Valence Bond Theory and Hybridisation

Valence Bond Theory

The Valence Bond Theory (VBT), proposed by Linus Pauling and others, is a model used to describe the formation of covalent bonds. It is based on the idea that a covalent bond is formed when two atomic orbitals, each containing an unpaired electron, overlap. The greater the extent of overlap, the stronger the bond.

VBT aims to explain the properties of molecules, such as bond length, bond strength, and molecular geometry, which are not always adequately explained by simpler models like Lewis structures alone.

Orbital Overlap Concept

The fundamental concept of Valence Bond Theory is that a chemical bond is formed by the overlap of atomic orbitals. For a stable covalent bond to form between two atoms:

Unpaired Electrons: Each atom must possess at least one unpaired electron in its valence shell.
Orbital Overlap: The atomic orbitals containing these unpaired electrons must overlap. Overlap means that the electron clouds of the two orbitals share a common region of space.
Energy Release: As the orbitals overlap, the electrons become attracted to both nuclei. This attraction leads to a decrease in potential energy, and the energy released during this process results in the formation of a stable bond. The extent of overlap is crucial for bond strength.
Pauli Exclusion Principle: The overlapping orbitals must contain electrons with opposite spins.

The region of overlap is where the shared electron pair resides, holding the two atoms together.

Directional Properties Of Bonds

Atomic orbitals have specific shapes and orientations in space (e.g., s orbitals are spherical, p orbitals are dumbbell-shaped and oriented along the x, y, and z axes). The directional properties of atomic orbitals are critical in VBT because they determine the directionality of the formed covalent bonds.

Bond Directionality: Covalent bonds are directional, meaning they are formed along specific directions in space. This directionality is dictated by the orientation of the overlapping atomic orbitals.
Molecular Shape: The directionality of covalent bonds is directly responsible for the specific shapes (geometries) of molecules. For example, the tetrahedral shape of methane ($$CH_4$$) arises from the overlapping of hydrogen 1s orbitals with the four sp³ hybrid orbitals of carbon, which are directed towards the corners of a tetrahedron.
Predicting Geometry: By understanding the overlap of hybridized atomic orbitals, VBT can predict the geometry of molecules, aligning with experimental observations and VSEPR theory.

Overlapping Of Atomic Orbitals

The formation of covalent bonds involves the overlap of atomic orbitals. The extent and type of overlap depend on the nature of the orbitals involved.

Sigma ($\sigma$) Bonds:
- Formed by the head-on or axial overlap of atomic orbitals.
- The overlap occurs along the internuclear axis.
- Electron density is concentrated along the internuclear axis.
- Types of overlap that form $\sigma$ bonds:
  - s-s overlap: Overlap between two spherical s orbitals. (e.g., in $$H_2$$)
  - s-p overlap: Overlap between an s orbital and a p orbital. (e.g., in HCl)
  - p-p overlap: Head-on overlap between two p orbitals along the internuclear axis. (e.g., in $$F_2$$)
  - Hybrid orbital overlap: Overlap between hybridized orbitals (e.g., sp³-sp³ overlap in $$C_2H_6$$).
- $\sigma$ bonds are generally stronger than $\pi$ bonds.
- Rotation around a $\sigma$ bond is generally free.
Pi ($\pi$) Bonds:
- Formed by the sideways or lateral overlap of atomic orbitals.
- The overlap occurs above and below the internuclear axis.
- Electron density is concentrated in two regions, one above and one below the internuclear axis.
- Types of overlap that form $\pi$ bonds:
  - p-p sideways overlap: Sideways overlap between two parallel p orbitals.
- $\pi$ bonds are generally weaker than $\sigma$ bonds because the sideways overlap is less effective than head-on overlap.
- Rotation around a $\pi$ bond is restricted, leading to geometric isomerism in molecules with double bonds.

In molecules with multiple bonds, there is always one $\sigma$ bond, and the remaining bonds are $\pi$ bonds. For example, a double bond consists of one $\sigma$ and one $\pi$ bond, while a triple bond consists of one $\sigma$ and two $\pi$ bonds.

