Werner’S Theory Of Coordination Compounds

In previous studies, we learned that transition metals frequently form compounds where a central metal atom or ion is surrounded by other ions or neutral molecules, held together by chemical bonds. These compounds are now known as coordination compounds.

The study of coordination compounds is a significant and dynamic field in modern inorganic chemistry. These compounds are not just laboratory curiosities; they play crucial roles in biological systems (e.g., chlorophyll in plants, haemoglobin in blood, vitamin B12), various industrial processes (e.g., catalysts), and analytical chemistry.

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The first systematic theoretical framework to explain the structure and bonding in coordination compounds was proposed by Swiss chemist Alfred Werner (1866-1919). Werner conducted extensive experimental work, preparing and characterising a large number of these compounds and studying their physical and chemical properties through simple techniques.

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One key observation made by Werner involved a series of compounds formed between cobalt(III) chloride (CoCl$_3$) and ammonia (NH$_3$). When these compounds were treated with excess silver nitrate solution in cold conditions, some chloride ions were precipitated as AgCl, while others remained in solution and did not precipitate. This indicated that not all chloride ions were identically bonded in these compounds.

Specific observations included:

• 1 mole of CoCl$_3 \cdot 6\text{NH}_3$ (Yellow) precipitated 3 moles of AgCl.
• 1 mole of CoCl$_3 \cdot 5\text{NH}_3$ (Purple) precipitated 2 moles of AgCl.
• 1 mole of CoCl$_3 \cdot 4\text{NH}_3$ (Green) precipitated 1 mole of AgCl.
• 1 mole of CoCl$_3 \cdot 4\text{NH}_3$ (Violet) precipitated 1 mole of AgCl.

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These findings, combined with conductivity measurements of the solutions (which indicated the number of ions present), led Werner to propose that in these compounds, a fixed number of groups (chloride ions or ammonia molecules, or both) remained directly bonded to the cobalt ion and formed a stable structural unit that did not dissociate in solution. This unit was enclosed in square brackets in his formulations (Table 9.1).

Colour	Formula	Solution conductivity corresponds to
Yellow	[Co(NH$_3$)$_6$]Cl$_3$	1:3 electrolyte (4 ions)
Purple	[CoCl(NH$_3$)$_5$]Cl$_2$	1:2 electrolyte (3 ions)
Green	[CoCl$_2$(NH$_3$)$_4$]Cl	1:1 electrolyte (2 ions)
Violet	[CoCl$_2$(NH$_3$)$_4$]Cl	1:1 electrolyte (2 ions)

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Notice that the green and violet compounds have the same empirical formula (CoCl$_3 \cdot 4\text{NH}_3$) but distinct properties, indicating they are isomers.

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Based on his observations, Werner developed his theory of coordination compounds (published in 1898). Its main postulates are:

1. In coordination compounds, metals exhibit two types of valences or linkages: primary valence and secondary valence.
2. Primary valences are typically ionisable and are satisfied by negative ions. They correspond to the oxidation state of the metal ion.
3. Secondary valences are non-ionisable. They are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number of the metal and has a fixed value for a given metal in a specific complex.
4. The ions or groups (ligands) bound to the metal by secondary linkages have a characteristic spatial arrangement around the central metal ion. This arrangement defines the geometry of the coordination compound.

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In modern terminology, the species enclosed within the square bracket, consisting of the central metal ion and the ligands directly attached to it, is called the coordination entity or complex. The ions written outside the square bracket are called counter ions; they balance the charge of the coordination entity but are not directly bonded to the metal ion.

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Werner further postulated that the common spatial arrangements for transition metal coordination compounds are octahedral, tetrahedral, and square planar geometries, determined by the metal's coordination number.

• Coordination number 6 often results in octahedral geometry, as seen in [Co(NH$_3$)$_6$]$^{3+}$, [CoCl(NH$_3$)$_5$]$^{2+}$, and [CoCl$_2$(NH$_3$)$_4$]$^{+}$.
• Coordination number 4 can result in either tetrahedral geometry (e.g., [Ni(CO)$_4$]) or square planar geometry (e.g., [PtCl$_4$]$^{2-}$).

Answer:

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Difference between a double salt and a complex:

Both double salts and coordination complexes are formed by combining two or more stable compounds in fixed proportions. However, they differ in their behaviour when dissolved in water:

• Double Salts: Examples include carnallite (KCl $\cdot$ MgCl$_2 \cdot$ 6H$_2$O), Mohr's salt (FeSO$_4 \cdot$(NH$_4$)$_2$SO$_4 \cdot$ 6H$_2$O), and potash alum (KAl(SO$_4$)$_2 \cdot$ 12H$_2$O). When dissolved in water, double salts completely dissociate into their constituent simple ions. For example, Mohr's salt solution gives positive tests for Fe$^{2+}$, NH$_4^+$, and SO$_4^{2-}$ ions.
• Complexes (Coordination Compounds): Examples include K$_4$[Fe(CN)$_6$]. When dissolved in water, coordination compounds form a complex ion (the coordination entity) which does not dissociate into its constituent ions within the bracket. For instance, K$_4$[Fe(CN)$_6$] dissociates into K$^+$ ions and the complex ion [Fe(CN)$_6$]$^{4-}$. The complex ion [Fe(CN)$_6$]$^{4-}$ remains intact and does not dissociate into Fe$^{2+}$ and CN$^-$ ions in solution.

Definitions Of Some Important Terms Pertaining To Coordination Compounds

Understanding specific terminology is crucial when studying coordination compounds.

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(a) Coordination entity: This is the central structural unit of a coordination compound. It consists of a central metal atom or ion that is chemically bonded to a fixed number of surrounding ions or molecules. The coordination entity is typically enclosed within square brackets in the chemical formula. Examples include [CoCl$_3$(NH$_3$)$_3$], [Ni(CO)$_4$], [PtCl$_2$(NH$_3$)$_2$], [Fe(CN)$_6$]$^{4-}$, and [Co(NH$_3$)$_6$]$^{3+}$.

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(b) Central atom/ion: Within a coordination entity, this is the atom or ion located at the center. It acts as an acceptor of electron pairs from the ligands and is bonded to a definite number of ligands arranged in a specific geometry around it. Examples include Ni$^{2+}$ in [NiCl$_2$(H$_2$O)$_4$], Co$^{3+}$ in [CoCl(NH$_3$)$_5$]$^{2+}$, and Fe$^{3+}$ in [Fe(CN)$_6$]$^{3-}$. Central metal atoms/ions in coordination compounds can be considered Lewis acids because they accept electron pairs.

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(c) Ligands: These are the ions or molecules that are directly bonded to the central metal atom or ion within the coordination entity. Ligands act as Lewis bases because they donate at least one electron pair to the central metal atom/ion to form coordinate covalent bonds. Ligands can be simple ions (like Cl$^-$), small molecules (like H$_2$O or NH$_3$), larger organic molecules (like H$_2$NCH$_2$CH$_2$NH$_2$, ethane-1,2-diamine), or even macromolecules (like proteins).

Ligands are classified based on the number of donor atoms they use to bind to the central metal ion:

• Unidentate: Ligands that bind through a single donor atom (e.g., Cl$^-$, H$_2$O, NH$_3$).
• Didentate (or Bidentate): Ligands that can bind through two donor atoms (e.g., H$_2$NCH$_2$CH$_2$NH$_2$ (ethane-1,2-diamine, abbreviated as 'en') which binds via two nitrogen atoms, or C$_2$O$_4^{2-}$ (oxalate ion) which binds via two oxygen atoms).
• Polydentate: Ligands that have several donor atoms and can bind through more than two atoms (e.g., N(CH$_2$CH$_2$NH$_2$)$_3$).
• Hexadentate: A specific type of polydentate ligand that binds through six donor atoms. Ethylenediaminetetraacetate ion (EDTA$^{4-}$) is a crucial example, binding through two nitrogen atoms and four oxygen atoms.

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When a di- or polydentate ligand uses two or more of its donor atoms to simultaneously bind to the *same* central metal ion, it forms a ring-like structure. Such ligands are called chelate ligands, and the complexes formed are called chelate complexes. The number of donor atoms used by a chelating ligand is called its denticity.

Chelate complexes are generally more stable than similar complexes formed with unidentate ligands. This increased stability is known as the chelate effect.

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An Ambidentate ligand is a unidentate ligand that possesses two different potential donor atoms, either of which can form a coordinate bond with the central metal ion. However, only one atom is bonded at a time.

