Comprehensive Chemical Bonding Notes: Valence Bond Theory, VSEPR, Hybridisation, MOT, and Hydrogen Bonding

Limitations of the Lewis Approach

• Bond Enthalpies and Bond Lengths: The Lewis approach does not provide any explanation for the difference in bond dissociation enthalpies and bond lengths in molecules like $H_2$ and $F_2$, despite a single covalent bond being formed in both cases by the sharing of an electron pair between the respective atoms.
• Polyatomic Shapes: It fails to give any idea regarding the geometric shapes of polyatomic molecules.

Valence Bond Theory (VBT)

• Origin: The theory was introduced by Walter Heitler and Fritz London, and further developed by Linus Pauling and others.
• Fundamental Cause of Bonding: According to VBT, the primary cause for chemical bonding is for atoms to acquire minimum energy and maximum stability.
• Mechanism of Molecule Formation (Example: $H_2$ Molecule):
  • Consider two hydrogen atoms $A$ and $B$ approaching each other. When the two atoms are at a large distance, there is no interaction between them.
  • As the two atoms approach each other, new attractive and repulsive forces begin to operate.
  • Attractive Forces arise between:
    • The nucleus of one atom and its own electron.
    • The nucleus of one atom and the electron of the other atom.
  • Repulsive Forces arise between:
    • The electrons of the two atoms.
    • The nuclei of the two atoms.
  • Energy and Stability Balance: Experimentally, the magnitude of the new attractive forces is found to be greater than the new repulsive forces. Consequently, as the two atoms approach each other, net potential energy decreases.
  • Equilibrium Distance: A stage is reached where the net force of attraction balances the force of repulsion, resulting in minimum potential energy. At this stage, the two hydrogen atoms form a stable molecule with a bond length of $74\,\text{pm}$.
  • Bond Enthalpy: The energy released during bond formation is called bond enthalpy or bond energy. The bond enthalpy for the $H_2$ molecule is $-435.8\,\text{kJ\,mol}^{-1}$.

Orbital Overlap Concept

• Lowering of Energy: According to VBT, lowering of energy takes place when the atomic orbitals of approaching atoms partially interpenetrate each other.
• Definition: The partial merging of atomic orbitals is called the overlapping of atomic orbitals, which results in the pairing of electrons.
• Mechanism: The formation of a covalent bond between two atoms occurs via the pairing of valence-shell electrons having opposite spins.
• Bond Strength: The extent of overlap decides the strength of a covalent bond. In general, greater orbital overlap produces a stronger chemical bond between two atoms.

Types of Overlapping and Nature of Covalent Bonds

Covalent bonds are classified into two main types depending on the mode of orbital overlapping:

• Axial / Head-On Overlapping ($\sigma$ Bond):
  • Formed by the end-to-end (head-on) overlap of bonding orbitals along the internuclear axis.
  • $s-s$ Overlapping: Overlap of two half-filled $s$-orbitals along the internuclear axis.
  • $s-p$ Overlapping: Overlap between a half-filled $s$-orbital of one atom and a half-filled $p$-orbital of another atom along the internuclear axis.
  • $p-p$ Overlapping: Overlap between half-filled $p$-orbitals of two approaching atoms along the internuclear axis.
• Sideways / Lateral Overlapping ($\pi$ Bond):
  • Formed when atomic orbitals overlap such that their axes remain parallel to each other and perpendicular to the internuclear axis.

Comparison Between Sigma ($\sigma$) and Pi ($\pi$) Bonds

• Strength Difference: Bond strength depends directly on the extent of overlapping. In a $\sigma$ bond, orbital overlap occurs to a larger extent, making it stronger than a $\pi$ bond, where overlap occurs to a smaller extent.

• Multiple Bonds: In the formation of multiple bonds between two atoms, $\pi$ bond(s) are always formed in addition to a primary $\sigma$ bond.

• Key Differences:

  1. Overlapping Mode: $\sigma$ bonds are formed by axial (head-on) overlapping; $\pi$ bonds are formed by sideways (lateral) overlapping.
  2. Extent of Overlap: Extent of overlap is greater in $\sigma$ bonds; extent of overlap is lesser in $\pi$ bonds.
  3. Bond Strength: $\sigma$ bonds are strong; $\pi$ bonds are weak.
  4. Participating Orbitals: $\sigma$ bonds involve $s-s$, $s-p$, or $p-p$ axial overlapping; $\pi$ bonds involve lateral $p-p$ overlapping.
  5. Existence: A $\sigma$ bond can exist independently or alongside $\pi$ bonds; a $\pi$ bond can exist only in combination with a $\sigma$ bond.