Types Of Overlapping And Nature Of Covalent Bonds

The type of overlap between atomic orbitals dictates the nature of the covalent bond formed:

Sigma ($\sigma$) Overlap: This is a head-on overlap of atomic orbitals along the internuclear axis. All single covalent bonds are $\sigma$ bonds. $\sigma$ bonds allow for free rotation around the bond axis because the electron density is concentrated symmetrically along the axis.
Pi ($\pi$) Overlap: This is a sideways overlap of atomic orbitals occurring above and below the internuclear axis. $\pi$ bonds are formed in addition to $\sigma$ bonds in double and triple bonds. The presence of a $\pi$ bond restricts rotation around the bond axis.

Nature of Covalent Bonds:

Single Bond: Consists of one $\sigma$ bond.
Double Bond: Consists of one $\sigma$ bond and one $\pi$ bond.
Triple Bond: Consists of one $\sigma$ bond and two $\pi$ bonds.

The combination of $\sigma$ and $\pi$ bonding determines the overall shape and chemical properties of a molecule.

Strength Of Sigma And Pi Bonds

The strength of a covalent bond is related to the effectiveness of the overlap between atomic orbitals.

Sigma ($\sigma$) Bonds:
- Formed by head-on overlap, which is generally more extensive and effective than sideways overlap.
- Therefore, $\sigma$ bonds are typically stronger than $\pi$ bonds.
- The electron density in a $\sigma$ bond is concentrated along the internuclear axis, leading to a strong attraction between the nuclei.
Pi ($\pi$) Bonds:
- Formed by sideways overlap, which is less effective than head-on overlap.
- Therefore, $\pi$ bonds are generally weaker than $\sigma$ bonds.
- The electron density in a $\pi$ bond is distributed above and below the internuclear axis, leading to weaker attraction compared to $\sigma$ bonds.

Implications:

In a double bond (one $\sigma$, one $\pi$), the presence of the $\pi$ bond makes the total bond stronger and shorter than a single ($\sigma$) bond, but the $\pi$ bond itself is the weaker component.
Similarly, in a triple bond (one $\sigma$, two $\pi$), the addition of $\pi$ bonds increases bond strength and decreases bond length compared to a single bond, but the $\pi$ bonds are weaker than the $\sigma$ bond.
The relative weakness of $\pi$ bonds makes them more susceptible to chemical reactions like addition reactions.

Valence Bond Theory, particularly when incorporating the concept of hybridization, provides a robust explanation for the observed geometries and bonding characteristics of molecules.

Hybridisation

Hybridisation is a concept introduced in Valence Bond Theory to explain the observed molecular geometries and equivalent bond lengths/angles that cannot be explained by the simple overlap of pure atomic orbitals. It is the process of mixing or blending atomic orbitals of slightly different energies (from the same atom) to form new, degenerate (equal energy) hybrid orbitals.

Why is Hybridisation Necessary?

Explaining Molecular Shapes: The shapes of molecules are often different from what would be predicted by the overlap of pure atomic orbitals. For example, if we consider carbon's atomic orbitals ($2s^2 2p^2$), it has only two unpaired electrons in the 2p orbitals, suggesting it should form only two bonds. However, carbon forms four equivalent bonds in methane ($CH_4$).
Equivalent Bonds: In molecules like $$CH_4$$, all four C-H bonds are identical in length and strength, and all H-C-H bond angles are 109.5°. This equivalence cannot be explained by the overlap of one 2s orbital and three different 2p orbitals with hydrogen's 1s orbital, as the p orbitals are at right angles to each other and the s orbital is spherical.
Valence Bond Theory's Solution: Hybridisation proposes that atomic orbitals of an atom mix to form new hybrid orbitals that have the correct orientation and number to account for the observed geometry and bonding. The number of hybrid orbitals formed is equal to the number of atomic orbitals that were mixed.