Examples:

• Nitrite ion (NO$_2^-$): Can coordinate through the Nitrogen atom (giving M–NO$_2$, called nitro) or through an Oxygen atom (giving M–ONO, called nitrito).
• Thiocyanate ion (SCN$^-$): Can coordinate through the Sulfur atom (giving M–SCN, called thiocyanato) or through the Nitrogen atom (giving M–NCS, called isothiocyanato).

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(d) Coordination number: The coordination number (CN) of a central metal atom or ion in a complex is defined as the total number of sigma ($\sigma$) bonds formed between the ligand donor atoms and the central metal atom/ion. It represents the number of ligand donor atoms directly attached to the metal.

For example:

• In [PtCl$_6$]$^{2-}$, there are 6 Cl$^-$ ligands, each binding through one atom. CN of Pt is 6.
• In [Ni(NH$_3$)$_4$]$^{2+}$, there are 4 NH$_3$ ligands, each binding through one atom. CN of Ni is 4.
• In [Fe(C$_2$O$_4$)$_3$]$^{3-}$, there are 3 oxalate (C$_2$O$_4^{2-}$) ligands. Oxalate is didentate, so each ligand forms 2 sigma bonds. Total sigma bonds = 3 ligands $\times$ 2 bonds/ligand = 6. CN of Fe is 6.
• In [Co(en)$_3$]$^{3+}$, there are 3 ethane-1,2-diamine (en) ligands. 'en' is didentate. Total sigma bonds = 3 ligands $\times$ 2 bonds/ligand = 6. CN of Co is 6.

It's important to remember that only the sigma bonds from the ligand donor atoms to the metal count towards the coordination number. Pi ($\pi$) bonds, which can also be formed in some complexes (e.g., with CO ligands), are not included when determining the coordination number.

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(e) Coordination sphere: This term collectively refers to the central metal atom or ion and all the ligands that are directly attached to it. The coordination sphere is the part of the complex entity that stays intact when the compound dissolves in a solvent (like water). In chemical formulas, the coordination sphere is always enclosed within square brackets [ ]. Any ions written outside these brackets are called counter ions; they are bonded by ionic forces and dissociate in solution. For example, in K$_4$[Fe(CN)$_6$], the coordination sphere is [Fe(CN)$_6$]$^{4-}$, and the counter ion is K$^+$.

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(f) Coordination polyhedron: This describes the specific three-dimensional spatial arrangement of the ligand donor atoms that are directly bonded to the central metal atom or ion. It defines the shape of the coordination entity around the central metal. The geometry is determined by the coordination number and the nature of the metal and ligands. The most common coordination polyhedra are:

• Octahedral: Coordination number 6 (e.g., [Co(NH$_3$)$_6$]$^{3+}$). The six ligands are located at the vertices of an octahedron around the central metal.
• Tetrahedral: Coordination number 4 (e.g., [Ni(CO)$_4$]). The four ligands are located at the vertices of a tetrahedron.
• Square planar: Coordination number 4 (e.g., [PtCl$_4$]$^{2-}$). The four ligands and the central metal lie in the same plane, with ligands at the corners of a square.

(The image would illustrate the shapes: Octahedral (6 ligands at octahedron vertices), Tetrahedral (4 ligands at tetrahedron vertices), Square Planar (4 ligands at square vertices in a plane with the metal)).

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(g) Oxidation number of central atom: This is the hypothetical charge that the central metal atom would possess if all the ligands were removed from the coordination entity, assuming that each ligand took away the electron pair it donated for bonding. It represents the oxidation state of the metal ion in the complex. The oxidation number is indicated by a Roman numeral in parentheses immediately following the name of the coordination entity in the nomenclature. For example, in [Cu(CN)$_4$]$^{3-}$, the oxidation state of Copper is +1, written as Copper(I).

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(h) Homoleptic and heteroleptic complexes: Coordination complexes are classified based on the types of ligands attached to the central metal.

• Homoleptic complexes: Complexes where the central metal atom or ion is bonded to only one type of ligand or donor group. An example is [Co(NH$_3$)$_6$]$^{3+}$ where all six ligands are ammonia molecules.
• Heteroleptic complexes: Complexes where the central metal atom or ion is bonded to more than one different type of ligand or donor group. An example is [Co(NH$_3$)$_4$Cl$_2$]$^+$ where both ammonia molecules and chloride ions are bonded to the cobalt ion.

Nomenclature Of Coordination Compounds

A systematic method for naming coordination compounds is essential to unambiguously describe their composition and structure, especially given the existence of isomers. The rules for naming and writing formulas for coordination entities are set by the International Union of Pure and Applied Chemistry (IUPAC).

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Formulas Of Mononuclear Coordination Entities

Mononuclear coordination entities contain only one central metal atom. The formula provides a concise representation of the compound's composition. The following rules are used for writing formulas:

1. The central metal atom or ion is written first.
2. Ligands are listed after the metal. When listing ligands, they are arranged in alphabetical order. The alphabetical order is determined by the first letter of the ligand's name (or abbreviation), *regardless* of whether the ligand is anionic, cationic, or neutral.
3. If a ligand is polydentate, it is still listed according to its name or abbreviation in alphabetical order. If an abbreviation is used for a ligand (like 'en' for ethane-1,2-diamine), the first letter of the abbreviation determines its alphabetical position.
4. The entire coordination entity, whether it has a net positive, negative, or zero charge, is enclosed within square brackets [ ]. If a ligand itself is polyatomic (consists of more than one atom), its formula is enclosed within parentheses ( ) within the square brackets. Ligand abbreviations are also placed within parentheses.
5. There should be no space between the metal symbol and the ligands, or between different ligands, within the square brackets representing the coordination sphere.
6. If the formula of a charged coordination entity is written alone (without the counter ion), the net charge of the entity is indicated outside the square brackets as a right superscript. The number of units of charge is written before the sign (e.g., [Co(CN)$_6$]$^{3-}$, [Cr(H$_2$O)$_6$]$^{3+}$).
7. When writing the formula for a complete coordination compound (with counter ions), the total positive charge from the cation(s) must be balanced by the total negative charge from the anion(s). The number of cations and anions needed to achieve charge balance is indicated by subscripts outside the brackets. The cation formula is written first, followed by the anion formula.

Naming Of Mononuclear Coordination Compounds

The names of coordination compounds are constructed using an additive system, where the ligands are named as prefixes before the name of the central metal atom/ion.

The following IUPAC rules are applied for naming coordination compounds:

1. In an ionic coordination compound, the cation is named first, followed by the anion. This applies regardless of whether the cation or anion is the coordination entity.
2. Within the coordination entity, the ligands are named first, followed by the name of the central metal atom or ion. The ligands are listed in alphabetical order. (Note: This is the reverse order compared to writing the formula).
3. Names of anionic ligands end in the suffix '-o'. For example, chloride becomes chlorido, cyanide becomes cyanido, sulphate becomes sulphato, oxalate becomes oxalato, etc. Neutral and cationic ligands generally keep their original names, with a few exceptions: H$_2$O is named aqua, NH$_3$ is named ammine (note the double 'm'), CO is named carbonyl, and NO is named nitrosyl.
4. Prefixes like di-, tri-, tetra-, penta-, hexa- are used to indicate the number of identical ligands. However, if the name of a ligand already includes a numerical prefix (like ethane-1,2-diamine or triphenylphosphine), or if it's an abbreviation, then the multiplying prefixes bis- (for two), tris- (for three), tetrakis- (for four), etc., are used. In such cases, the name of the ligand is enclosed in parentheses. For example, [NiCl$_2$(PPh$_3$)$_2$] is named dichloridobis(triphenylphosphine)nickel(II).
5. The oxidation state of the central metal atom or ion is indicated by a Roman numeral in parentheses immediately following the name of the metal. This applies whether the coordination entity is a cation, anion, or neutral molecule.
6. If the coordination entity is a cation, the name of the metal element is used directly (e.g., Cobalt, Platinum). If the coordination entity is an anion, the name of the metal ends with the suffix '-ate' (e.g., cobaltate for Co, ferrate for Fe, argentate for Ag, cuprate for Cu, platina te for Pt). Some metals use their Latin names in the anionic complex (e.g., ferrate for Iron, argentate for Silver, cuprate for Copper).
7. A neutral coordination compound is named similarly to a complex cation, i.e., the metal name is used directly without the '-ate' suffix.
8. Spaces are introduced in the full name of the compound between the cation and anion. Within the name of the coordination entity itself (e.g., triamminetriaquachromium(III)), there are no spaces.