Valence Shell Electron Pair Repulsion (VSEPR) Theory

• Basis: Predicts molecular shapes based on repulsion interactions among electron pairs in the valence shell of central atoms.

• Postulates:

  1. The shape of a molecule depends on the total number of valence shell electron pairs (bonding and non-bonding/lone pairs) around the central atom.
  2. Electron pairs in the valence shell repel one another because their electron clouds are negatively charged.
  3. Valence electron pairs occupy positions in space that minimize repulsion and maximize inter-pair distance, achieving maximum stability.
  4. Repulsive interactions differ depending on electron pair types. Repulsion decreases in the order:        $\text{lone pair - lone pair} > \text{lone pair - bond pair} > \text{bond pair - bond pair}$
  5. Repulsive forces decrease sharply as the bond angle increases (maximum repulsion at $90^\circ$, minimum repulsion at $180^\circ$).
  6. Multiple bonds are treated as if they were a single electron pair (or a single super pair).

• Geometries of Molecules with No Lone Pairs (Regular Geometries):

  • $AB_2$: 2 electron pairs; Linear arrangement; Bond angle $180^\circ$; Shape: Linear (Examples: $BeCl_2$, $HgCl_2$).
  • $AB_3$: 3 electron pairs; Trigonal planar arrangement; Bond angle $120^\circ$; Shape: Trigonal planar (Examples: $BF_3$, $BCl_3$).
  • $AB_4$: 4 electron pairs; Tetrahedral arrangement; Bond angle $109.5^\circ$; Shape: Tetrahedral (Examples: $CH_4$, $NH_4^+$).
  • $AB_5$: 5 electron pairs; Trigonal bipyramidal arrangement; Shape: Trigonal bipyramidal (Example: $PCl_5$).
  • $AB_6$: 6 electron pairs; Octahedral arrangement; Shape: Octahedral (Example: $SF_6$).

Shapes of Polyatomic Molecules with Lone Pairs

When non-bonding lone pairs ($E$) are present on the central atom, repulsions cause molecular geometry distortions:

• $AB_2E$ Type (2 Bonding Pairs, 1 Lone Pair):
  • Arrangement: Trigonal planar.
  • Shape: Bent / V-shaped (Examples: $SO_2$, $O_3$).
  • Explanation: Repulsion between the lone pair and bond pairs is greater than between bond pairs, reducing the bond angle from $120^\circ$ to $119.5^\circ$.
• $AB_3E$ Type (3 Bonding Pairs, 1 Lone Pair):
  • Arrangement: Tetrahedral.
  • Shape: Trigonal pyramidal (Examples: $NH_3$, $PCl_3$, $NF_3$, $H_3O^+$).
  • Explanation: With a lone pair present, greater lone pair - bond pair repulsion compresses the bond angle from the ideal tetrahedral angle of $109.5^\circ$ ($109^\circ 28'$) down to $107^\circ$.
• $AB_2E_2$ Type (2 Bonding Pairs, 2 Lone Pairs):
  • Arrangement: Tetrahedral.
  • Shape: Bent / Angular (Example: $H_2O$).
  • Explanation: Presence of two lone pairs causes strong lone pair - lone pair repulsion (which exceeds lone pair - bond pair and bond pair - bond pair repulsions), reducing the bond angle from $109.5^\circ$ to $104.5^\circ$.
• $AB_4E$ Type (4 Bonding Pairs, 1 Lone Pair):
  • Arrangement: Trigonal bipyramidal.
  • Shape: See-saw / Distorted tetrahedron (Example: $SF_4$).
  • Explanation: The lone pair occupies an equatorial position to minimize repulsions. In an equatorial position, it experiences only two $90^\circ$ lone pair - bond pair repulsions, compared to three if placed axially.
• $AB_3E_2$ Type (3 Bonding Pairs, 2 Lone Pairs):
  • Arrangement: Trigonal bipyramidal.
  • Shape: T-shaped (Example: $ClF_3$).
  • Explanation: Both lone pairs reside in equatorial positions to minimize lone pair - bond pair repulsions, making the T-shaped structure the most stable arrangement.

