UNIT-3: Coordination Chemistry

1. Werner’s Theory of Coordination Compounds

Alfred Werner developed the first coherent theory of coordination chemistry in 1893. He proposed that transition metals exhibit two distinct types of valencies to satisfy their coordination requirements:

Primary Valency: This corresponds to the oxidation state of the metal ion. It is ionizable, non-directional, and must be satisfied by negative ions (anions).

Secondary Valency: This corresponds to the coordination number of the metal ion. It is non-ionizable, highly directional in space (defining the geometry of the complex), and can be satisfied by negative ions, neutral molecules, or occasionally positive ions.

Experimental Verification

Werner verified his theory by treating different cobalt-amine complexes with excess silver nitrate (AgNO3) solution to precipitate chloride ions as silver chloride (AgCl). The variations in the amount of precipitate and conductivity demonstrated the distinction between primary and secondary valencies:

Exam-Oriented Note: Species enclosed within the square brackets (coordination sphere) are tightly bound by secondary valencies and do not dissociate in water. Only species outside the brackets (ionization sphere) can dissociate and participate in precipitation reactions.

2. Valence Bond Theory (VBT) and Orbital Complexes

Developed by Linus Pauling, Valence Bond Theory (VBT) explains the bond formation, geometry, and magnetic properties of complexes through hybridization of metal atomic orbitals.

Key Postulates

• The central metal ion provides empty s, p, and d orbitals equal to its coordination number.
• These empty atomic orbitals hybridize to form a set of equivalent, directional hybrid orbitals.
• Each ligand donates a lone pair of electrons into these empty hybrid orbitals to form a coordinate covalent bond.

Inner vs. Outer Orbital Complexes

For octahedral complexes (Coordination Number 6), VBT classifies structures based on the d-orbitals used during hybridization:

Step-by-Step Electronic Calculations

Example 1: [Co(NH3)6]3+ (Inner Orbital Complex)

1. Oxidation state of Co is +3. Electron configuration of Co is [Ar] 3d7 4s2; thus, Co3+ is [Ar] 3d6.
2. NH3 behaves as a strong ligand here, forcing the 6 electrons in the 3d orbitals to pair up, leaving two empty 3d orbitals.
3. The two empty 3d, one 4s, and three 4p orbitals hybridize to form six empty d2sp3 hybrid orbitals.
4. Magnetic Property: Diamagnetic (0 unpaired electrons).

Example 2: [CoF6]3- (Outer Orbital Complex)

1. Oxidation state of Co is +3. Configuration of Co3+ is [Ar] 3d6.
2. F- is a weak-field ligand and cannot force pairing. The five 3d orbitals remain occupied by 6 electrons (one pair and four unpaired).
3. The metal uses its outer 4s, 4p, and 4d orbitals to form six empty sp3d2 hybrid orbitals.
4. Magnetic Property: Paramagnetic (4 unpaired electrons).

Common Mistake: Do not assume ligands are always "strong" or "weak" in absolute terms; pairing is also influenced by the oxidation state and identity of the metal (e.g., all ligands tend to act as strong-field ligands with 4d and 5d metal series).

3. Electroneutrality Principle and Back Bonding

Pauling’s Electroneutrality Principle

According to the electroneutrality principle, electronic structures of molecules or complexes are most stable when the formal net charge on each individual atom is close to zero (typically between -1 and +1).

In a standard coordination complex, the coordination of multiple electron-donating ligands to a highly positive metal cation would theoretically transfer a large amount of negative charge to the metal, making it highly negative. To prevent this destabilizing charge accumulation, the metal redistributes this negative charge through polar covalent bonding or back donation.

Back Bonding (Synergic Bonding)

This process is highly prevalent in metal carbonyls (e.g., [Ni(CO)4], [Fe(CO)5]) and other pi-acid complexes where the ligand possesses empty anti-bonding pi-star (pi*) orbitals.

• Sigma donation: The ligand donates its lone pair from a filled carbon orbital into an empty d-hybrid orbital of the metal.
• Pi back donation: The filled metal d-orbitals overlap side-on with empty pi* anti-bonding orbitals of the carbon monoxide (CO) ligand.

This mutual reinforcement is called synergic bonding. The back donation decreases electron density on the metal (satisfying electroneutrality) while strengthening the Metal-Carbon (M-C) bond and weakening the Carbon-Oxygen (C-O) bond.