Examples illustrating nomenclature:

1. [Cr(NH$_3$)$_3$(H$_2$O)$_3$]Cl$_3$ is named as: triamminetriaquachromium(III) chloride.

   Explanation: The complex ion [Cr(NH$_3$)$_3$(H$_2$O)$_3$]$^{3+}$ is the cation, and Cl$^-$ is the anion. Ligands are ammine (NH$_3$) and aqua (H$_2$O). Alphabetical order: ammine comes before aqua. There are three of each, so use prefixes 'tri-'. The ligands are neutral. The compound is neutral, and there are 3 Cl$^-$ counter ions (charge -1 each), so the complex cation must have a charge of +3. All ligands are neutral, so the oxidation state of Cr is +3. The complex ion is a cation, so use 'chromium'. The counter ion is 'chloride'. The total name is "triamminetriaquachromium(III) chloride". Note: The number of counter ions (tri-chloride) is not indicated in the name.

2. [Co(H$_2$NCH$_2$CH$_2$NH$_2$)$_3$]$_2$(SO$_4$)$_3$ is named as: tris(ethane-1,2-diamine)cobalt(III) sulphate.

   Explanation: The cation is the complex ion [Co(en)$_3$]$^{3+}$, and the anion is sulphate (SO$_4^{2-}$). There are 3 sulphate ions (charge -2 each) and 2 complex cations. Total negative charge = 3 $\times$ (-2) = -6. Total positive charge must be +6, so each of the 2 complex cations must have a charge of +3. The ligand is ethane-1,2-diamine (en), which is neutral and polydentate (didentate). Since its name contains a numerical prefix ('di'), we use 'tris-' to indicate three such ligands. The complex ion is a cation, so use 'cobalt'. The ligand is neutral, so the charge on the complex (+3) is the oxidation state of Co, hence Cobalt(III). The anion is 'sulphate'. The name is "tris(ethane-1,2-diamine)cobalt(III) sulphate".

3. [Ag(NH$_3$)$_2$][Ag(CN)$_2$] is named as: diamminesilver(I) dicyanidoargentate(I).

   Explanation: This compound contains both a complex cation and a complex anion. The compound is neutral overall. Let's assume the oxidation state of Ag in both entities is +1 (a common state for Ag).
   Cation: [Ag(NH$_3$)$_2$]$^x$. NH$_3$ is neutral (0). If Ag is +1, charge $x = +1 + 2(0) = +1$. Name: Two ammine ligands (diammine), central metal is Silver in a cation (silver), oxidation state is +1 (silver(I)). Name: diammine silver(I).
   Anion: [Ag(CN)$_2$]$^y$. CN$^-$ is anionic (-1). If Ag is +1, charge $y = +1 + 2(-1) = -1$. Name: Two cyanido ligands (dicyanido), central metal is Silver in an anion (argentate), oxidation state is +1 (argentate(I)). Name: dicyanido argentate(I).
   The cation is named first, then the anion: diammine silver(I) dicyanido argentate(I). The total charge balance (cation +1, anion -1) confirms the proposed oxidation states are consistent with the neutral compound.

Answer:

Answer:

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Note: The IUPAC recommendations updated in 2004 suggest that anionic ligands should end in '-ido' (e.g., chlorido instead of chloro) and that ligands should be sorted alphabetically irrespective of their charge. The text and examples provided use slightly older conventions ('chloro' instead of 'chlorido'). I will follow the conventions used in the provided text.

Isomerism In Coordination Compounds

Isomers are distinct chemical compounds that share the same molecular formula but differ in the arrangement of their atoms. This difference in arrangement leads to variations in their physical and chemical properties.

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Coordination compounds exhibit various types of isomerism, broadly classified into two main categories:

1. Stereoisomerism: Isomers that have the same chemical formula and the same chemical bonds (connectivity between atoms) but differ in the relative spatial arrangement of their atoms or groups. Stereoisomerism includes Geometrical isomerism and Optical isomerism.
2. Structural isomerism: Isomers that have the same chemical formula but differ in the way the atoms are connected or bonded (different chemical bonds). Structural isomerism includes Linkage isomerism, Coordination isomerism, Ionisation isomerism, and Solvate (or Hydrate) isomerism.

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A detailed description of these isomer types is given below:

Geometric Isomerism

This type of isomerism occurs in heteroleptic complexes (those with more than one type of ligand). It arises because the different ligands can be arranged in different spatial positions relative to each other around the central metal ion.

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Geometrical isomerism is commonly observed in coordination complexes with coordination numbers 4 (square planar) and 6 (octahedral).

• Coordination Number 4 (Square Planar):

  For a square planar complex of the formula [MX$_2$L$_2$], where M is the metal and X and L are different unidentate ligands, two geometrical isomers are possible:

  • cis-isomer: The two identical ligands (X or L) are located adjacent to each other.
  • trans-isomer: The two identical ligands (X or L) are located opposite to each other.

  (The image would show diagrams of [Pt(NH$_3$)$_2$Cl$_2$], one with two Cl cis to each other, and one with two Cl trans to each other).

  For a square planar complex of the type [MABCD], where A, B, C, and D are four different unidentate ligands, three geometrical isomers are possible. These can be viewed as one ligand (say A) having B, C, or D placed trans to it, giving three distinct arrangements (A-trans-B, A-trans-C, A-trans-D).

  Note that tetrahedral complexes (also coordination number 4) **do not exhibit geometrical isomerism**. This is because in a tetrahedral geometry, all adjacent positions are equidistant, and all positions are essentially 'cis' to each other; there are no 'trans' positions.

• Coordination Number 6 (Octahedral):

  Geometrical isomerism is also possible in octahedral complexes. For a complex of the formula [MX$_2$L$_4$], where M is the metal and X and L are different unidentate ligands, cis and trans isomers exist:

  • cis-isomer: The two identical ligands (X) are located adjacent to each other (e.g., at 90° apart).
  • trans-isomer: The two identical ligands (X) are located opposite to each other (e.g., at 180° apart).

  (The image would show diagrams of [Co(NH$_3$)$_4$Cl$_2$]$^+$, one with two Cl cis to each other, and one with two Cl trans to each other).

  Geometrical isomerism also occurs in octahedral complexes containing didentate ligands. For a complex of the formula [MX$_2$(L–L)$_2$], where X is a unidentate ligand and L-L is a didentate ligand (like 'en'), cis and trans isomers are possible based on the arrangement of the unidentate ligands (X).

  (The image would show diagrams of [CoCl$_2$(en)$_2$]$^+$, one with two Cl cis to each other, and one with two Cl trans to each other, with 'en' bridging positions).

  Another type of geometrical isomerism specific to octahedral complexes of the type [Ma$_3$b$_3$] (where 'a' and 'b' are different unidentate ligands) is fac-mer isomerism, seen in complexes like [Co(NH$_3$)$_3$(NO$_2$)$_3$].

  • facial (fac) isomer: The three identical ligands (a or b) occupy three adjacent positions on one triangular face of the octahedron.
  • meridional (mer) isomer: The three identical ligands (a or b) are arranged around a meridian of the octahedron, forming a plane containing the metal and two trans ligands and one cis ligand from the set of three.

  (The image would show diagrams of [Co(NH$_3$)$_3$(NO$_2$)$_3$] in fac and mer forms).

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Optical Isomerism

Optical isomers (also called enantiomers) are stereoisomers that are non-superimposable mirror images of each other. These molecules or ions are referred to as chiral. Just like your left and right hands are mirror images but cannot be perfectly overlaid, chiral molecules have a 'handedness'.

Optical isomers are distinguished by their effect on plane-polarised light. One isomer rotates the plane of polarised light in one direction (clockwise, denoted as dextrorotatory or d-form), while the other isomer rotates it by the same amount but in the opposite direction (counter-clockwise, denoted as levorotatory or l-form).

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Optical isomerism is particularly common in octahedral complexes, especially those involving didentate ligands.

For example, a complex of the type [M(L-L)$_3$]$^{n+}$, where L-L is a symmetric didentate ligand (like 'en' or oxalate), exists as a pair of enantiomers.

(The image would show the structures of [Co(en)$_3$]$^{3+}$ as two non-superimposable mirror images, illustrating the chirality).

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In a coordination entity of the type [MX$_2$(L–L)$_2$]$^{n+}$ (e.g., [PtCl$_2$(en)$_2$]$^{2+}$), only the cis-isomer can exhibit optical activity. The trans-isomer is symmetrical and superimposable on its mirror image, hence it is achiral (optically inactive).

(The image would show the structures of the cis isomer of [PtCl$_2$(en)$_2$]$^{2+}$ and its mirror image, showing they are not superimposable. It would also show the trans isomer which is superimposable on its mirror image).