Concept and Salient Features of Hybridisation

• Definition: Hybridisation is the process of mixing atomic orbitals of slightly different energies in the valence shell of an atom to produce an equal number of new orbitals having identical energy, shape, and properties.
• Salient Features:
  1. The number of hybrid orbitals formed equals the number of atomic orbitals that undergo hybridisation.
  2. Hybrid orbitals are equivalent in energy and shape.
  3. Hybrid orbitals form more stable and effective covalent bonds than pure atomic orbitals.
  4. Hybrid orbitals are oriented in specific spatial directions to minimize electron pair repulsions and maximize stability.
  5. The type of hybridisation directly determines the geometric shape of the molecule.
• Conditions for Hybridisation:
  1. Only orbitals present in the valence shell undergo hybridisation.
  2. Orbitals undergoing hybridisation must have almost equal energy.
  3. Promotion of an electron prior to hybridisation is not an essential requirement.
  4. It is not necessary for only half-filled orbitals to participate; completely filled or empty valence orbitals can also undergo hybridisation.

Types of Hybridisation and Examples

• Overview of Hybridisation Types and Geometries:

  • $sp$: Linear ($180^\circ$)
  • $sp^2$: Trigonal planar ($120^\circ$)
  • $sp^3$: Tetrahedral ($109.5^\circ$)
  • $dsp^2$: Square planar
  • $sp^3d$ / $dsp^3$: Trigonal bipyramidal
  • $sp^3d^2$ / $d^2sp^3$: Octahedral
  • $sp^3d^3$: Pentagonal bipyramidal

• $sp$ Hybridisation:

  • Description: Involves the mixing of one $s$-orbital and one $p$-orbital of the valence shell to form two equivalent $sp$ hybrid orbitals. Each $sp$ hybrid orbital possesses $50\%$ $s$-character and $50\%$ $p$-character.
  • Example 1: Beryllium Chloride ($BeCl_2$):
    • Ground state configuration of Beryllium: $1s^2 2s^2$.
    • Excited state configuration of Beryllium: $1s^2 2s^1 2p_x^1$.
    • The $2s$ and $2p_x$ orbitals hybridise into two $sp$ orbitals directed at $180^\circ$. Each $sp$ orbital overlaps axially with a $3p$ orbital of Chlorine to form two $\sigma$ $Be-Cl$ bonds, resulting in linear geometry.
  • Example 2: Ethyne ($C_2H_2$):
    • Both Carbon atoms undergo $sp$ hybridisation, leaving two unhybridised $p$-orbitals ($2p_y, 2p_z$) on each Carbon.
    • One $sp$ orbital on each Carbon overlaps axially to form a $C-C$ $\sigma$ bond. The second $sp$ orbital on each Carbon overlaps axially with an $H$ $1s$ orbital to form two $C-H$ $\sigma$ bonds.
    • The two unhybridised $p$-orbitals on each Carbon overlap sideways to form two $C-C$ $\pi$ bonds. The triple bond thus consists of one $\sigma$ bond and two $\pi$ bonds.

• $sp^2$ Hybridisation:

  • Description: Mixing of one $s$-orbital and two $p$-orbitals of the valence shell to form three equivalent $sp^2$ hybrid orbitals ($33.3\%$ $s$-character, $66.7\%$ $p$-character).
  • Example 1: Boron Trichloride ($BCl_3$):
    • Ground state configuration of Boron: $1s^2 2s^2 2p_x^1$.
    • Excited state configuration of Boron: $1s^2 2s^1 2p_x^1 2p_y^1$.
    • The $2s$, $2p_x$, and $2p_y$ orbitals hybridise to form three $sp^2$ orbitals in a trigonal planar arrangement with a bond angle of $120^\circ$. These overlap with Chlorine $3p$ orbitals to form three $B-Cl$ $\sigma$ bonds.
  • Example 2: Ethene ($C_2H_4$):
    • Both Carbon atoms are $sp^2$ hybridised.
    • Axial overlap of one $sp^2$ orbital from each Carbon forms a $C-C$ $\sigma$ bond. The remaining two $sp^2$ orbitals on each Carbon overlap with Hydrogen $1s$ orbitals to form four $C-H$ $\sigma$ bonds.
    • Unhybridised $2p_z$ orbitals on each Carbon overlap sideways to form one $C-C$ $\pi$ bond.
    • Bond angles: $\angle HCH = 117.6^\circ$, $\angle HCC = 121^\circ$.

