Valence Bond Theory, Hybridization & Molecular Orbital Theory | Chemistry Class 11 - NEET PDF Download

Valence Bond Theory

The valence bond (VB) theory was introduced by Heitler and London (1927) and developed further by Linus Pauling and others. VB theory explains covalent bond formation in terms of overlap of atomic orbitals and pairing of electrons with opposite spins. A discussion of VB theory requires prior knowledge of atomic orbitals, electronic configurations, overlap criteria, hybridisation and the principles of superposition and variation.

Formation of the H₂ molecule (illustrative example)

Consider two hydrogen atoms A and B with nuclei N_A, N_B and electrons e_A, e_B. When the atoms are far apart there is negligible interaction. As they approach, new attractive and repulsive interactions appear:

• Attractive interactions arise between N_A-e_A, N_B-e_B (intra-atomic) and between N_A-e_B, N_B-e_A (inter-atomic).
• Repulsive interactions arise between e_A-e_B (electron-electron) and N_A-N_B (nucleus-nucleus).
• Attractive forces tend to bring atoms together; repulsive forces push them apart. Experimentally the net effect is that attraction dominates at intermediate distances so the potential energy decreases and reaches a minimum at the equilibrium bond length.
• For H₂ the bond length is 74 pm, and the bond dissociation enthalpy is 435.8 kJ mol^-1. Thus

H₂(g) + 435.8 kJ mol^-1 → H(g) + H(g)

Forces of attraction and repulsion during the formation of H₂ molecule

Potential energy curve for the formation of H₂ molecule as a function of the internuclear distance of the H atoms

Overlapping of Atomic Orbitals

Orbital overlap concept

When two atoms come close enough for bonding, their atomic orbitals may overlap. Overlap allows electrons from different atoms to occupy a common region in space, pair with opposite spins and form a covalent bond. The extent and sign (phase) of overlap determine the bond strength and bonding/antibonding character.

Key points on orbital overlap

• Overlap may be positive, negative or zero depending on the relative phase of the orbital wave functions. The signs refer to the mathematical sign (phase) of the wavefunction, not electrical charge.
• Only overlapping orbitals having the same phase in the region of overlap give constructive interaction and lead to bond formation.
• Overlap is essential for covalent bonding in homonuclear and heteronuclear diatomic molecules as well as in polyatomic species.
• Simple overlap of unhybridised atomic orbitals cannot always explain molecular shapes and bond angles (for example, CH₄, NH₃, H₂O), which leads to the concept of hybridisation.

Positive, Negative, and Zero Overlap of Atomic Orbitals

Types of overlapping and nature of covalent bonds

Covalent bonds are classified according to how atomic orbitals overlap:

• Sigma (σ) bond: Formed by end-to-end (head-on) overlap of orbitals along the internuclear axis. Examples: s-s, s-p (end to end), p-p (end to end) overlaps produce σ bonds. σ bonds have cylindrical symmetry around the bond axis and usually display larger overlap (stronger).
• Pi (π) bond: Formed by side-by-side overlap of parallel p (or other) orbitals whose axes are parallel to each other but perpendicular to the internuclear axis. π bonds have lobes above and below the internuclear plane and involve less overlap (weaker) than σ bonds.

s-s Overlapping

s-p Overlapping

p-p Overlapping

Pi Bond

Relative strength of σ and π bonds

• Bond strength depends on the extent of overlap. Greater overlap gives stronger bonds.
• σ bonds generally have greater overlap and are stronger than π bonds formed between the same pair of atoms.
• Multiple bonds between atoms always include one σ bond and one or more π bonds (for example, a double bond = 1 σ + 1 π; a triple bond = 1 σ + 2 π).

Hybridisation

Definition

Hybridisation is the mixing of atomic orbitals of the same atom having comparable energies to form a new set of equivalent hybrid orbitals. These hybrid orbitals have identical energies and shapes suitable for the geometry adopted by the bonded atom.