4. Crystal Field Theory (CFT) & CFSE

Crystal Field Theory treats the interaction between the central metal and ligands as purely electrostatic (ionic), considering ligands as negative point charges or point dipoles.

Splitting of d-orbitals in an Octahedral Field

In a free metal ion, all five d-orbitals (dxy, dyz, dxz, dx2-y2, dz2) are degenerate. When surrounded by an octahedral field of six ligands:

• Ligands approach along the x, y, and z axes.
• The orbitals pointing directly along these axes (dx2-y2 and dz2, called the eg set) experience maximum electrostatic repulsion and rise in energy.
• The orbitals pointing between the axes (dxy, dyz, dxz, called the t2g set) experience less repulsion and remain lower in energy.

The energy separation between the t2g and eg sets is defined as 10 Dq or Δo (octahedral splitting energy).

Energy of eg orbitals = +0.6 Δo (or +6 Dq) above the barycenter
Energy of t2g orbitals = -0.4 Δo (or -4 Dq) below the barycenter

Crystal Field Stabilization Energy (CFSE)

CFSE is the thermodynamic stabilization energy gained by placing electrons in the split d-orbitals relative to the average energy in a spherical field.

CFSE = [(-0.4 x n_t2g) + (0.6 x n_eg)] x Δo + m x P

Where:

• n_t2g: Number of electrons in t2g orbitals
• n_eg: Number of electrons in eg orbitals
• P: Pairing energy (energy required to pair two electrons in the same orbital)
• m: Number of newly formed electron pairs in the complex relative to the free metal ion

Pairing Energies in Weak and Strong Fields

For configurations d4 through d7, the actual electron distribution is dictated by the relative values of Δo and P:

5. Factors Affecting the Magnitude of 10 Dq (Δo, Δt)

The extent of crystal field splitting depends on several factors:

1. Oxidation State of the Metal: Ions with higher oxidation states have higher positive charges, pulling the ligands closer and creating stronger electrostatic fields. Thus, Δo increases with increasing oxidation state (e.g., Fe3+ has a larger Δo than Fe2+).
2. Transition Series (3d vs. 4d vs. 5d): On descending a group, the d-orbitals increase in size and extend further from the nucleus, overlapping more effectively with ligands. Splitting increases by approximately 30% to 50% from 3d to 4d, and 4d to 5d. Consequently, 4d and 5d complexes are almost exclusively low-spin.
3. Geometry of the Complex: Tetrahedral splitting (Δt) is substantially smaller than octahedral splitting (Δo) because there are only 4 ligands instead of 6, and they do not point directly at any of the d-orbitals.

Δt = (4 / 9) x Δo

Because Δt is very small, the pairing energy (P) is almost always greater than Δt. Therefore, tetrahedral complexes are nearly always high-spin.

4. Nature of the Ligand (Spectrochemical Series): Ligands have varying abilities to split d-orbitals, arranged experimentally in the spectrochemical series:

I- < Br- < S2- < SCN- < Cl- < N3- < F- < OH- < C2O42- < H2O < NCS- < CH3CN < py < NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO

6. Octahedral vs. Tetrahedral Coordination & Tetragonal Distortions

Structural Differences

Tetragonal Distortions from Octahedral Geometry

When an octahedral complex undergoes distortion along the z-axis, it is referred to as a tetragonal distortion:

• Z-out (Tetragonal Elongation): The two trans-ligands along the z-axis are pulled further away from the metal. Repulsion decreases along the z-axis, causing orbitals with z-components (dz2, dxz, dyz) to fall in energy while orbitals in the xy-plane (dx2-y2, dxy) rise in energy. This is the most common distortion.
• Z-in (Tetragonal Compression): The two trans-ligands along the z-axis are compressed closer to the metal, causing orbitals with z-components to rise in energy.

7. Jahn-Teller Theorem and Square Planar Geometry

The Jahn-Teller Theorem

The Jahn-Teller theorem states that any non-linear molecular system in an electronically degenerate ground state will undergo a geometrical distortion that lowers its symmetry, removes the degeneracy, and lowers the overall electronic energy.