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A mixture containing equal amounts of the d- and l-isomers is called a racemic mixture. Racemic mixtures are optically inactive because the rotations of plane-polarised light by the two enantiomers cancel each other out.

Answer:

Linkage Isomerism

This type of structural isomerism occurs when a coordination compound contains an ambidentate ligand. As defined earlier, an ambidentate ligand is a unidentate ligand that can bind to the central metal ion through different donor atoms.

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The isomers formed are called linkage isomers, and they differ in which donor atom of the ambidentate ligand is directly bonded to the metal center.

A classic example involves complexes containing the nitrite ion (NO$_2^-$). The nitrite ion can bind through its nitrogen atom (-NO$_2$, called nitro) or through one of its oxygen atoms (-ONO, called nitrito).

For instance, Jørgensen discovered linkage isomerism in the complex with empirical formula [Co(NH$_3$)$_5$(NO$_2$)]Cl$_2$. This compound exists in two forms:

• The yellow form, where the nitrite ligand is bonded through Nitrogen, [Co(NH$_3$)$_5$(-NO$_2$)]Cl$_2$.
• The red form, where the nitrite ligand is bonded through Oxygen, [Co(NH$_3$)$_5$(-ONO)]Cl$_2$.

Another example is the thiocyanate ligand (SCN$^-$), which can bind through Sulfur (-SCN, called thiocyanato) or Nitrogen (-NCS, called isothiocyanato).

Coordination Isomerism

This type of structural isomerism occurs in coordination compounds where both the cation and the anion are complex entities. Coordination isomers arise from the interchange of ligands between the cationic and anionic coordination spheres.

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This requires having at least two different metals (or the same metal in different oxidation states) in the cation and anion, and the possibility of exchanging ligands between them.

An example is provided by the pair of coordination isomers with the empirical formula [Co(NH$_3$)$_6$][Cr(CN)$_6$]. In this compound, the NH$_3$ ligands are bonded to the Co$^{3+}$ ion in the cationic complex, and the CN$^-$ ligands are bonded to the Cr$^{3+}$ ion in the anionic complex.

Its coordination isomer is [Cr(NH$_3$)$_6$][Co(CN)$_6$]. In this isomer, the NH$_3$ ligands are bonded to the Cr$^{3+}$ ion, and the CN$^-$ ligands are bonded to the Co$^{3+}$ ion. The metals and ligands have swapped between the cation and anion complex entities.

Ionisation Isomerism

This type of structural isomerism occurs when the counter ion in a coordination compound salt is itself a potential ligand, and it can swap places with a ligand that is initially bonded within the coordination sphere. The isomers produce different ions when dissolved in solution.

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Ionisation isomers have the same overall chemical formula but differ in which ion is the counter ion and which is a ligand directly bound to the metal.

A common example is the pair of ionisation isomers [Co(NH$_3$)$_5$(SO$_4$)]Br and [Co(NH$_3$)$_5$Br]SO$_4$.

• In [Co(NH$_3$)$_5$(SO$_4$)]Br, the sulphate ion (SO$_4^{2-}$) is a ligand coordinated to the Cobalt ion within the complex cation [Co(NH$_3$)$_5$(SO$_4$)]$^+$, and the bromide ion (Br$^-$) is the counter ion. When dissolved in water, it produces [Co(NH$_3$)$_5$(SO$_4$)]$^+$ and Br$^-$ ions. It will give a precipitate with Ag$^+$ ions (forming AgBr) but not with Ba$^{2+}$ ions (as SO$_4^{2-}$ is coordinated).
• In [Co(NH$_3$)$_5$Br]SO$_4$, the bromide ion (Br$^-$) is a ligand within the complex cation [Co(NH$_3$)$_5$Br]$^{2+}$, and the sulphate ion (SO$_4^{2-}$) is the counter ion. When dissolved in water, it produces [Co(NH$_3$)$_5$Br]$^{2+}$ and SO$_4^{2-}$ ions. It will give a precipitate with Ba$^{2+}$ ions (forming BaSO$_4$) but not with Ag$^+$ ions (as Br$^-$ is coordinated).

These isomers will show different reactions with reagents that test for the free counter ions (like Ag$^+$ for halide ions or Ba$^{2+}$ for sulphate ions).

Solvate Isomerism

This type of structural isomerism is a specific case of ionisation isomerism where the solvent molecule (most commonly water) is involved. When water is the solvent, this is often referred to as hydrate isomerism.

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Solvate isomers differ based on whether solvent molecules are directly bonded to the central metal ion as ligands or are present as free solvent molecules within the crystal lattice (lattice solvent).

An example is the complex with empirical formula CrCl$_3 \cdot$ 6H$_2$O, which can exist as different solvate isomers:

• [Cr(H$_2$O)$_6$]Cl$_3$ (violet colour): Here, all six water molecules are ligands, and the three chloride ions are counter ions.
• [Cr(H$_2$O)$_5$Cl]Cl$_2 \cdot$ H$_2$O (grey-green colour): Here, five water molecules and one chloride ion are ligands within the complex cation [Cr(H$_2$O)$_5$Cl]$^{2+}$. Two chloride ions are counter ions, and one water molecule is lattice water.
• Other isomers like [Cr(H$_2$O)$_4$Cl$_2$]Cl $\cdot$ 2H$_2$O (dark green colour) also exist.

These isomers will have different numbers of coordinated water molecules, different numbers of coordinated chloride ions, different numbers of counter ions, and potentially different colours.

Answer:

Bonding In Coordination Compounds

While Werner's theory successfully explained the basic structure, nomenclature, and isomerism in coordination compounds, it did not provide answers to fundamental questions about the nature of bonding:

• Why do only certain elements (mainly transition metals) form coordination compounds?
• What gives the bonds in coordination compounds their directional properties (leading to specific geometries)?
• What causes coordination compounds to exhibit characteristic magnetic and optical (colour) properties?

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To address these questions and provide a deeper understanding of bonding in coordination compounds, several theories have been developed, including Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT), and Molecular Orbital Theory (MOT). We will explore the basic applications of VBT and CFT.

Valence Bond Theory

According to the Valence Bond Theory (VBT), developed by Linus Pauling, the bond between the central metal atom or ion and the ligands is primarily covalent, specifically involving coordinate covalent bonds (where the ligand donates a lone pair of electrons to the metal).

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The central metal atom or ion is assumed to undergo hybridisation under the influence of the approaching ligands. This involves mixing its valence atomic orbitals (which can be $(n-1)d$, $ns$, $np$, or $ns$, $np$, $nd$ orbitals, depending on the period) to form a set of equivalent hybrid orbitals. These hybrid orbitals have a definite orientation in space, determining the geometry of the complex (Table 9.2).

Coordination number	Type of hybridisation	Distribution of hybrid orbitals in space (Geometry)
4	sp$^3$	Tetrahedral
4	dsp$^2$	Square planar
5	sp$^3$d	Trigonal bipyramidal
6	sp$^3$d$^2$	Octahedral
6	d$^2$sp$^3$	Octahedral

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These hybridised orbitals of the metal then overlap with filled orbitals on the ligands (those containing the lone pairs to be donated). This overlap forms coordinate covalent sigma bonds between the metal and the ligand donor atoms.

VBT uses the magnetic behaviour of a complex to infer its hybridisation and geometry. The presence of unpaired electrons, detected through paramagnetism, indicates how electrons are arranged in the metal's d orbitals during complex formation.

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Examples based on VBT:

• [Co(NH$_3$)$_6$]$^{3+}$ (Diamagnetic):

  Central ion: Co$^{3+}$. Electronic configuration: [Ar] 3d$^6$. Coordination number: 6 (octahedral). NH$_3$ is generally considered a strong field ligand in this context, capable of causing electron pairing.

  Since the complex is diamagnetic, all electrons must be paired. In the 3d$^6$ configuration, this requires pairing the electrons in the 3d orbitals, which makes two 3d orbitals available for hybridisation.

  Hybridisation: Two 3d orbitals, one 4s orbital, and three 4p orbitals hybridise to form six equivalent d$^2$sp$^3$ hybrid orbitals.

  Orbitals of Co$^{3+}$ ion:

  (The image would show the orbital diagram: Co$^{3+}$ (3d$^6$) initially with 4 unpaired electrons. Then, pairing of 3d electrons, leaving two 3d orbitals empty. Followed by the d$^2$sp$^3$ hybridisation involving these two 3d, one 4s, and three 4p orbitals. Finally, six arrows representing electron pairs from 6 NH$_3$ ligands filling the six hybrid orbitals, resulting in all paired electrons).

