Bonding in Coordination Compounds: VBT and CFT

Table of Contents
1. What is Valence Bond Theory (VBT)?
2. Magnetic Properties of Complexes
3. What is Crystal Field Theory (CFT)?
4. Colour of Complexes
5. Bonding in Metal Complexes
6. Applications of Coordination Compounds
7. Organometallic Compounds
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What is Valence Bond Theory (VBT)?

According to the Valence Bond Theory, electrons in a molecule occupy atomic orbitals rather than molecular orbitals. Chemical bonds form when appropriate atomic orbitals on two atoms overlap and a pair of electrons is shared in the region of overlap. Greater overlap leads to stronger covalent bonding. VBT emphasises electronic configuration, orbital overlap and the hybridisation of atomic orbitals of the central atom to explain geometry and bonding in molecules and complexes.

In coordination compounds the metal-ligand bond has significant covalent character. VBT treats bonding in metal complexes as arising from overlap between ligand lone-pair orbitals and suitable hybrid orbitals on the metal ion. The concept of resonance (or electronic delocalisation) helps to visualise the bonding as a network of overlapping two-centre bonds.

History of Valence Bond Theory

The Lewis approach introduced shared electron pairs but could not explain why bonds form in terms of wave mechanics. To provide a quantum mechanical foundation of covalent bonding, Walter Heinrich Heitler and Fritz London applied the Schrödinger wave equation to the hydrogen molecule and developed the first valence bond description of the H-H bond. Later Linus Pauling extended valence bond ideas to include hybridisation of atomic orbitals (s, p, d) to explain molecular shapes and bonding in polyatomic species.

VBT describes the formation of bonds by the overlap of atomic orbitals localised between the nuclei of bonding atoms. It also emphasises that each nucleus attracts the electrons associated with neighbouring atoms, giving rise to net bonding.

Postulates of Valence Bond Theory

The main postulates (as used in coordination chemistry) are:

• Central metal ion and ligands form bonds by overlap between ligand lone-pair orbitals and appropriate atomic or hybrid orbitals on the metal.
• Under the influence of strong-field ligands, electrons on the central metal ion may pair up (contrary to Hund's rule) so as to occupy lower energy hybrid orbitals; this can produce inner-orbital (low-spin) complexes.
• In the presence of weak-field ligands electron pairing is unfavourable and electrons occupy higher energy orbitals leading to outer-orbital (high-spin) complexes.
• If the complex contains unpaired electrons it is paramagnetic; if it contains no unpaired electrons it is diamagnetic. The magnetic moment (spin-only) is given by M = √(n(n+2)) BM, where n = number of unpaired electrons and BM = Bohr magneton.
  Relation between unpaired electrons and magnetic moment

  Magnetic moment (Bohr magnetons)	0	1.73	2.83	3.87	4.90	5.92
  Number of unpaired electrons	0	1	2	3	4	5

• Ligands can be arranged in an experimentally determined spectrochemical series according to their ability to split the metal d-orbitals (i.e., their field strength).
• The central metal ion provides empty orbitals equal in number to its coordination number to accept electron pairs from ligands.
• The type of hybridisation used by the metal ion (for example, (n-1)d ns np or ns np nd) determines the geometry of the complex; inner or outer d orbitals may be involved giving rise to inner- or outer-orbital complexes respectively.
  MULTIPLE CHOICE QUESTION

  Try yourself: According to VBT, the direction of a bond which is formed due to overlapping will be _____________

  A

  In the same direction in which orbitals are concentrated

  B

  In the opposite direction in which orbitals are concentrated

  C

  Perpendicular to the direction in which orbitals are concentrated

  D

  None of the mentioned

  View Solution

  Correct Answer: AHide Explanation ⌃

  The direction of the bond formed will be in that direction in which the orbitals are concentrated. For Example: When two p_x orbitals overlap, the bond is formed along the x-axis.