Degeneracy in d-orbitals can occur in either the t2g or eg levels:

• Strong Jahn-Teller Distortion: Occurs when the degeneracy lies in the eg orbitals because they point directly at the incoming ligands (e.g., high-spin d4, low-spin d7, and d9 systems like Cu2+).
• Weak Jahn-Teller Distortion: Occurs when the degeneracy is in the t2g orbitals because they point between the ligands and exert less electrostatic influence (e.g., d1, d2, low-spin d4, low-spin d5).

Square Planar Geometry

If the tetragonal z-out elongation becomes extremely large, the two trans-ligands on the z-axis are completely removed, resulting in a square planar complex (Coordination Number 4).

This extreme distortion drastically splits the d-orbitals: dx2-y2 is shifted to very high energy, followed by dxy, dz2, and finally the degenerate dxz and dyz orbitals at the lowest energy level. This geometry is exceptionally stable for d8 metal ions (e.g., Ni2+ with strong ligands, Pd2+, Pt2+) because the highly destabilized dx2-y2 orbital remains empty, while the remaining eight electrons pair up in the lower-energy orbitals.

8. Qualitative Aspect of Ligand Field and Molecular Orbital Theory

While Crystal Field Theory is computationally straightforward, it fails to explain the covalent character of complexes and the anomalous positions of neutral ligands in the spectrochemical series. Molecular Orbital Theory (MOT) and Ligand Field Theory (LFT) overcome this by treating metal-ligand bonds as covalent interactions involving orbital overlap.

Qualitative MO Diagram for Octahedral Complexes

In an octahedral complex, the central transition metal utilizes nine valence atomic orbitals: five nd, one (n+1)s, and three (n+1)p orbitals. These overlap with six Symmetry-Adapted Linear Combinations (SALCs) of ligand orbitals.

• Sigma-bonding: Six bonding molecular orbitals (eg, a1g, t1u) are formed, which are lower in energy and mostly ligand-like in character. Six corresponding anti-bonding molecular orbitals (eg*, a1g*, t1u*) are also formed, which are higher in energy and mostly metal-like.
• Non-bonding: The metal t2g orbitals (dxy, dyz, dxz) do not have correct symmetry to form sigma bonds with ligands and remain non-bonding (in the absence of pi-bonding).
• Interpretation of Splitting (Δo): The splitting parameter Δo is defined as the energy gap between the non-bonding t2g orbitals and the anti-bonding eg* orbitals.

When pi-bonding is included:

• Pi-donor ligands (e.g., F-, Cl-): Ligands have filled p-orbitals lower in energy than the metal t2g. They donate electrons to form bonding t2g orbitals, pushing the metal-like t2g* (now anti-bonding) up in energy, which decreases Δo.
• Pi-acceptor ligands (e.g., CO, CN-): Ligands have empty, high-energy pi* orbitals. They accept electrons from the metal t2g orbitals. This stabilizes the metal t2g orbitals, shifting them lower in energy and increasing Δo.

9. IUPAC (2005) Nomenclature of Coordination Compounds

The International Union of Pure and Applied Chemistry (IUPAC) rules for naming coordination compounds are summarized below:

1. Order of Naming: The cation is always named first, followed by the anion, regardless of whether the complex is cationic, anionic, or neutral.
2. Naming the Coordination Sphere: Within the coordination sphere, ligands are named first in alphabetical order, followed by the central metal atom.
3. Ligand Names:
   • Anionic ligands end in "-o" (e.g., Cl- is chlorido, CN- is cyanido, C2O42- is oxalato).
   • Neutral ligands keep their names with major exceptions: H2O is aqua, NH3 is ammine, CO is carbonyl, and NO is nitrosyl.
4. Numerical Prefixes: Simple ligands use di-, tri-, tetra-, penta-, hexa-. For complex ligands that already contain numerical prefixes (e.g., ethylenediamine), use bis-, tris-, tetrakis-, and enclose the ligand name in parentheses.
5. Oxidation State: The oxidation state of the metal is designated by a Roman numeral in parentheses immediately after the metal's name (e.g., iron(II)).
6. Anionic Complexes: If the complex sphere is an anion, the metal name must end with the suffix "-ate" (e.g., cobaltate, ferrate, platinate, plumbate). For cationic or neutral spheres, the metal's common name is kept unchanged.

