Theory doesn’t apply here: Octahedral almost always has larger crystal field splitting than tetrahedral.

○ Octahedral structures absorb high-energy short wavelengths (visible and ultraviolet light).

○ Tetrahedral structures absorb lower-energy, relatively longer wavelengths.

○ Square planar structures absorb the **shortest wavelen

⑤ Crystal Field Stabilization Energy (CFSE)ndConsidering only Coulombic energy

○ Definition: The stabilization energy when a metal ion (treated as a spherical field) is placed in the crystal field created by ligands in a coordination compound.

○ Considers only Coulombic energy.

○ Denoted as Δ or Δ_o.

○ For an octahedral geometry, it is expressed as follows.

⑥ Pairing energy (P): determined by considering both Coulombic energy and electron exchange energy.

⑸ Classification of sp³d² complexes based on crystal-field splitting

① sp³d² complexes are classified as low-spin or high-spin depending on the magnitude of the crystal-field splitting (Δ) caused by electron repulsion.

② High spin: an electron configuration with a large number of unpaired electrons

○ The energy difference between the d_x²-y², d_z² orbitals and the d_xy, d_yz, d_xz orbitals is small, so electrons are arranged to maximize spin (as in Hund’s rule).

○ Condition: when P > Δ, it corresponds to a weak-field ligand.

○ Because the energy difference between e_g and t_2g is similar, they are regarded as having the same energy level, and electrons are arranged to maximize the number of unpaired electrons.

○ Even in the high-spin case, there is still an energy ordering, so electrons are placed last in the d_x²-y² and d_z² orbitals.

③ Low spin: an electron configuration with a small number of unpaired electrons

○ The energy difference between the d_x²-y², d_z² orbitals and the d_xy, d_yz, d_xz orbitals is large, so there is less spin (fewer unpaired electrons) than in the high-spin case.

○ Condition: when P < Δ, it corresponds to a strong-field ligand.

○ Because e_g > t_2g is clear, electrons are filled starting from t_2g.

④ Other

○ K₂[MnCl₄] has a tetrahedral geometry and is high spin, so the number of unpaired electrons is 5.

⑹ Color of Complexes

① Larger crystal field splitting (Δ) results in shorter maximum absorption wavelength (λmax).

② The color of a solution is the color of the light that remains after absorption, so the complementary color is observed.

○ If the absorbed wavelength is long, a color close to its complementary color, blue, is observed.

○ If the absorbed wavelength is short, a color close to its complementary color, red, is observed.

○ As the splitting increases → the absorbed wavelength decreases → determine the complementary color using a color wheel/chart.

**Figure 13. Absorption Wavelength and Complementary Color

③ Some complexes like Ni(H2O)62+ and Ni(en)32+ don’t follow the simple principle of complementary colors.

**Figure 14. Absorption Spectra of Ni(H2O)62+ and Ni(en)32+]

○ Ni(H2O)62+ appears green.

○ Ni(en)32+ appears blue.

○ Expected: Increased crystal field splitting (en > H2O) → decreased absorption wavelength (en < H2O) → increased observed wavelength (en > H2O).

○ Reality: Observed wavelength of Ni(en)32+ is shorter than Ni(H2O)62+.

○ Reason: Interference by other peaks in the case of Ni complexes.

○ In Ni(H2O)62+ absorption, another peak absorbs at 400 nm, resulting in an observed color around 500 nm.

○ In Ni(en)32+ absorption, less interference by other peaks, leading to an observed color around 450 nm according to the principle of complementary colors.

⑺ Magnetic Properties of Complexes

① Principle: Presence of unpaired electrons leads to paramagnetism, absence leads to diamagnetism.

○ Examples: d0 and d10 complexes are always diamagnetic.

○ Reason: Unpaired electrons are not possible, fundamentally due to the impossibility of t2g → eg electron transitions.

② 4-Coordinate Complexes

○ Square planar: Paramagnetic

○ Square planar (d8): Diamagnetic

③ 6-Coordinate Complexes

○ d6 complex + Low Spin: Diamagnetic

○ d6 complex + High Spin: Paramagnetic

○ Others: Paramagnetic

Input: January 2, 2019, 19:42

Modified: June 3, 2023, 20:49