Important points about hybridisation

• Only orbitals of comparable energy belonging to the same atom can hybridise.
• The number of hybrid orbitals formed equals the number of atomic orbitals mixed.
• Fully filled orbitals can also participate if their energies are close; it is not necessary that all participating orbitals be half-filled.
• Hybridisation occurs during bond formation; it is not a property of isolated atoms.
• The type of hybridisation determines the geometry of the molecule and approximate bond angles.
• Hybrid orbitals are directional; typically the larger lobe has the positive phase and points towards bonding partners.

Common types of hybridisation

• sp hybridisation: Mixing of one s and one p orbital gives two equivalent sp hybrid orbitals oriented linearly at 180°.
• sp² hybridisation: Mixing of one s and two p orbitals gives three equivalent sp² hybrids oriented in a trigonal planar arrangement at 120°; one unhybridised p orbital remains perpendicular to the plane.
• sp³ hybridisation: Mixing of one s and three p orbitals gives four equivalent sp³ hybrids oriented tetrahedrally with ideal bond angle 109.5° (109° 28′).

sp Hybridization

Studying formation of various molecules (using hybridisation and overlap)

• Methane, CH₄: Carbon is sp³ hybridised, forming four equivalent sp³ hybrid orbitals. Each C-H σ bond arises from overlap of a C-sp³ orbital with an H-1s orbital.
• Ethane, C₂H₆: Each carbon is sp³ hybridised. Six C-H σ bonds are formed by overlap of C-sp³ with H-1s. The C-C σ bond forms by overlap of two C-sp³ orbitals.
• Ammonia, NH₃: Nitrogen is approximately sp³ hybridised; three sp³ hybrids each overlap with H-1s to give three N-H σ bonds. One sp³ orbital contains a lone pair. The lone pair causes slight compression of the H-N-H angle from the ideal 109.5° to about 107°.
• Water, H₂O: Oxygen is sp³ hybridised with two lone pairs occupying two sp³ orbitals. The H-O-H bond angle is about 104.5° (often quoted as 105°), smaller than 109.5° due to lone pair-bond pair repulsion.
• Ethene, C₂H₄: Each carbon is sp² hybridised. The sp² orbitals form σ bonds (C-H and C-C σ), while the unhybridised p orbitals on each carbon overlap sideways to form a π bond, giving the C=C double bond.
• Acetylene, C₂H₂: Each carbon is sp hybridised. Two sp orbitals form σ bonds (one C-H and one C-C σ). The two remaining unhybridised p orbitals on each carbon form two π bonds (perpendicular to each other), giving the C≡C triple bond (one σ + two π).

Predicting hybridisation

To estimate the number of hybrid orbitals (X) formed by a central atom, the following empirical relation is often used (suitable for many covalent molecules):

X = 1/2 [VE + MA - c + a]

Where:

• VE = valence electrons on the central atom
• MA = number of monovalent atoms or groups bonded to the central atom (monovalent substituents counted as 1; for divalent groups MA = 0)
• c = positive charge on the species (if cation), or negative count if anion (sign convention as used in the source)
• a = negative charge on the species (if anion)
• If X = 2 → sp hybridisation
• If X = 3 → sp² hybridisation
• If X = 4 → sp³ hybridisation
• And so on (see commonly used correlation table).

Molecular Orbital Theory (MOT)

The Molecular Orbital Theory (MOT), developed by F. Hund and R. S. Mulliken, explains bonding by combining atomic orbitals from all atoms to produce molecular orbitals (MOs) that extend over the entire molecule. MOT can explain phenomena not handled well by simple VB theory, such as delocalised bonding, bond orders between integer values and magnetic properties (e.g., O₂ paramagnetism).

Key principles of MOT

• Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO).
• The number of molecular orbitals formed equals the number of atomic orbitals combined.
• Two types of molecular orbitals result from combination: bonding (lower in energy than parent AOs) and antibonding (higher in energy).
• Bonding MOs stabilise the molecule; antibonding MOs destabilise it.

Common MO combinations

Filling of molecular orbitals

• Electrons occupy MOs according to the Aufbau principle, Pauli exclusion principle and Hund's rule, filling lower energy MOs first and placing unpaired electrons, if any, singly into degenerate MOs before pairing.
• For diatomics formed from second-period elements the relative ordering of σ and π MOs depends on total electron count. A common convention:
  • For molecules with ≤ 14 electrons the π(2p) MOs lie below σ(2p) (the modified order).
  • For molecules with > 14 electrons the σ(2p) MO lies below the π(2p) MOs (simple order).