  Report a problem

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Number of Orbitals and Types of Hybridisation

VBT assumes the metal atom/ion may use combinations of its (n-1)d, ns and np orbitals (or ns, np, nd) to form equivalent hybrid orbitals with definite directional properties. These hybrid orbitals accept lone pairs from ligands to give coordination bonds. Common hybridisation schemes and their geometries are:

Limitations of Valence Bond Theory

1. VBT cannot always predict accurately the magnetic moments of complexes from first principles (it uses experimental pairing and assumptions about orbital energies).
2. It does not provide a detailed explanation for the origin of the colour (electronic spectra) of complexes, which arises from d-d transitions and ligand-metal charge transfer.
3. VBT does not quantitatively explain why some complexes are inner-orbital (low-spin) while others are outer-orbital (high-spin); it assumes hybridisation without providing the energetic justification.
4. For some complexes, VBT requires electronic promotion (e.g., moving an electron from 3d to 4p) but does not account for the energetic cost of such promotions; this leaves unexplained why certain complexes do not show expected redox or reducing behaviour.

Applications of Valence Bond Theory

1. Explains covalent bond formation by maximum overlap condition; useful for simple molecules (H2, HF, F2) where bond strength and length correlate with orbital overlap.
2. Accounts for shapes of many simple molecules and complexes via hybridisation (e.g., sp3, dsp2, d2sp3).
3. Helps rationalise paramagnetism/diamagnetism qualitatively by counting unpaired electrons in the assumed hybrid/d orbital distribution.

Magnetic Properties of Complexes

Complexes with unpaired electrons are paramagnetic; those without are diamagnetic. The spin-only magnetic moment (in Bohr magnetons, BM) is calculated by the expression:

• M = √(n(n+2)) BM
• BM = Bohr magneton

The magnetic moment of a complex depends on:

1. Type of hybridisation and orbital occupancy (inner- or outer-orbital).
2. Oxidation state of the central transition metal ion (which affects d-electron count and splitting).
3. Number of unpaired electrons (n).

What is Crystal Field Theory (CFT)?

Crystal Field Theory treats the interaction between the central metal cation and ligands as essentially electrostatic. Ligands are considered as point charges (or dipoles) whose fields interact with the d-electrons of the metal ion, causing a removal of degeneracy (energy splitting) of the five d orbitals. CFT explains many spectrochemical, magnetic and structural features of coordination compounds by considering how ligands perturb the energies of metal d-orbitals.

• CFT is widely used because it offers a simple explanation for d-orbital splitting and the resultant magnetic and spectral properties of complexes.
• The metal ion is treated as a positive point charge (charge = oxidation state) surrounded by negative ligands or neutral molecules oriented so that their donor end points toward the metal.
• Electrons on the metal d-orbitals experience repulsion from ligand electron pairs; orbitals pointing towards ligands rise in energy more than those oriented between ligand directions.

Overview of Crystal Field Theory - Basic Assumptions

The main assumptions of CFT are:

• Ligands act as point charges (or point dipoles for neutral donors).
• There is no covalent overlap between metal and ligand orbitals in the simplest CFT model (purely electrostatic approach).
• In the free metal ion all five d orbitals are degenerate; on complex formation the ligand field (unless spherically symmetric) removes the degeneracy and splits the d levels.
•  However, the energy of the orbitals is raised because of repulsion between the field of ligands and electrons on the metal. In most transition metal complexes, either six or four ligands surround the metal, giving octahedral or tetrahedral structures. In both these cases, the field produced by the ligands is not spherically symmetrical. Thus, the d orbitals are not all affected equally by the ligand field.

High Spin and Low Spin Complexes

When crystal field splitting (Δ) is small compared to the pairing energy (P), electrons prefer to occupy higher energy orbitals singly to minimise pairing; this results in high-spin complexes (maximum unpaired electrons), typical for weak-field ligands. When Δ is large (Δ > P), electrons pair in lower energy orbitals and give low-spin complexes (minimum unpaired electrons), typical for strong-field ligands.

• High spin - maximum number of unpaired electrons (Δ small).
• Low spin - minimum number of unpaired electrons (Δ large).

Example:

Crystal Field Splitting in Octahedral Complexes

In an octahedral field six ligands are located along the ±x, ±y and ±z axes around the metal ion. The d-orbitals split into two sets:

• eg set: d(x₂-y₂), d(z₂) - lobes point along axes and experience greater repulsion from ligands; energy increases.
• t2g set: d(xy), d(xz), d(yz) - lobes point between axes and experience less repulsion; energy decreases.