• $sp^3$ Hybridisation:

  • Description: Mixing of one $s$-orbital and three $p$-orbitals of the valence shell to form four equivalent $sp^3$ hybrid orbitals ($25\%$ $s$-character, $75\%$ $p$-character).
  • Example 1: Methane ($CH_4$):
    • Ground state configuration of Carbon: $1s^2 2s^2 2p_x^1 2p_y^1$.
    • Excited state configuration of Carbon: $1s^2 2s^1 2p_x^1 2p_y^1 2p_z^1$.
    • The $2s$ and three $2p$ orbitals form four $sp^3$ hybrid orbitals directed towards the corners of a regular tetrahedron with bond angles of $109.5^\circ$.
    • Each $sp^3$ orbital overlaps axially with a Hydrogen $1s$ orbital to form four $C-H$ $\sigma$ bonds.

*   **Example 2: Ethane ($C_2H_6$):**
    *   Both Carbon atoms are $sp^3$ hybridised. Axial overlap between one $sp^3$ orbital from each Carbon forms a $C-C$ $\sigma$ bond. The other three $sp^3$ orbitals on each Carbon form $C-H$ $\sigma$ bonds with Hydrogen $1s$ orbitals.
*   **Example 3: Ammonia ($NH_3$):**
    *   Electronic configuration of Nitrogen ($Z=7$): $1s^2 2s^2 2p_x^1 2p_y^1 2p_z^1$.
    *   The $2s$ and three $2p$ orbitals hybridise into four $sp^3$ orbitals directed towards tetrahedral corners.
    *   Three $sp^3$ orbitals hold single electrons and overlap with Hydrogen $1s$ orbitals to form three $N-H$ $\sigma$ bonds; the fourth $sp^3$ orbital holds a non-bonding lone pair.
    *   Lone pair - bond pair repulsion reduces the ideal tetrahedral bond angle from $109.5^\circ$ ($109^\circ 28'$) to $107^\circ$, producing a trigonal pyramidal shape.
*   **Example 4: Water ($H_2O$):**
    *   Electronic configuration of Oxygen ($Z=8$): $1s^2 2s^2 2p_x^2 2p_y^1 2p_z^1$.
    *   The $2s$ and three $2p$ orbitals undergo $sp^3$ hybridisation to form four $sp^3$ orbitals.
    *   Two $sp^3$ orbitals contain single electrons and form $O-H$ $\sigma$ bonds; two $sp^3$ orbitals contain lone pairs.
    *   Strong lone pair - lone pair repulsion distorts the tetrahedral shape, reducing the $H-O-H$ bond angle to $104.5^\circ$ with a bent geometry.

• $sp^3d$ Hybridisation:

  • Example: Phosphorus Pentachloride ($PCl_5$):
    • Outer valence configuration of Phosphorus ($Z=15$):
      • Ground state: $3s^2 3p_x^1 3p_y^1 3p_z^1 3d^0$
      • Excited state: $3s^1 3p_x^1 3p_y^1 3p_z^1 3d^1$
    • One $3s$, three $3p$, and one $3d$ orbital hybridise to form five $sp^3d$ hybrid orbitals oriented towards the corners of a trigonal bipyramid.
    • Bond Types:
      • Equatorial Bonds: Three $P-Cl$ bonds lie in one plane at $120^\circ$ angles to one another.
      • Axial Bonds: Two $P-Cl$ bonds lie above and below the equatorial plane at $90^\circ$ angles.
    • Reactivity: Axial bond pairs experience greater repulsive interaction from equatorial bond pairs. Consequently, axial bonds are slightly longer and weaker than equatorial bonds, making $PCl_5$ highly reactive.

• $sp^3d^2$ Hybridisation:

  • Example: Sulfur Hexafluoride ($SF_6$):
    • Outer valence configuration of Sulfur ($Z=16$):
      • Ground state: $3s^2 3p^4 3d^0$
      • Excited state: $3s^1 3p^3 3d^2$
    • One $3s$, three $3p$, and two $3d$ orbitals hybridise to give six $sp^3d^2$ hybrid orbitals directed towards the corners of a regular octahedron.
    • These overlap with single occupied Fluorine $2p$ orbitals to form six $S-F$ bonds, giving $SF_6$ an octahedral geometry with $90^\circ$ bond angles.