  Geometry: Octahedral. Magnetic property: Diamagnetic (no unpaired electrons).

  Since inner d orbitals (3d) are used for hybridisation, this complex is called an inner orbital complex or low spin complex (spin paired).

• [CoF$_6$]$^{3-}$ (Paramagnetic):

  Central ion: Co$^{3+}$. Electronic configuration: [Ar] 3d$^6$. Coordination number: 6 (octahedral). F$^-$ is considered a weak field ligand in this context, generally not causing pairing of 3d electrons.

  Since the complex is paramagnetic with 4 unpaired electrons (as per experimental observation), the 3d electrons do not pair up extensively. The available orbitals for hybridisation must be outside the 3d shell.

  Hybridisation: One 4s orbital, three 4p orbitals, and two 4d orbitals hybridise to form six equivalent sp$^3$d$^2$ hybrid orbitals.

  Orbitals of Co$^{3+}$ ion:

  (The image would show the orbital diagram: Co$^{3+}$ (3d$^6$) with 4 unpaired electrons. Followed by sp$^3$d$^2$ hybridisation involving one 4s, three 4p, and two 4d orbitals. Finally, six arrows representing electron pairs from 6 F$^-$ ligands filling the six hybrid orbitals, leaving 4 unpaired electrons in the 3d orbitals).

  Geometry: Octahedral. Magnetic property: Paramagnetic (4 unpaired electrons).

  Since outer d orbitals (4d) are used for hybridisation, this complex is called an outer orbital complex or high spin complex (spin free).

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For Tetrahedral complexes:

Typically, one s and three p orbitals hybridise to form four equivalent sp$^3$ hybrid orbitals, oriented tetrahedrally. This is seen in complexes with coordination number 4 that are paramagnetic or formed with weak field ligands where dsp$^2$ hybridisation (square planar) is not favoured.

• [NiCl$_4$]$^{2-}$ (Paramagnetic):

  Central ion: Ni$^{2+}$. Electronic configuration: [Ar] 3d$^8$. Coordination number: 4 (tetrahedral). Cl$^-$ is a weak field ligand.

  Experimental results show this complex is paramagnetic with 2 unpaired electrons.

  Hybridisation: One 4s orbital and three 4p orbitals hybridise to form four equivalent sp$^3$ hybrid orbitals.

  Orbitals of Ni$^{2+}$ ion:

  (The image would show the orbital diagram: Ni$^{2+}$ (3d$^8$) with 2 unpaired electrons. Followed by sp$^3$ hybridisation involving one 4s and three 4p orbitals. Finally, four arrows representing electron pairs from 4 Cl$^-$ ligands filling the four hybrid orbitals, leaving 2 unpaired electrons in the 3d orbitals).

  Geometry: Tetrahedral. Magnetic property: Paramagnetic (2 unpaired electrons).

• [Ni(CO)$_4$] (Diamagnetic):

  Central atom: Ni. Oxidation state: 0. Electronic configuration: [Ar] 3d$^8$ 4s$^2$. Coordination number: 4 (tetrahedral). CO is a strong field ligand, causing pairing of electrons.

  Experimental results show this complex is diamagnetic (0 unpaired electrons).

  Hybridisation: The 4s electrons are paired into the 3d subshell, resulting in a 3d$^{10}$ configuration (all paired). One 4s orbital and three 4p orbitals hybridise to form four sp$^3$ hybrid orbitals.

  Orbitals of Ni atom:

  (The image would show the orbital diagram: Ni (3d$^8$ 4s$^2$) initially. Then, pairing of 4s electrons into 3d, resulting in 3d$^{10}$ (all paired). Followed by sp$^3$ hybridisation involving one 4s and three 4p orbitals. Finally, four arrows representing electron pairs from 4 CO ligands filling the four hybrid orbitals. The 3d subshell remains full with 5 paired electron sets).

  Geometry: Tetrahedral. Magnetic property: Diamagnetic (0 unpaired electrons).

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For Square Planar complexes:

These complexes with coordination number 4 typically involve dsp$^2$ hybridisation, requiring one d orbital, one s orbital, and two p orbitals.

• [Ni(CN)$_4$]$^{2-}$ (Diamagnetic):

  Central ion: Ni$^{2+}$. Electronic configuration: [Ar] 3d$^8$. Coordination number: 4 (square planar). CN$^-$ is a strong field ligand, causing pairing of 3d electrons.

  Experimental results show this complex is diamagnetic (0 unpaired electrons). In the 3d$^8$ configuration, strong ligand field causes pairing, making one 3d orbital available for hybridisation.

  Hybridisation: One 3d orbital, one 4s orbital, and two 4p orbitals hybridise to form four equivalent dsp$^2$ hybrid orbitals.

  Orbitals of Ni$^{2+}$ ion:

  (The image would show the orbital diagram: Ni$^{2+}$ (3d$^8$) with 2 unpaired electrons. Then, pairing of 3d electrons leaving one 3d orbital empty. Followed by dsp$^2$ hybridisation involving this 3d, one 4s, and two 4p orbitals. Finally, four arrows representing electron pairs from 4 CN$^-$ ligands filling the four hybrid orbitals, resulting in all paired electrons).

  Geometry: Square planar. Magnetic property: Diamagnetic (0 unpaired electrons).

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According to VBT, the decision between sp$^3$ (tetrahedral) and dsp$^2$ (square planar) hybridisation for coordination number 4, or d$^2$sp$^3$ (inner orbital octahedral) and sp$^3$d$^2$ (outer orbital octahedral) for coordination number 6, depends on whether the ligands are strong enough to force the pairing of electrons in the metal's d orbitals. Strong field ligands favour pairing and inner orbital complexes (d$^2$sp$^3$ or dsp$^2$), while weak field ligands do not force pairing, leading to outer orbital complexes (sp$^3$d$^2$) or tetrahedral complexes (sp$^3$).

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It is important to note that hybrid orbitals are a theoretical construct used to explain bonding and geometry. They do not exist as distinct physical entities but represent mathematical combinations of atomic orbitals.

Magnetic Properties Of Coordination Compounds

The magnetic properties (paramagnetism or diamagnetism) of coordination compounds, which can be measured experimentally using techniques like magnetic susceptibility, provide valuable information about the number of unpaired electrons in the complex. As discussed earlier, the number of unpaired electrons allows us to calculate the magnetic moment using the 'spin-only' formula and, based on VBT, predict the hybridisation and structure.

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For metal ions with d$^1$ (Ti$^{3+}$), d$^2$ (V$^{3+}$), or d$^3$ (Cr$^{3+}$) configurations in an octahedral field, there are always two vacant (n-1)d orbitals available for d$^2$sp$^3$ hybridisation without needing to pair electrons (according to Hund's rule). The magnetic behaviour of these complexes is usually straightforward and corresponds to the number of unpaired electrons in the free ion.

However, for metal ions with d$^4$, d$^5$, or d$^6$ configurations, forming an inner orbital (d$^2$sp$^3$) octahedral complex requires pairing electrons in the (n-1)d orbitals to free up two d orbitals. This pairing uses energy. VBT explains the observed magnetic moments by proposing that strong field ligands are able to provide enough energy (Pairing Energy, P) to overcome the repulsion and force electron pairing in the (n-1)d orbitals, forming low-spin complexes. Weak field ligands do not provide sufficient energy, so electrons remain unpaired in the (n-1)d orbitals, and the metal uses outer nd orbitals for hybridisation (sp$^3$d$^2$), forming high-spin complexes.

• d$^4$ (e.g., Cr$^{2+}$, Mn$^{3+}$): Can be high spin (sp$^3$d$^2$, 4 unpaired) or low spin (d$^2$sp$^3$, 2 unpaired).
• d$^5$ (e.g., Mn$^{2+}$, Fe$^{3+}$): Can be high spin (sp$^3$d$^2$, 5 unpaired) or low spin (d$^2$sp$^3$, 1 unpaired).
• d$^6$ (e.g., Fe$^{2+}$, Co$^{3+}$): Can be high spin (sp$^3$d$^2$, 4 unpaired) or low spin (d$^2$sp$^3$, 0 unpaired, diamagnetic).