The energy difference between the two sets is the octahedral splitting Δ_o (also written as 10Dq). Relative to the barycentre, eg orbitals are raised by +0.6Δ_o and t₂g orbitals lowered by -0.4Δ_o.

Crystal Field Splitting in Tetrahedral Complexes

In a tetrahedral field four ligands occupy alternate corners of a cube (or the vertices of a tetrahedron).Relation of the tetrahedron to a cube

The pattern of splitting is reversed compared to octahedral: the t₂ set (three orbitals) is at higher energy and the e set (two orbitals) at lower energy. The splitting magnitude Δ_t is smaller than Δ_o (roughly 4/9 Δ_o), because fewer ligands approach along the axes and there is less direct d-orbital repulsion.

Limitations of Crystal Field Theory

1. The assumption of purely electrostatic metal-ligand interaction is an approximation; many complexes show significant covalent character and orbital overlap (ligand-metal bonding cannot be ignored).
2. CFT considers only metal d-orbitals; s and p orbitals of the metal and ligand orbitals are not treated explicitly in the simplest model.
3. CFT alone cannot explain why some ligands produce much larger splitting than others (it does not account for ligand orbital energies and covalency effects that influence Δ).
4. CFT rules out p-bonding and back-bonding; this is a serious drawback because π-bonding and π-back donation exist in many complexes (e.g., metal carbonyls).
5. The theory gives no description of ligand orbitals or their interactions with metal orbitals; for such cases Ligand Field Theory or molecular orbital theory is required for a more complete explanation.

Crystal Field Stabilization Energy (CFSE)

When d orbitals split in energy due to a ligand field, electrons occupying the lower t2g orbitals stabilise the complex while electrons in eg orbitals destabilise it. The difference in energy between eg and t2g is Δ (or 10Dq). Each electron in t2g stabilises by -0.4Δ relative to the barycentre and each electron in eg destabilises by +0.6Δ. The net stabilisation due to this occupancy is called Crystal Field Stabilization Energy (CFSE) or Ligand Field Stabilization Energy (LFSE).

Examples:

d5 (high spin, octahedral): 3 electrons in t2g and 2 in eg 
→ net CFSE = 3(-0.4Δ) + 2(+0.6Δ) = -1.2Δ + 1.2Δ = 0.

d10: all d orbitals filled → net CFSE = 0.

CFSE Table (Octahedral and Tetrahedral)

The magnitude of splitting depends on the ligand field strength and the metal ion charge. An experimentally determined spectrochemical series ranks ligands by their field strength (weak → strong):

I^- < Br^- < Cl^- < SCN^- < F^- < OH^- < C²O₄^2- < H₂O < NCS- < EDTA^4- < NH₃ < en < CN^- < CO

Filling of d-orbitals takes place in the following manner; the first three electrons are arranged in t_2g level as per Hund's rule. The fourth electron can either enter into t_2g level giving a configuration of t_2g⁴e_g⁰ or can enter the eg orbital giving a configuration of t_2g³e_g¹. This depends on two parameters magnitude of crystal field splitting, Δ_o and pairing energy, P. The possibilities of two cases can better be explained as:

• If Δo > P: electrons pair in t2g first → low-spin configuration (strong-field ligands).
• If Δo < P: electrons occupy eg singly before pairing → high-spin configuration (weak-field ligands).

Stability of Complexes

Complex formation usually occurs stepwise. For formation of ML4 the steps have equilibrium constants K₁, K₂, K₃ and K₄. The overall formation (stability) constant β is the product β = K₁ × K₂ × K₃ × K₄. The reciprocal 1/β is the instability constant.

Factors affecting stability of complexes

1. Charge density on the metal ion: higher charge density → stronger attraction for donor pairs → greater stability.
2. Basicity of ligand: more basic ligands donate electron pairs more readily → more stable complexes. (Example: CN- and NH₃ form more stable complexes than halides.)
3. Oxidation state of metal: higher oxidation state generally increases complex stability (e.g., [Co(NH₃)₆]³⁺ > [Co(NH3)₆]²⁺). Similarly, [Fe(CN)₆]^3- is more stable than [Fe(CN)₆]^4-.
4. Chelation: polydentate ligands form chelates which are more stable than analogous monodentate complexes (chelate effect).