Molecular Orbital Theory (MOT)

• Salient Features (Postulates):

  1. Molecular orbitals are formed by the Linear Combination of Atomic Orbitals (LCAO).
  2. A molecular orbital represents a region in space where the probability of finding electrons is maximum in a molecule.
  3. Combination of two atomic orbitals yields two molecular orbitals: a Bonding Molecular Orbital (BMO) and an Antibonding Molecular Orbital (ABMO).
  4. A bonding molecular orbital has lower energy and higher stability than combining atomic orbitals; an antibonding molecular orbital has higher energy and lower stability.
  5. Molecular orbitals are polycentric (electrons move under the influence of all nuclei in the molecule), whereas atomic orbitals are monocentric.
  6. Shapes of molecular orbitals depend on the shapes of the combining atomic orbitals.
  7. Only atomic orbitals possessing similar energy and proper symmetry/orientation combine to form molecular orbitals.
  8. Each molecular orbital can accommodate a maximum of two electrons with opposite spins.
  9. Electron filling in molecular orbitals follows the Aufbau principle, Pauli exclusion principle, and Hund's rule of maximum multiplicity.

• Linear Combination of Atomic Orbitals (LCAO) Principle:

  • Consider two hydrogen atoms $A$ and $B$ with atomic orbitals represented by wavefunctions $\psi_A$ and $\psi_B$.
  • Symmetric Combination (Bonding Molecular Orbital - BMO):
    • Wavefunctions add constructively: $\psi_{AB} = \psi_A + \psi_B$.
    • Probability density: $\psi_{AB}^2 = \psi_A^2 + \psi_B^2 + 2\psi_A\psi_B$.
    • Electron density between nuclei increases. Energy is lower than that of the isolated atomic orbitals, favoring bond formation ($\sigma 1s$).
  • Asymmetric Combination (Antibonding Molecular Orbital - ABMO):
    • Wavefunctions subtract destructively: $\psi_{AB}^* = \psi_A - \psi_B$.
    • Probability density: $(\psi_{AB}^*)^2 = \psi_A^2 + \psi_B^2 - 2\psi_A\psi_B$.
    • Electron density between nuclei decreases (creates a nodal plane). Energy is higher than atomic orbitals, disfavoring bond formation ($\sigma^* 1s$).

• Comparison Between BMO and ABMO:

  • 1. BMO is formed by symmetric combination ($\psi_A + \psi_B$); ABMO is formed by asymmetric combination ($\psi_A - \psi_B$).
  • 2. BMO has higher electron density between nuclei; ABMO has lower electron density between nuclei.
  • 3. BMO has lower energy than combining atomic orbitals; ABMO has higher energy than combining atomic orbitals.
  • 4. BMO favors bond formation; ABMO disfavors bond formation.

• Conditions for the Combination of Atomic Orbitals:

  1. Similar Energy: Combining atomic orbitals must have the same or nearly the same energy (e.g., $1s$ can combine with $1s$, but not with $2s$).
  2. Same Symmetry: Combining atomic orbitals must have the same symmetry about the molecular axis (by convention, the $z$-axis is taken as the molecular axis; e.g., $2p_z$ combines with $2p_z$, but not with $2p_x$ or $2p_y$).
  3. Maximum Overlap: Combining atomic orbitals must overlap to the maximum possible extent.

• Types of Molecular Orbitals:

  • Sigma ($\sigma$) Molecular Orbitals: Cylindrically symmetrical around the bond axis; formed by axial overlap ($\sigma 1s, \sigma^* 1s, \sigma 2s, \sigma^* 2s, \sigma 2p_z, \sigma^* 2p_z$).
  • Pi ($\pi$) Molecular Orbitals: Not symmetrical around the bond axis; formed by sideways overlap ($\pi 2p_x, \pi 2p_y, \pi^* 2p_x, \pi^* 2p_y$).

Electronic Configuration and Properties of Diatomic Molecules

• Energy Level Sequences of Molecular Orbitals:

  • For molecules with total electrons > 14 (e.g., $O_2$, $F_2$, $Ne_2$; atomic number $Z > 7$):$\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \sigma 2p_z < (\pi 2p_x = \pi 2p_y) < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$
  • For molecules with total electrons $\le 14$ (e.g., $Li_2$, $Be_2$, $B_2$, $C_2$, $N_2$; atomic number $Z \le 7$):$\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < (\pi 2p_x = \pi 2p_y) < \sigma 2p_z < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$(Note: In lighter molecules, $\sigma 2p_z$ lies higher in energy than $\pi 2p_x$ and $\pi 2p_y$).