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Examples illustrating the concept of inner/outer orbital complexes based on magnetic data (as explained by VBT):

• [Mn(CN)$_6$]$^{3-}$ has a magnetic moment corresponding to 2 unpaired electrons (low spin, d$^2$sp$^3$). CN$^-$ is a strong field ligand.
• [MnCl$_6$]$^{3-}$ has a magnetic moment corresponding to 4 unpaired electrons (high spin, sp$^3$d$^2$). Cl$^-$ is a weak field ligand.
• [Fe(CN)$_6$]$^{3-}$ has a magnetic moment corresponding to 1 unpaired electron (low spin, d$^2$sp$^3$). CN$^-$ is a strong field ligand.
• [FeF$_6$]$^{3-}$ has a magnetic moment corresponding to 5 unpaired electrons (high spin, sp$^3$d$^2$). F$^-$ is a weak field ligand.
• [Co(C$_2$O$_4$)$_3$]$^{3-}$ is diamagnetic (0 unpaired electrons, low spin, d$^2$sp$^3$). Oxalate is a strong field ligand.
• [CoF$_6$]$^{3-}$ is paramagnetic with 4 unpaired electrons (high spin, sp$^3$d$^2$). F$^-$ is a weak field ligand.

Thus, VBT relates the observed magnetic properties to the hybridisation scheme, allowing us to differentiate between inner and outer orbital complexes based on whether electron pairing has occurred in the inner d orbitals.

Answer:

Limitations Of Valence Bond Theory

Despite its success in explaining the formation, structures, and magnetic behaviour of many coordination compounds, the Valence Bond Theory has several limitations:

1. It relies on a significant number of assumptions, such as the specific orbitals involved in hybridisation and whether electron pairing occurs, which are often justified only by the experimental results they are meant to predict (like magnetic moment).
2. It does not provide a quantitative interpretation of magnetic properties; it only predicts the integer number of unpaired electrons. It cannot explain the exact values of magnetic moments observed.
3. It fails to explain the colour exhibited by many coordination compounds. VBT focuses on bonding and does not account for electronic transitions that give rise to colour.
4. It does not provide a quantitative understanding of the thermodynamic stability or kinetic lability/inertness of coordination compounds.
5. It does not offer a clear way to make exact predictions about whether a 4-coordinate complex will adopt a tetrahedral (sp$^3$) or square planar (dsp$^2$) structure without prior knowledge of its magnetic properties.
6. It does not distinguish between weak field ligands and strong field ligands in a fundamental way, only classifying them based on whether they cause pairing or not, which is again inferred from experimental magnetic data.

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These limitations prompted the development of more advanced theories like Crystal Field Theory and Ligand Field Theory.

Crystal Field Theory

The Crystal Field Theory (CFT) is an electrostatic model that views the bond between the central metal ion and the ligands as purely ionic. It considers the interaction to arise from the electrostatic attraction between the positive charge of the metal ion and the negative charge of the ligands. Ligands are treated as point charges (if they are anions) or as point dipoles (if they are neutral molecules, with the negative end of the dipole pointing towards the metal).

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In an isolated gaseous metal atom or ion, the five d orbitals (d$_{xy}$, d$_{yz}$, d$_{xz}$, d$_{x^2-y^2}$, d$_{z^2}$) are said to be degenerate, meaning they all have the same energy. This degeneracy is maintained if the metal is surrounded by a perfectly spherical field of negative charge. However, when the negative field is provided by ligands in a specific geometrical arrangement, the field is no longer spherically symmetrical. This asymmetrical field causes the degeneracy of the d orbitals to be lifted, resulting in the splitting of the d orbital energies.

The specific pattern of splitting depends on the geometry of the ligand arrangement (the crystal field).

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(a) Crystal field splitting in octahedral coordination entities:

In an octahedral complex, there are six ligands located along the x, -x, y, -y, z, and -z axes around the central metal ion. When these ligands approach the metal ion, there is electrostatic repulsion between the electrons in the metal's d orbitals and the electron density (or negative charge) of the ligands.

The d orbitals have different spatial orientations:

• The d$_{x^2-y^2}$ and d$_{z^2}$ orbitals (collectively called the e$_g$ set) point directly along the axes, i.e., towards the positions where the ligands are located.
• The d$_{xy}$, d$_{yz}$, and d$_{xz}$ orbitals (collectively called the t$_{2g}$ set) are oriented in the regions between the axes, i.e., between the ligands.

Because the e$_g$ orbitals point towards the ligands, electrons in these orbitals experience greater electrostatic repulsion from the approaching ligands compared to electrons in the t$_{2g}$ orbitals, which are directed between the ligands.

This differential repulsion causes the energy of the e$_g$ orbitals to be raised and the energy of the t$_{2g}$ orbitals to be lowered relative to the average energy of the d orbitals in a hypothetical spherical field (called the barycenter).

The splitting of the d orbitals in an octahedral field results in the formation of two sets of orbitals:

• Three lower-energy t$_{2g}$ orbitals (d$_{xy}$, d$_{yz}$, d$_{xz}$).
• Two higher-energy e$_g$ orbitals (d$_{x^2-y^2}$, d$_{z^2}$).

This energy separation or splitting is called the crystal field splitting energy for octahedral complexes, denoted by $\Delta_o$ or 10 Dq (where 'o' stands for octahedral).

The total energy of the d electrons is conserved relative to the barycenter. The energy of the two e$_g$ orbitals increases by +(3/5) $\Delta_o$ each (total energy increase = 2 $\times$ (3/5) $\Delta_o$ = 6/5 $\Delta_o$), while the energy of the three t$_{2g}$ orbitals decreases by -(2/5) $\Delta_o$ each (total energy decrease = 3 $\times$ (2/5) $\Delta_o$ = 6/5 $\Delta_o$). The net change in energy is zero, placing the barycenter as the average energy level.

(The image would show a diagram with: Left: Five degenerate d orbitals in isolation. Middle: Hypothetical barycenter energy level in a spherical field. Right: Splitting into lower t$_{2g}$ (3 orbitals) and higher e$_g$ (2 orbitals) levels in an octahedral field, with energy differences indicated as -2/5 $\Delta_o$ and +3/5 $\Delta_o$ relative to the barycenter, and the total splitting $\Delta_o$).

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The magnitude of the crystal field splitting energy, $\Delta_o$, is influenced by several factors, primarily:

• The nature of the ligand: Some ligands produce a stronger field and cause larger splitting, while others produce a weaker field and cause smaller splitting.
• The charge on the metal ion: Higher charge density on the metal ion leads to greater attraction for the ligands and usually results in larger splitting.
• The position of the metal in the periodic table (3d vs 4d vs 5d series): $\Delta_o$ generally increases down a group (5d > 4d > 3d) for the same ligands and oxidation state.

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Based on their ability to cause crystal field splitting, ligands can be arranged in a series called the spectrochemical series. This is an experimentally determined series (often based on the absorption spectra of complexes) that ranks ligands in order of increasing field strength (increasing $\Delta$ value):

Weak field ligands (small $\Delta$) $\rightarrow$ Strong field ligands (large $\Delta$)

I$^-$ < Br$^-$ < SCN$^-$ < Cl$^-$ < S$^{2-}$ < F$^-$ < OH$^-$ < C$_2$O$_4^{2-}$ < H$_2$O < NCS$^-$ < edta$^{4-}$ < NH$_3$ < en < CN$^-$ < CO

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The spectrochemical series is crucial for understanding how electrons are filled into the split d orbitals, particularly for d$^4$, d$^5$, d$^6$, and d$^7$ configurations.

For d$^1$, d$^2$, d$^3$ configurations in an octahedral field, the electrons simply occupy the lower-energy t$_{2g}$ orbitals singly according to Hund's rule. For example, d$^3$ will have t$_{2g}^3$ e$_g^0$.

For d$^4$ configuration, the fourth electron has two possibilities:

1. It can enter one of the t$_{2g}$ orbitals and pair up with an existing electron. This requires energy, known as the pairing energy (P), which is the energy needed to pair two electrons in the same orbital.
2. It can jump to one of the higher-energy e$_g$ orbitals to avoid pairing. This requires energy equal to the crystal field splitting energy, $\Delta_o$.

The actual distribution of the fourth electron depends on the relative magnitudes of $\Delta_o$ and P:

• If $\Delta_o$ < P (small splitting, typically with weak field ligands), it is energetically more favourable for the electron to occupy the higher e$_g$ level rather than pairing in t$_{2g}$. The configuration will be t$_{2g}^3$ e$_g^1$. These complexes are called high spin complexes because the number of unpaired electrons is maximised (as if there were no splitting, following Hund's rule).
• If $\Delta_o$ > P (large splitting, typically with strong field ligands), it is energetically more favourable for the electron to pair up in a t$_{2g}$ orbital rather than jumping to the higher e$_g$ level. The configuration will be t$_{2g}^4$ e$_g^0$. These complexes are called low spin complexes because electron pairing reduces the number of unpaired electrons.