Colour of Complexes

Many transition metal complexes are coloured because of electronic transitions. The most common are d-d transitions, where an electron is promoted from a t2g to an eg orbital (absorption of visible light). Ligand-to-metal and metal-to-ligand charge transfer transitions also produce intense colours in some complexes.

The colour of a complex depends on:

1. Number of unpaired electrons and d-electron configuration.
2. Nature of ligands (which affects Δ and therefore the energy of absorbed light).
3. Oxidation state of the central metal ion.
4. Wavelength of light absorbed (difference in d-orbital energies) and light emitted.
5. Proportion and arrangement of ligands in the coordination sphere.

Example: On adding ethylenediamine (en) to [Ni(H₂O)₆]²⁺ the complex changes from pale green/blue to another shade due to change in ligand field and d-orbital splitting:

[Ni(H₂O)₆]⁺²+ en(aq) → [Ni(H₂O)₄en]⁺² (Green Pale blue)

Bonding in Metal Complexes

Some ligands and complexes require concepts beyond simple VBT or CFT.

Metal carbonyls: In complexes such as [Ni(CO)₄] and [Fe(CO)₅], CO behaves as a ligand that donates electron density from a filled lone-pair orbital on carbon into a vacant metal orbital (σ donation) and simultaneously accepts electron density from filled metal d orbitals into its empty π* orbitals (π back-bonding). This synergic σ-π bonding explains the stability and often low oxidation state (0) of metal carbonyls.

Example: [Ni(CO)₄] and [Fe(CO)₅] - σ donation from CO to metal; π back donation from metal to CO.

Applications of Coordination Compounds

Coordination compounds are widely useful because complexation changes physical and chemical properties of metal ions. Important applications include:

1. Qualitative detection and gravimetric estimation of metal ions using specific complexing reagents (e.g., Ni²⁺ gives a scarlet red complex with dimethylglyoxime (DMG)).
2. Quantitative volumetric analysis using complexing agents like EDTA for Ca²⁺, Mg²⁺ and Zn²⁺ determination.
3.  Fe³⁺ is detected by formation of a blood red coloured complex with KSCN.

   

4. Many ligands (organic reagents) are used for the gravimetric estimation of number of metal ions.

   Metal ion to be estimated	Cu2+	Ni2+	Fe3+	Al3+	Co2+
   Organic reagents used	Benzoin oxime	Dimethyl glyoxime	1,20-phena-  nthroline	8-hydroxy quinoline	α-nitroso β-naphthol

5. Photography: hypo (sodium thiosulphate) dissolves unreacted AgBr as a soluble complex.
   AgBr + 2Na₂S₂O₃ Na₃[Ag(S₂O₃)₂ ] + NaBr
                                                (soluble) (soluble)
6. Electroplating: cyanide complexes provide stable metal complexes that release metal ions slowly for uniform deposition.
7. Biological systems: haemoglobin (Fe(II) complex) transports O_2, chlorophyll (Mg complex) is essential in photosynthesis, and vitamin B12 is a Co complex involved in enzyme chemistry.

Metallurgical process 

Silver and gold are extracted by the use of complex formation. Silver ore is treated with sodium cyanide solution with continuous passing of air through the solution. Silver dissolves as a cyanide complex and silver is precipitated by the addition of scrap zinc.

b) Native Gold and Silver also dissolve in NaCN solution in presence of the oxygen (air).

4 Ag + 8NaCN + O₂ + 2H₂O 3Na[Ag(CN)₂] + 3NaOH

Silver and Gold are precipitated by addition of scrap zinc. Nickel is extracted by converting it into a volatile complex, nickel carbonyl, by use of carbon monoxide (Mond's process). The complex decomposes on heating again into pure nickel and carbon monoxide.