• Molecular Parameters Derived from Molecular Electronic Configuration:

  • Bond Order ($B.O.$): Defined as half the difference between the number of electrons in bonding orbitals ($N_b$) and antibonding orbitals ($N_a$):         $\text{Bond Order (B.O.)} = \frac{1}{2} (N_b - N_a)$
  • Molecular Stability:
    • If $N_b > N_a$ ($B.O. > 0$), the molecule/ion is stable.
    • If $N_b \le N_a$ ($B.O. \le 0$), the molecule/ion is unstable and does not exist.
  • Nature of Bonds: Bond orders of 1, 2, and 3 indicate single, double, or triple covalent bonds between atoms.
  • Bond Length: Bond order is inversely proportional to bond length. Greater bond order corresponds to shorter bond length.
  • Magnetic Nature:
    • Diamagnetic: All electrons in molecular orbitals are paired.
    • Paramagnetic: One or more unpaired electrons exist in molecular orbitals.

• Bonding in Specific Homonuclear Diatomic Molecules:

  • Hydrogen Molecule ($H_2$):
    • Total electrons = 2.
    • Configuration: $(\sigma 1s)^2$
    • $\text{Bond Order} = \frac{2 - 0}{2} = 1$
    • Stable single covalent bond ($H-H$); diamagnetic.
  • Helium Molecule ($He_2$):
    • Total electrons = 4.
    • Configuration: $(\sigma 1s)^2 (\sigma^* 1s)^2$
    • $\text{Bond Order} = \frac{2 - 2}{2} = 0$
    • Unstable; $He_2$ does not exist.
  • Beryllium Molecule ($Be_2$):
    • Total electrons = 8.
    • Configuration: $(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 (\sigma^* 2s)^2$
    • $\text{Bond Order} = \frac{4 - 4}{2} = 0$
    • Unstable; $Be_2$ does not exist.
  • Lithium Molecule ($Li_2$):
    • Total electrons = 6.
    • Configuration: $(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2$ or $KK(\sigma 2s)^2$
    • $\text{Bond Order} = \frac{4 - 2}{2} = 1$
    • Stable single bond; diamagnetic.
  • Carbon Molecule ($C_2$):
    • Total electrons = 12.
    • Configuration: $(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 (\sigma^* 2s)^2 (\pi 2p_x)^2 (\pi 2p_y)^2$
    • $\text{Bond Order} = \frac{8 - 4}{2} = 2$
    • Special Note: The double bond in $C_2$ consists entirely of two $\pi$ bonds because four valence electrons reside in two $\pi$ molecular orbitals. Diamagnetic.
  • Oxygen Molecule ($O_2$):
    • Total electrons = 16.
    • Configuration: $(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 (\sigma^* 2s)^2 (\sigma 2p_z)^2 (\pi 2p_x)^2 (\pi 2p_y)^2 (\pi^* 2p_x)^1 (\pi^* 2p_y)^1$
    • $\text{Bond Order} = \frac{10 - 6}{2} = 2$
    • Paramagnetic due to the presence of two unpaired electrons in $\pi^* 2p_x$ and $\pi^* 2p_y$ orbitals.

Hydrogen Bonding

• Cause of Formation: When Hydrogen is bonded to a strongly electronegative element ($X = F, O, N$), the shared electron pair shifts towards $X$. Hydrogen acquires a partial positive charge ($\delta+$), while $X$ acquires a partial negative charge ($\delta-$), generating a polar molecule.
• Definition: The electrostatic force of attraction that binds a hydrogen atom covalently bonded to an electronegative atom of one molecule with the electronegative atom ($F, O, N$) of another or the same molecule is called a hydrogen bond.
• Representation: A hydrogen bond is represented by a dotted line ($\cdots$), whereas a covalent bond is represented by a solid line ($-$).
• Strength & State Influence: Hydrogen bonds are weaker than covalent bonds. The magnitude of hydrogen bonding is maximum in the solid state and minimum in the gaseous state, significantly influencing physical properties such as melting and boiling points.
• Types of Hydrogen Bonding:
  1. Intermolecular Hydrogen Bond:
     • Formed between two different molecules of the same or different compounds.
     • Examples: $HF$ molecule, $H_2O$, alcohols.
     • Example in HF: $\cdots H^{\delta+} - F^{\delta-} \cdots H^{\delta+} - F^{\delta-} \cdots H^{\delta+} - F^{\delta-} \cdots$
  2. Intramolecular Hydrogen Bond:
     • Formed when a hydrogen atom lies between two highly electronegative atoms ($F, O, N$) present within the same molecule.
     • Example: $o$-Nitrophenol (ortho-nitrophenol), where hydrogen forms a bridge between oxygen atoms of the same molecule.
     • Consequence: $o$-Nitrophenol possesses intramolecular hydrogen bonding, leading to a lower melting point and boiling point compared to its intermolecularly bonded isomers.