Key Features of Hybridisation:

Atomic orbitals mix to form hybrid orbitals of equivalent energy and shape.
The number of hybrid orbitals formed is equal to the number of atomic orbitals mixed.
The hybrid orbitals are oriented in space in a way that minimizes electron-pair repulsion, leading to specific molecular geometries (as described by VSEPR theory).
Hybrid orbitals have better overlap ability than pure atomic orbitals, leading to stronger bonds.

Types Of Hybridisation

The type of hybridisation depends on the number of atomic orbitals (s, p, and sometimes d) that are mixed.

1. sp Hybridisation:

Mixing: One s orbital and one p orbital are mixed.
Formation: Two sp hybrid orbitals are formed.
Geometry: The two sp hybrid orbitals are oriented linearly, with an angle of 180° between them. This results in a linear electron domain geometry.
Remaining Orbitals: Two unhybridized p orbitals remain, oriented perpendicular to each other and to the axis of the sp orbitals. These p orbitals are available for forming $\pi$ bonds.
Bonding: Typically involved in forming molecules with a triple bond (one $\sigma$ + two $\pi$) or two double bonds (two $\sigma$ + two $\pi$, as in $$CO_2$$ where C is sp hybridized).
Example: Ethyne ($$C_2H_2$$). Each carbon atom is sp hybridized. The sp orbitals form a C-C $\sigma$ bond and two C-H $\sigma$ bonds. The two remaining p orbitals on each carbon overlap sideways to form two C≡C $\pi$ bonds.

Orbital overlap diagram for ethyne (acetylene) showing sp hybridization.

2. sp² Hybridisation:

Mixing: One s orbital and two p orbitals are mixed.
Formation: Three sp² hybrid orbitals are formed.
Geometry: The three sp² hybrid orbitals lie in a plane, pointing towards the corners of an equilateral triangle, with angles of 120° between them. This results in a trigonal planar electron domain geometry.
Remaining Orbitals: One unhybridized p orbital remains, oriented perpendicular to the plane of the sp² orbitals. This p orbital is available for forming one $\pi$ bond.
Bonding: Typically involved in forming molecules with a double bond (one $\sigma$ + one $\pi$).
Example: Ethene ($$C_2H_4$$). Each carbon atom is sp² hybridized. The sp² orbitals form C-C $\sigma$ bond and two C-H $\sigma$ bonds. The unhybridized p orbitals on each carbon overlap sideways to form a C=C $\pi$ bond.

Orbital overlap diagram for ethene showing sp2 hybridization.

3. sp³ Hybridisation:

Mixing: One s orbital and three p orbitals are mixed.
Formation: Four sp³ hybrid orbitals are formed.
Geometry: The four sp³ hybrid orbitals are directed towards the corners of a tetrahedron, with angles of approximately 109.5° between them. This results in a tetrahedral electron domain geometry.
Remaining Orbitals: No unhybridized p orbitals remain.
Bonding: Typically involved in forming molecules with only single bonds (all $\sigma$ bonds).
Example: Methane ($$CH_4$$). The carbon atom is sp³ hybridized. Each of the four sp³ hybrid orbitals overlaps with the 1s orbital of a hydrogen atom to form four equivalent C-H $\sigma$ bonds.

Orbital overlap diagram for methane showing sp3 hybridization.

Other Examples Of Sp3, Sp2 And Sp Hybridisation

Let's look at more examples to solidify the understanding of different hybridisation types.

sp³ Hybridisation Examples:

Ammonia ($$NH_3$$): Nitrogen is sp³ hybridized. It has 3 bonding pairs (N-H) and 1 lone pair. The electron domain geometry is tetrahedral, but the molecular geometry is trigonal pyramidal. The H-N-H bond angle is about 107° due to lone pair repulsion.
Water ($$H_2O$$): Oxygen is sp³ hybridized. It has 2 bonding pairs (O-H) and 2 lone pairs. The electron domain geometry is tetrahedral, but the molecular geometry is bent or V-shaped. The H-O-H bond angle is about 104.5° due to greater lone pair repulsion.