Ni + 4CO Ni(CO)₄ Ni + 4 CO

Organometallic Compounds

Organometallic compounds contain a direct metal-carbon bond where carbon belongs to an organic group (often alkyl or aryl). Compounds of B, Si, P with organic groups are often included under organometallic chemistry. Many organometallics are valuable reagents in synthesis and catalysis.

Classification of Organometallic Compounds

Organometallics are commonly classified as:

• Sigma (σ)-bonded organometallics: metal-carbon bond is a σ bond. Examples: Grignard reagents R-Mg-X and R₂Zn such as (C₂H₅)₂Zn. (isolated by Frankland).. Many main-group organometallics (e.g., R4Sn, R4Pb) belong here. Other similar compounds are (CH₃)₄Sn, (C₂H₅)₄Pb, Al₂(CH₃)₆, Al₂(C₂H₅)₆, Pb(CH₃)₄ etc.
• Pi (π)-bonded organometallics: bonding involves π-electrons of alkenes, alkynes or aromatic rings donated to the metal. Examples: Zeise's salt K[PtCl₃(η²-C₂H₄)], ferrocene Fe(η⁵-C₅H₅)₂ and dibenzene chromium.
• Both σ and π bonded: metal carbonyls (M-CO) have σ donation from CO to metal and π back-donation from metal to CO π* orbitals, e.g., Ni(CO)4, Fe(CO)5. These often have metal in low/zero oxidation states and show characteristic bonding features.

Dimeric examples such as Al2(CH3)6 are electron deficient and show bridging methyl groups similar to diborane structures.

Notation: ηn indicates the hapticity - number of contiguous atoms of a ligand bonded to the metal (η², η⁵, η⁶ etc.).

In a metal carbonyl, the metal-carbon bond possesses both the s-and p-character. An s-bond between metal and the carbon atom is formed when a vacant hybrid orbital of the metal atom overlap with an orbital on a C atom of carbon monoxide containing a lone pair of electrons.

Formation of p-bond is caused when a filled orbital of the metal atom overlaps with a vacant antibonding p* orbital of C atom of carbon monoxide. This overlap is also called back donation of electrons by metal atom to carbon.

The p-overlap is perpendicular to the nodal plane of the s-bond.

In olefinic complexes, the bonding p-orbital electrons are donated to the empty orbital of the metal atom and at the same time to the back bonding p-orbital of the olefin.

Applications of Organometallic Compounds

1. Tetraethyl lead (TEL) was used historically as an anti-knock additive in petrol (note environmental concerns have led to phase-out).
2. Wilkinson's catalyst [Rh(PPh3)3Cl] is an important homogeneous catalyst for alkene hydrogenation.
3. The Mond process uses volatile Ni(CO)4 for nickel purification (formation/decomposition exploited industrially).
4. Ziegler-Natta catalysts (trialkylaluminium + TiCl4) are heterogeneous catalysts for polymerisation of ethylene and propylene to PE and PP.

Points to be remembered

• CH₃B(OCH₃) is an organometallic compound but B(OCH₃) is not.
• Closed ring complexes formed by polydentate ligands are called chelates; chelation increases stability (chelate effect).
• Estimation of nickel (II) is done by complexing with dimethyl glyoxime (DMG) whereas that of Ca ² and Mg²  ions is done by titrating against EDTA.
• Labile complexes are those in which ligands can be readily substituted; 
  [Cu(NH₃)₄]²⁺  + 4CN^- → [Cu(CN)₄]₂ + 4NH₃
  (less stable)                  (more stable)
• Octahedral complexes Ma₃b₃ show geometric isomerism: facial (fac) where three identical donor atoms occupy one face, and meridional (mer) where they lie around a meridian.
• Biological metal complexes: haemoglobin (Fe), chlorophyll (Mg), vitamin B12 (Co).
• σ-bonded organometallics typically involve main-group metals bound to carbon (e.g., R-MgX). π-bonded organometallics involve donation from π systems . For example Zeise's salt K[PtCl₃h² C₂H₄] and Ferrocene Fe(h⁵-C₅H₅)₂
• Grignard reagents (R-MgX) are highly polar and exceptionally useful in organic synthesis for forming C-C bonds. (C^d-Mg^d )