Chemical Bonding and Molecular Structure revision notes

Kössel-Lewis Approach & Octet Rule

Types of Bonds

Lattice Enthalpy

The energy required to completely separate one mole of a solid ionic compound into gaseous constituent ions. JEE Tip Even if the sum of ionization enthalpy and electron gain enthalpy is positive (endothermic), an ionic crystal gets stabilized strictly due to the massive energy released during lattice formation.

Bond Parameters

Resonance

When a single Lewis structure cannot accurately describe a molecule, a hybrid of multiple canonical (resonance) structures describes it.

Bond Polarity & Dipole Moment

Hydrogen Bonding

The attractive force binding a hydrogen atom of one molecule with a strongly electronegative atom ($\text{F}, \text{O}, \text{N}$) of another molecule.

The Valence Shell Electron Pair Repulsion (VSEPR) theory determines molecular shapes based on the repulsion between electron pairs in the valence shell.

• Key Postulate: Electron pairs tend to occupy positions in space that minimize repulsion and maximize distance. A multiple bond is treated as a single super pair.
• Repulsion Order: Lone pair (lp) - Lone pair (lp) > lp - bond pair (bp) > bp - bp. JEE Tip Lone pairs occupy more space because they are localized on the central atom, whereas bond pairs are shared between two nuclei.

Geometries (No lone pairs)

• $\text{AB}_2$: Linear ($180^\circ$), e.g., $\text{BeCl}_2$.
• $\text{AB}_3$: Trigonal planar ($120^\circ$), e.g., $\text{BCl}_3$.
• $\text{AB}_4$: Tetrahedral ($109.5^\circ$), e.g., $\text{CH}_4$.
• $\text{AB}_5$: Trigonal bipyramidal, e.g., $\text{PCl}_5$.
• $\text{AB}_6$: Octahedral, e.g., $\text{SF}_6$.

Geometries (With lone pairs)

• $\text{AB}_2\text{E}$ (1 lp): Bent/V-shaped. Angle is reduced from $120^\circ$ to $119.5^\circ$ (e.g., $\text{SO}_2$, $\text{O}_3$).
• $\text{AB}_3\text{E}$ (1 lp): Trigonal pyramidal. Angle reduced from $109.5^\circ$ to $107^\circ$ (e.g., $\text{NH}_3$).
• $\text{AB}_2\text{E}_2$ (2 lp): Bent. Angle reduced to $104.5^\circ$ (e.g., $\text{H}_2\text{O}$).
• $\text{AB}_4\text{E}$ (1 lp): See-saw. JEE Tip The lone pair occupies the equatorial position to minimize lp-bp repulsions (e.g., $\text{SF}_4$).
• $\text{AB}_3\text{E}_2$ (2 lp): T-shaped. Both lone pairs are equatorial (e.g., $\text{ClF}_3$).

Valence Bond Theory (VBT) explains bond formation via the partial interpenetration (overlap) of atomic orbitals.

• Detailed VBT Forces: When two atoms approach each other, new attractive forces arise between the nucleus of one atom and its own electron ($N_A-e_A$), and the nucleus of one atom and the electron of the other atom ($N_A-e_B$). Repulsive forces arise between electrons of the two atoms ($e_A-e_B$) and the nuclei of the two atoms ($N_A-N_B$). JEE Tip The magnitude of the new attractive forces is always greater than the new repulsive forces, leading to minimum energy and bond formation.
• Orbital Overlap: Bond strength depends on the extent of overlap. Overlap must be positive (same phase/sign and orientation).
• Sign (Phase) of Orbital Wave Functions: The positive (+) and negative (-) signs on boundary surface diagrams of orbitals show the sign (phase) of the orbital wave function and are strictly not related to electrical charge.

Sigma ($\sigma$) vs Pi ($\pi$) Bonds

• $\sigma$-bond: Head-on/axial overlap. Stronger due to a larger extent of overlapping.
• $\pi$-bond: Sidewise/lateral overlap. Creates two saucer-type charged clouds above and below the internuclear axis. Weaker than $\sigma$-bonds. Multiple bonds consist of one $\sigma$ and remaining $\pi$ bonds.

Hybridisation: Mixing of atomic orbitals of slightly different energies to form an equal number of equivalent hybrid orbitals.