Examples

• [Co(NH3)6]Cl3: Hexaamminecobalt(III) chloride
• K4[Fe(CN)6]: Potassium hexacyanidoferrate(II)
• [CoCl(NH3)5]Cl2: Pentaamminechloridocobalt(III) chloride
• [Pt(NH3)2Cl2]: Diamminedichloridoplatinum(II)

10. Isomerism and Stereochemistry (CN 4 and 6)

Isomers are compounds that share the same chemical formula but differ in structural linkage or spatial configuration.

Structural Isomerism

• Ionization Isomerism: Exchange of counter-ions and ligand ions between the coordination sphere and the outside environment. (e.g., [Co(NH3)5SO4]Br and [Co(NH3)5Br]SO4).
• Hydrate (Solvate) Isomerism: Difference in the number of water molecules bound as ligands vs. trapped in the crystal lattice. (e.g., [Cr(H2O)6]Cl3 and [Cr(H2O)5Cl]Cl2 . H2O).
• Linkage Isomerism: Occurs when an ambidentate ligand (e.g., NO2- vs. ONO-, SCN- vs. NCS-) coordinates through different donor atoms.
• Coordination Isomerism: Occurs in salts containing both complex cations and anions, through exchange of ligands between the two metal centers. (e.g., [Co(NH3)6][Cr(CN)6] and [Cr(NH3)6][Co(CN)6]).

Stereoisomerism and Coordination Numbers

Coordination Number 4 (Tetrahedral and Square Planar)

• Tetrahedral complexes: Geometrical isomerism is impossible because all four coordination sites are adjacent (equivalent) to one another. They can show optical isomerism only if they contain four different ligands or unsymmetrical bidentate ligands (chiral center).
• Square planar complexes: Do not show optical isomerism because they possess a molecular plane of symmetry. However, they show geometrical isomerism:
  • MA2B2 type: Can exist as cis (similar ligands on adjacent corners) and trans (similar ligands on opposite corners).
  • MABCD type: Yields three distinct geometrical isomers.

Coordination Number 6 (Octahedral Geometry)

• Geometrical Isomerism:
  • MA4B2 type: Exists as cis and trans isomers.
  • MA3B3 type: Exists as facial (fac - three identical ligands occupy one triangular face of the octahedron) and meridional (mer - three identical ligands form a meridian around the center).
• Optical Isomerism: Extremely common in octahedral complexes containing chelating bidentate ligands (e.g., [Co(en)3]3+ or cis-[Co(en)2Cl2]+). They lack a plane of symmetry and exist as non-superimposable d (dextro) and l (laevo) enantiomers. (Note: trans-[Co(en)2Cl2]+ is optically inactive due to its plane of symmetry).

11. Chelate Effect, Polynuclear Complexes, and Labile/Inert Complexes

The Chelate Effect

The chelate effect refers to the enhanced thermodynamic stability of coordination complexes containing cyclic chelate rings (formed by polydentate ligands) compared to complexes containing monodentate ligands of similar chemical nature.

This stabilization is primarily driven by entropy (ΔS). Consider the ligand displacement reaction:

[Ni(H2O)6]2+ + 3 en -> [Ni(en)3]2+ + 6 H2O

In this reaction, 4 reacting particles produce 7 product particles. The net increase in the number of independent, free molecules increases the system's molecular disorder, resulting in a large, positive ΔS. This positive entropy change drives the free energy (ΔG = ΔH - TΔS) to be highly negative, thermodynamically stabilizing the chelated product.

Polynuclear Complexes

Polynuclear complexes contain multiple metal atoms bonded together directly or connected by bridging ligands (e.g., OH-, NH2-, Cl-, CO). Bridging ligands are denoted in nomenclature by the Greek letter mu (μ-) placed directly before the ligand name.

For example, a binuclear cobalt complex with bridging amido and hydroxido groups is written and named as:
[(NH3)4Co(μ-NH2)(μ-OH)Co(NH3)4]4+ : Octaammine-μ-amido-μ-hydroxidodicobalt(III) ion.

Labile and Inert Complexes (Kinetic Stability)

Henry Taube classified complexes based on their substitution rates (kinetic stability), which is independent of thermodynamic stability (represented by stability constants):

• Labile Complexes: Undergo very rapid ligand substitution reactions (typically within seconds).
• Inert Complexes: Undergo extremely slow ligand substitution reactions (often taking hours or days).