sp² Hybridisation Examples:

Boron trifluoride ($$BF_3$$): Boron is sp² hybridized. It has 3 bonding pairs (B-F) and no lone pairs. The electron domain geometry and molecular geometry are both trigonal planar, with F-B-F bond angles of 120°.
Carbon dioxide ($$CO_2$$): Carbon is sp hybridized (as mentioned before), forming two double bonds (C=O). Each double bond counts as one electron domain, leading to a linear geometry.
Formaldehyde ($CH_2O$$): The carbon atom is sp² hybridized, forming a double bond with oxygen (C=O) and single bonds with two hydrogen atoms (C-H). The electron domain geometry and molecular geometry are trigonal planar, with H-C-H and H-C=O bond angles close to 120°.

sp Hybridisation Examples:

Beryllium chloride ($$BeCl_2$$): Beryllium is sp hybridized. It forms two Be-Cl single bonds. The electron domain geometry and molecular geometry are both linear, with Cl-Be-Cl bond angles of 180°.
Carbon dioxide ($$CO_2$$): As mentioned, the central carbon atom is sp hybridized, forming two double bonds. The molecule is linear with O=C=O bond angles of 180°.

Hybridisation Of Elements Involving D Orbitals

Elements in the third period and beyond (like Phosphorus, Sulfur, Chlorine, etc.) can utilize their empty d orbitals in addition to s and p orbitals for hybridisation, leading to expanded octets and different geometries.

1. sp³d Hybridisation:

Mixing: One s orbital, three p orbitals, and one d orbital are mixed.
Formation: Five sp³d hybrid orbitals are formed.
Geometry: These five orbitals are oriented towards the corners of a trigonal bipyramid.
Bond Angles: Three orbitals lie in the equatorial plane (forming angles of 120°), and two orbitals lie along the axial positions (forming angles of 90° with the equatorial plane and 180° with each other).
Examples:

Phosphorus pentachloride ($$PCl_5$$): Phosphorus is sp³d hybridized. It forms 3 equatorial P-Cl bonds and 2 axial P-Cl bonds. The molecular geometry is trigonal bipyramidal.
Sulfur tetrafluoride ($$SF_4$$): Sulfur is sp³d hybridized. It has 4 bonding pairs (S-F) and 1 lone pair. The lone pair occupies an equatorial position to minimize repulsion. The molecular geometry is see-saw.
Chlorine trifluoride ($$ClF_3$$): Chlorine is sp³d hybridized. It has 3 bonding pairs (Cl-F) and 2 lone pairs. The two lone pairs occupy equatorial positions. The molecular geometry is T-shaped.
Xenon difluoride ($$XeF_2$$): Xenon is sp³d hybridized. It has 2 bonding pairs (Xe-F) and 3 lone pairs. The three lone pairs occupy equatorial positions. The molecular geometry is linear.

2. sp³d² Hybridisation:

Mixing: One s orbital, three p orbitals, and two d orbitals are mixed.
Formation: Six sp³d² hybrid orbitals are formed.
Geometry: These six orbitals are directed towards the corners of an octahedron, with all bond angles being 90° or 180°.
Examples:

Sulfur hexafluoride ($$SF_6$$): Sulfur is sp³d² hybridized. It forms six S-F bonds. The molecular geometry is octahedral.
Iodine pentafluoride ($$IF_5$$): Iodine is sp³d² hybridized. It has 5 bonding pairs (I-F) and 1 lone pair. The lone pair occupies one of the axial positions. The molecular geometry is square pyramidal.
Xenon tetrafluoride ($$XeF_4$$): Xenon is sp³d² hybridized. It has 4 bonding pairs (Xe-F) and 2 lone pairs. The two lone pairs occupy opposite axial positions. The molecular geometry is square planar.

Hybridisation is a powerful model that successfully explains the observed geometries of many molecules by considering the mixing of atomic orbitals to form new hybrid orbitals that are suitably oriented for maximum overlap and minimum repulsion.