• Conditions: Orbitals must belong to the valence shell and have almost equal energy. JEE Tip Promotion of electrons is not an essential condition, and fully filled orbitals can also participate in hybridisation.
• $sp$ Hybridisation: Mixing of one $s$ and one $p$ orbital. Linear geometry ($180^\circ$), $50\%$ s-character (e.g., $\text{BeCl}_2$, $\text{C}_2\text{H}_2$).
• $sp^2$ Hybridisation: Mixing of one $s$ and two $p$ orbitals. Trigonal planar geometry ($120^\circ$), $33\%$ s-character (e.g., $\text{BCl}_3$, $\text{C}_2\text{H}_4$).
• $sp^3$ Hybridisation: Mixing of one $s$ and three $p$ orbitals. Tetrahedral geometry ($109.5^\circ$), $25\%$ s-character (e.g., $\text{CH}_4$, $\text{NH}_3$, $\text{H}_2\text{O}$).
• $dsp^2$ Hybridisation: Mixing of one $d$, one $s$, and two $p$ orbitals. Square Planar geometry (e.g., $\text{[Ni(CN)}_4\text{]}^{2-}$, $\text{[Pt(Cl)}_4\text{]}^{2-}$).
• $sp^3d$ Hybridisation: Mixing of $s$, $p(3)$, and $d$. Trigonal bipyramidal geometry (e.g., $\text{PCl}_5$).
• $sp^3d^2$ Hybridisation: Mixing of $s$, $p(3)$, and $d(2)$. Octahedral geometry (e.g., $\text{SF}_6$).

MOT describes bonding via molecular orbitals (polycentric) formed by the Linear Combination of Atomic Orbitals (LCAO).

Bonding vs Antibonding MOs

• Addition of wave functions ($\psi_A + \psi_B$) forms a Bonding MO ($\sigma$) with high electron density between nuclei and lower energy.
• Subtraction ($\psi_A - \psi_B$) forms an Antibonding MO ($\sigma^*$) with a nodal plane between nuclei and higher energy.
• Conditions for LCAO: Combining atomic orbitals must have same/nearly same energy, same symmetry about the molecular axis ($z$-axis conventionally), and maximum overlap.
• Specific Symmetry constraints for LCAO: $2p_z$ of one atom can only combine with $2p_z$ of another atom. It cannot combine with $2p_x$ or $2p_y$ because they have different symmetries with respect to the internuclear axis.
• Types of MOs: While $\sigma$ and $\pi$ are common, $\delta$ (delta) molecular orbitals also exist in MO nomenclature.

Energy Level Sequences

• For $\text{O}_2$ and $\text{F}_2$: $\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \mathbf{\sigma 2p_z < (\pi 2p_x = \pi 2p_y)} < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$.
• JEE Tip For $\text{B}_2$, $\text{C}_2$, and $\text{N}_2$, the energy of $\sigma 2p_z$ shifts higher due to 2s-2p mixing: $\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \mathbf{(\pi 2p_x = \pi 2p_y) < \sigma 2p_z} < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z$.
• Stability & Magnetism: Stable if $N_b > N_a$. Diamagnetic if all electrons are paired; paramagnetic if unpaired electrons are present.
• Existence of $\text{Li}_2$ and $\text{C}_2$: Both $\text{Li}_2$ and $\text{C}_2$ have positive bond orders and are diamagnetic. JEE Tip They are experimentally known to exist specifically in the vapour phase.

• Kössel's Principle of Ionic Bonds: Highly electronegative halogens and electropositive alkali metals easily form negative and positive ions, stabilizing as an electrostatic lattice.

• LCAO Principle: Number of molecular orbitals equals the number of combining atomic orbitals. Electrons fill MOs following Aufbau, Pauli Exclusion, and Hund's rules.