This competition between crystal field splitting energy ($\Delta_o$) and pairing energy (P) determines whether high-spin or low-spin complexes are formed for d$^4$, d$^5$, d$^6$, and d$^7$ configurations in octahedral fields. For d$^8$, d$^9$, d$^{10}$, the configurations are fixed regardless of field strength as pairing is necessary to fill the orbitals (e.g., d$^8$ is t$_{2g}^6$ e$_g^2$, d$^{10}$ is t$_{2g}^6$ e$_g^4$).

CFT predicts that complexes with d$^4$ to d$^7$ configurations are generally more stable with strong field ligands (low spin) compared to weak field ligands (high spin) due to the increased Crystal Field Stabilisation Energy (CFSE).

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(b) Crystal field splitting in tetrahedral coordination entities:

In a tetrahedral complex, there are four ligands located at the corners of a tetrahedron around the metal ion. The orientation of the ligands relative to the d orbitals is different from the octahedral case.

In a tetrahedral field, the t$_{2}$ orbitals (d$_{xy}$, d$_{yz}$, d$_{xz}$) which lie between the axes are closer to the ligands (compared to octahedral) and experience more repulsion. The e orbitals (d$_{x^2-y^2}$, d$_{z^2}$) which lie along the axes are further from the ligands and experience less repulsion.

This results in the splitting of the d orbitals in a tetrahedral field into two sets:

• Two lower-energy e orbitals (d$_{x^2-y^2}$, d$_{z^2}$).
• Three higher-energy t$_{2}$ orbitals (d$_{xy}$, d$_{yz}$, d$_{xz}$).

The energy separation is called the crystal field splitting energy for tetrahedral complexes, denoted by $\Delta_t$.

The splitting pattern is inverted compared to the octahedral case. The magnitude of splitting in tetrahedral fields ($\Delta_t$) is significantly smaller than in octahedral fields ($\Delta_o$) for the same metal, ligands, and metal-ligand distance. It can be shown theoretically that $\Delta_t \approx (4/9) \Delta_o$.

(The image would show a diagram with: Left: Five degenerate d orbitals in isolation. Middle: Barycenter. Right: Splitting into lower e (2 orbitals) and higher t$_2$ (3 orbitals) levels in a tetrahedral field, with energy differences relative to the barycenter).

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Because $\Delta_t$ is much smaller than P (pairing energy) for virtually all ligands, the energy required to pair electrons in the lower-energy orbitals is almost always greater than the energy needed to excite an electron to the higher-energy orbitals. Consequently, electron pairing in tetrahedral complexes is rare, and they are almost exclusively high spin complexes, following Hund's rule for filling the split orbitals.

Note that the 'g' subscript (t$_{2g}$, e$_g$) is used for energy levels in octahedral and square planar complexes because these geometries have a center of symmetry. Tetrahedral complexes lack a center of symmetry, so the 'g' subscript is not used (t$_2$, e).

Colour In Coordination Compounds

One of the most striking properties of transition metal coordination compounds is their vibrant colours. This colour is directly explained by Crystal Field Theory as arising from d-d electronic transitions within the split d orbitals.

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When a coordination compound absorbs light from the visible region of the electromagnetic spectrum, the energy of the absorbed light corresponds to the energy difference ($\Delta_o$ or $\Delta_t$) between the split d orbital levels. An electron in a lower-energy d orbital (t$_{2g}$ in octahedral, e in tetrahedral) can absorb a photon of light with this specific energy and get excited to a higher-energy d orbital (e$_g$ in octahedral, t$_2$ in tetrahedral).

When white light (which contains all colours of the visible spectrum) passes through a sample of the complex, certain wavelengths (colours) are absorbed due to these d-d transitions. The light that is transmitted or reflected to our eyes is the remaining light, which appears as the colour complementary to the colour that was absorbed.

For example, if a complex absorbs light in the blue-green region, the transmitted light is enriched in red-violet colours, so the complex appears violet.

Coordination entity	Wavelength of light absorbed (nm)	Colour of light absorbed	Colour of coordination entity (Observed Colour)
[CoCl(NH$_3$)$_5$]$^{2+}$	535	Yellow	Violet
[Co(NH$_3$)$_5$(H$_2$O)]$^{3+}$	500	Blue Green	Red
[Co(NH$_3$)$_6$]$^{3+}$	475	Blue	Yellow Orange
[Co(CN)$_6$]$^{3-}$	310	Ultraviolet	Pale Yellow
[Cu(H$_2$O)$_4$]$^{2+}$	600	Red	Blue
[Ti(H$_2$O)$_6$]$^{3+}$	498	Blue Green	Violet

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Consider the complex [Ti(H$_2$O)$_6$]$^{3+}$. Ti is in the +3 oxidation state. Electronic configuration of Ti$^{3+}$ is [Ar] 3d$^1$. In the octahedral [Ti(H$_2$O)$_6$]$^{3+}$ complex, the single d electron occupies one of the lower-energy t$_{2g}$ orbitals in the ground state. The higher-energy e$_g$ orbitals are empty. When this complex is exposed to visible light, it absorbs light with energy corresponding to the splitting energy $\Delta_o$ (approximately 498 nm, which is in the blue-green region). This energy excites the electron from the t$_{2g}$ level to the e$_g$ level (t$_{2g}^1$ e$_g^0$ $\rightarrow$ t$_{2g}^0$ e$_g^1$). The colours remaining in the transmitted light (complementary colour to blue-green) are perceived as violet.

(The image would show the split d orbitals (t$_{2g}$ and e$_g$) for [Ti(H$_2$O)$_6$]$^{3+}$ in the ground state (electron in t$_{2g}$) and excited state (electron in e$_g$), with an arrow indicating the absorption of a photon corresponding to $\Delta_o$ to cause the transition).

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If a complex has a d$^0$ (empty d orbitals) or d$^{10}$ (completely filled d orbitals) configuration (e.g., Sc$^{3+}$ (3d$^0$), Ti$^{4+}$ (3d$^0$), Zn$^{2+}$ (3d$^{10}$)), it cannot undergo d-d transitions because there are no electrons to be excited (d$^0$) or no vacant higher-energy d orbitals to receive excited electrons (d$^{10}$). Consequently, such complexes are typically colourless.

The presence of ligands and the resulting crystal field splitting are essential for colour in most transition metal complexes. For example, anhydrous CuSO$_4$ (which does not have ligands bonded to Cu$^{2+}$) is white, but CuSO$_4 \cdot 5\text{H}_2\text{O}$ is blue because the Cu$^{2+}$ ions are coordinated by water molecules to form [Cu(H$_2$O)$_4$]$^{2+}$ and lattice water, leading to d-d transitions.

The colour of a complex can also change if the ligands are changed, as this alters the magnitude of the crystal field splitting ($\Delta$) according to the spectrochemical series. For example, replacing water ligands in the green [Ni(H$_2$O)$_6$]$^{2+}$ complex with ethane-1,2-diamine (en), a stronger field ligand, changes the colour:

• [Ni(H$_2$O)$_6$]$^{2+}$ (green) + en $\rightarrow$ [Ni(H$_2$O)$_4$(en)]$^{2+}$ (pale blue) + 2H$_2$O
• [Ni(H$_2$O)$_4$(en)]$^{2+}$ (pale blue) + en $\rightarrow$ [Ni(H$_2$O)$_2$(en)$_2$]$^{2+}$ (blue/purple) + 2H$_2$O
• [Ni(H$_2$O)$_2$(en)$_2$]$^{2+}$ (blue/purple) + en $\rightarrow$ [Ni(en)$_3$]$^{2+}$ (violet) + 2H$_2$O

As the stronger field ligand 'en' replaces water, the crystal field splitting energy increases. This changes the wavelength of light absorbed, leading to a change in the observed colour.

(The image would visually show solutions of [Ni(H$_2$O)$_6$]$^{2+}$, [Ni(H$_2$O)$_4$(en)]$^{2+}$, [Ni(H$_2$O)$_2$(en)$_2$]$^{2+}$, and [Ni(en)$_3$]$^{2+}$ showing the progression of colours from green to pale blue to blue/purple to violet).

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The colours of many gemstones are also due to transition metal ions acting as impurities within host lattices. For example, Ruby is aluminium oxide (Al$_2$O$_3$) containing Cr$^{3+}$ ions (d$^3$) in octahedral sites. d-d transitions in these Cr$^{3+}$ ions cause the absorption of green and violet light, resulting in the transmission of red light, hence the red colour of ruby.