Bond order and magnetic properties

Bond order (B.O.) is a measure of the net bonding in a molecule and is given by:

B.O. = 1/2 (N_B - N_A)

Where N_B is the number of electrons in bonding MOs and N_A is the number in antibonding MOs.

• A stable molecule generally has N_B > N_A.
• If a molecule has unpaired electrons in molecular orbitals it is paramagnetic; if all electrons are paired it is diamagnetic.
• Higher bond order corresponds to shorter bond length and greater bond energy.

Examples (common diatomic oxygen species):

• O₂ (neutral): bond order = 2; paramagnetic (two unpaired electrons in π* orbitals).
• O₂^- (superoxide): bond order = 1.5.
• O₂^2- (peroxide): bond order = 1.

Conditions for atomic orbitals to form MOs

• Combining atomic orbitals should be of comparable energy.
• Atomic orbitals must have compatible symmetry and sufficient overlap; greater overlap produces more stabilising bonding MOs.

Relative energies of MOs

Energy level diagrams illustrate the relative energy positions of bonding, non-bonding and antibonding MOs. These diagrams are useful for assigning electrons, determining bond order and predicting magnetism.

M.O Energy level diagram for O₂, F₂ and Ne

M.O energy diagram for Li₂, Be₂, B₂, C₂ and N₂ molecule

Crystal Field Theory (CFT)

Crystal Field Theory is an electrostatic model developed to explain the electronic structure, colours and magnetic properties of coordination compounds. It corrects or supplements interpretations where basic VB theory for coordination complexes is insufficient.

Basic ideas of CFT

• Ligands are treated as point charges (for anionic ligands) or point dipoles (for neutral ligands such as NH₃, H₂O).
• In an isolated gaseous metal ion the five d orbitals are degenerate (same energy). In a complex the approach of ligands produces an asymmetric electrostatic field that removes this degeneracy and causes splitting of d orbital energies.
• The magnitude and pattern of splitting depend on the geometry of the complex (octahedral, tetrahedral, square planar, etc.) and the nature of ligands and metal ion.

Octahedral crystal field splitting

In an octahedral complex (six ligands along the Cartesian axes), d orbitals split into two sets:

• t_2g set: d_xy, d_yz, d_zx - lower in energy (point between ligand axes).
• e_g set: d_x²-y², d_z² - higher in energy (pointing towards ligands along axes).

The energy gap between these sets is called the crystal field splitting energy and is denoted by Δ_o (subscript o for octahedral). Electrons occupy these levels according to Hund's rule and the pairing energy; the relative sizes of Δ_o and the pairing energy determine whether a complex is high-spin or low-spin.

Factors influencing the magnitude of Δ_o (CFSE)

• Oxidation state of the metal: Higher oxidation states generally increase Δ_o (greater effective nuclear charge, stronger metal-ligand interaction).
• Identity and electronic configuration of the metal: For the same oxidation state different metals give different CFSE values; heavier congeners and those with larger principal quantum number n often give larger splitting.
• Nature of the ligand: Ligands that cause stronger field (e.g., CN^-, CO) increase Δ_o; weaker field ligands (e.g., I^-, Br^-) give smaller splitting.
• Geometry and coordination number: Octahedral, tetrahedral and square planar arrangements give different splitting patterns and magnitudes (tetrahedral splitting Δ_t is smaller and inverted relative to octahedral).
• Chelation and ligand charge distribution: Chelating ligands and ligands providing greater donor interaction often increase splitting.

Summary

Valence Bond Theory explains covalent bonding in terms of orbital overlap and electron pairing and introduces hybridisation to account for molecular geometry. Molecular Orbital Theory, using LCAO, provides a delocalised picture of bonding, explains bond orders that are fractional and correctly predicts magnetic behaviour (for example, O₂ paramagnetism). Crystal Field Theory applies to coordination compounds and explains splitting of d orbitals, magnetism and colour of complexes. Together these models give complementary insights important for understanding bonding, structure and properties of molecules and complexes.