Emerald is beryl (Be$_3$Al$_2$Si$_6$O$_{18}$) also containing Cr$^{3+}$ ions in octahedral sites. In this lattice, the crystal field splitting energy is slightly different, shifting the absorption bands to longer wavelengths (yellow-red and blue), causing the transmission of green light and the green colour of emerald.

(The image would show pictures of a ruby and an emerald).

Limitations Of Crystal Field Theory

While Crystal Field Theory is quite successful in explaining many aspects of coordination compounds, including their formation, structure, magnetic properties, and colour, it also has limitations:

1. The assumption that the metal-ligand bond is purely ionic and that ligands are just point charges is a simplification. This model struggles to explain why neutral ligands like CO and NH$_3$ often produce stronger crystal fields than anionic ligands like halides (e.g., CO and CN$^-$ are strong field ligands, but are placed after H$_2$O and NH$_3$ in some simplified series or show stronger effects than expected based on charge alone). The ionic model predicts that anionic ligands, being negative charges, should cause the largest splitting, but this is not always observed in the spectrochemical series (anionic ligands like I$^-$ and Br$^-$ are at the weak field end).
2. CFT does not take into account the covalent character of the metal-ligand bond, which is present to varying degrees in coordination compounds.

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These limitations are addressed by more sophisticated theories like Ligand Field Theory (which incorporates aspects of both ionic and covalent bonding) and Molecular Orbital Theory, but these are beyond the scope of basic study.

Bonding In Metal Carbonyls

Metal carbonyls are coordination compounds where Carbon Monoxide (CO) molecules act as the sole ligands. They are typically formed by transition metals in low oxidation states, often zero.

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Homoleptic carbonyls (containing only CO ligands) have characteristic and well-defined structures:

• Tetracarbonylnickel(0), [Ni(CO)$_4$], is tetrahedral.
• Pentacarbonyliron(0), [Fe(CO)$_5$], is trigonal bipyramidal.
• Hexacarbonylchromium(0), [Cr(CO)$_6$], is octahedral.

(The image would show the structures of [Ni(CO)$_4$], [Fe(CO)$_5$], and [Cr(CO)$_6$]).

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Some metal carbonyls are polynuclear, containing more than one metal atom, and may have bridging CO ligands. Examples include:

• Decacarbonyldimanganese(0), [Mn$_2$(CO)$_{10}$], consists of two Mn(CO)$_5$ square pyramidal units joined by a metal-metal bond (Mn-Mn).
• Octacarbonyldicobalt(0), [Co$_2$(CO)$_8$], exists in equilibrium between forms with and without bridging CO groups. One common structure has a Co-Co bond bridged by two CO groups.

(The image would show the structures of [Mn$_2$(CO)$_{10}$] and a bridged form of [Co$_2$(CO)$_8$]).

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The bonding between the metal and the carbonyl ligand (M-CO) is unique and involves both sigma ($\sigma$) and pi ($\pi$) interactions, creating a synergic effect that strengthens the bond.

The bonding can be described as follows:

1. A sigma ($\sigma$) bond is formed by the donation of a lone pair of electrons from the carbon atom of the CO ligand into a vacant hybrid orbital of the metal atom. This is a typical ligand-to-metal coordinate covalent bond.
2. A pi ($\pi$) bond is formed by the donation of a pair of electrons from a filled metal d orbital (specifically, a d orbital with appropriate symmetry) into a vacant antibonding pi ($\pi^*$) molecular orbital of the carbon monoxide molecule. This is called back-bonding or pi back-donation (metal-to-ligand $\pi$ bonding).

This metal-to-ligand $\pi$ back-donation reinforces the metal-carbon $\sigma$ bond (and vice-versa). The ligand-to-metal $\sigma$ donation increases the electron density on the metal, which is then reduced by the metal-to-ligand $\pi$ back-donation. This synergic bonding results in a strong M-CO bond and is responsible for the stability of metal carbonyls, especially those with metals in low oxidation states.

(The image would show a diagram depicting the M-CO bond, showing an arrow from a lone pair on C to a metal orbital (sigma donation) and an arrow from a filled metal d orbital to a CO $\pi^*$ antibonding orbital (pi back-donation)).

Importance And Applications Of Coordination Compounds

Coordination compounds are of immense significance in various fields, ranging from natural biological processes to advanced industrial applications, analytical techniques, and medicine.

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Their importance and applications include:

• Analytical Chemistry:
  • Coordination complex formation is the basis for many qualitative and quantitative analytical methods for detecting and estimating metal ions. Characteristic colour reactions with specific ligands (especially chelating ones like EDTA, dimethylglyoxime (DMG), etc.) are used for identifying and quantifying metal ions via classical methods (like titrations) or instrumental techniques (like spectrophotometry).
  • The hardness of water (due to Ca$^{2+}$ and Mg$^{2+}$ ions) is commonly determined by titrating with Na$_2$EDTA, which forms stable complexes with these ions. Selective estimation is possible due to differences in the stability constants of the Ca-EDTA and Mg-EDTA complexes.
• Metallurgy:
  • Complex formation is employed in the extraction and purification of some metals. For example, gold is extracted from its ore by forming a soluble coordination entity, [Au(CN)$_2$]$^-$, in the presence of cyanide, oxygen, and water. Gold metal is then recovered by adding zinc, which is a stronger reducing agent and displaces gold from the complex. ($2\text{Au(s)} + 4\text{CN}^-\text{(aq)} + \text{O}_2\text{(g)} + 2\text{H}_2\text{O(l)} \rightarrow 2[\text{Au(CN)}_2]^-\text{(aq)} + \text{H}_2\text{O}_2$; $\text{Zn(s)} + 2[\text{Au(CN)}_2]^-\text{(aq)} \rightarrow [\text{Zn(CN)}_4]^{2-}\text{(aq)} + 2\text{Au(s)}$).
  • Impurification of metals can also be achieved by forming a volatile coordination compound, which is then decomposed to yield pure metal. The Mond process for purifying nickel involves forming tetracarbonylnickel(0), [Ni(CO)$_4$], from impure nickel and CO at moderate temperature, and then decomposing the volatile [Ni(CO)$_4$] at a higher temperature to deposit pure nickel.
• Biological Systems:
  • Many essential biological molecules are coordination compounds. Chlorophyll, the pigment responsible for photosynthesis in plants, is a coordination compound of Magnesium (Mg$^{2+}$) within a porphyrin ring.
  • Haemoglobin, the red pigment in blood that transports oxygen, is a coordination compound of Iron (Fe$^{2+}$) within a porphyrin-like ring system (heme).
  • Vitamin B$_{12}$ (cyanocobalamin), crucial for metabolism and red blood cell formation, is a coordination compound of Cobalt (Co$^{3+}$).
  • Several enzymes, which are biological catalysts, contain coordinated metal ions necessary for their function. Examples include carboxypeptidase A (contains Zn$^{2+}$) and carbonic anhydrase (contains Zn$^{2+}$).
• Industry:
  • Coordination compounds serve as catalysts in numerous industrial chemical processes. Wilkinson's catalyst, [(Ph$_3$P)$_3$RhCl], a coordination compound of Rhodium, is used for the hydrogenation of alkenes.
  • Complexes are used in electroplating to obtain smoother and more uniform metal deposits. For example, silver and gold are electroplated from solutions containing the complex ions [Ag(CN)$_2$]$^-$ and [Au(CN)$_2$]$^-$.
  • In black and white photography, after developing the film, unexposed silver bromide (AgBr) is removed by washing with a 'hypo' solution (sodium thiosulphate, Na$_2$S$_2$O$_3$). The thiosulphate forms a soluble complex ion with Ag$^+$: AgBr(s) + 2S$_2$O$_3^{2-}$(aq) $\rightarrow$ [Ag(S$_2$O$_3$)$_2$]$^{3-}$(aq) + Br$^-$(aq). This "fixes" the image by dissolving away the unreacted silver salt.
• Medicine:
  • Chelate therapy is a promising area in medicinal chemistry. Chelating ligands are used to remove toxic metal ions from the body by forming stable, soluble complexes that can be excreted. Examples include D-penicillamine and desferrioxime B used to treat excess copper and iron respectively, and EDTA used to treat lead poisoning.
  • Certain coordination compounds exhibit anti-cancer properties. For example, **cis-platin** (cis-[Pt(NH$_3$)$_2$Cl$_2$]), a square planar complex of Platinum(II), and related compounds are effective in inhibiting the growth of tumours.

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