• Noble Gas Compounds: The octet rule states atoms react to achieve inert noble gas configurations. Exception: Noble gases like Xenon and Krypton are not completely inert and form compounds with highly electronegative elements (e.g., $\text{XeF}_2$, $\text{KrF}_2$, $\text{XeOF}_2$).
• Sulphur's Dual Behavior: Sulphur forms compounds where it strictly obeys the octet rule (e.g., $\text{SCl}_2$ has 8 electrons around S) but also frequently forms expanded octet exceptions (e.g., $\text{SF}_6$ has 12, $\text{H}_2\text{SO}_4$ has 12).
• Non-Metallic Cation in Ionic Bonds: Most ionic compounds have cations derived from metallic elements. Exception: The ammonium ion ($\text{NH}_4^+$) is entirely made of non-metals but acts as the stable cation in numerous ionic compounds.
• Endothermic Ion Formation vs. Ionic Stability: The formation of $\text{Na}^+$ and $\text{Cl}^-$ actually results in a net positive (endothermic) energy sum ($+147.1 \text{ kJ mol}^{-1}$). Anomaly: The compound easily forms anyway because the massive lattice enthalpy released during crystal formation ($-788 \text{ kJ mol}^{-1}$) forcefully drives the reaction to stability.
• Bond Enthalpy of Identical Bonds: In $\text{H}_2\text{O}$, the two identical $\text{O-H}$ bonds do not require the same energy to break. Anomaly: The first $\text{O-H}$ breaks at $502 \text{ kJ mol}^{-1}$, but the second breaks at $427 \text{ kJ mol}^{-1}$ because the chemical environment changes after the first cleavage. Hence, we must use average bond enthalpy.
• Dipole Moment Vector Convention: The physics convention draws dipole moment from negative to positive. Exception: In chemistry, the crossed arrow ($\rightarrow$) symbolises the shift of electron density and is drawn opposite to the conventional physics vector (head points to the negative end).
• The $\text{NH}_3$ vs. $\text{NF}_3$ Dipole Anomaly: Despite F being far more electronegative than N, $\text{NH}_3$ ($4.90 \times 10^{-30}\text{ C m}$) has a higher dipole moment than $\text{NF}_3$ ($0.8 \times 10^{-30}\text{ C m}$). Why: In $\text{NH}_3$, the lone pair's orbital dipole reinforces the $\text{N-H}$ bond dipoles. In $\text{NF}_3$, the lone pair's dipole points opposite to the $\text{N-F}$ bond dipoles, heavily cancelling them out.
• $\text{PCl}_5$ Bond Length Anomaly: Not all bonds in trigonal bipyramidal $\text{PCl}_5$ are equal. Anomaly: The two axial bonds are longer and weaker than the three equatorial bonds because axial pairs suffer higher repulsion from three equatorial pairs at $90^\circ$.
• MOT Energy Sequence Shift: The standard MOT energy order has $\sigma 2p_z$ lower than $\pi 2p_x = \pi 2p_y$. Exception: For elements up to Nitrogen ($\text{B}_2, \text{C}_2, \text{N}_2$), $2s-2p$ mixing pushes the $\sigma 2p_z$ orbital higher in energy than the $\pi 2p_x = \pi 2p_y$ orbitals.
• The $\text{C}_2$ Molecule Bonding Anomaly: Standard double bonds consist of one $\sigma$ and one $\pi$ bond. Exception: According to MOT, the $\text{C}_2$ molecule double bond consists entirely of two $\pi$ bonds (no $\sigma$ bond at all) because its last 4 electrons fill the $\pi 2p_x$ and $\pi 2p_y$ molecular orbitals exclusively.
• $\text{O}_2$ Magnetism Anomaly: Lewis dot structures show all electrons paired in $\text{O}_2$ (predicting diamagnetism). Anomaly: Liquid $\text{O}_2$ is attracted to a magnet. MOT explains this by revealing two unpaired electrons residing in the degenerate $\pi^* 2p_x$ and $\pi^* 2p_y$ antibonding orbitals.

• Bond Parameters Trend: $\text{Bond Order} \propto \text{Bond Enthalpy} \propto \frac{1}{\text{Bond Length}}$.
• Covalent Character Trend: Covalent character in ionic bonds increases with decreasing cation size, increasing anion size, increasing charge, and pseudo-noble gas configuration (Fajans' Rules).

• Paramagnetic/Diamagnetic Species: Frequently tested using MOT to find unpaired electrons in fractional/integral bond order species ($\text{O}_2$, $\text{O}_2^+$, $\text{O}_2^-$, $\text{C}_2$, $\text{N}_2$).
• VSEPR Geometry vs Shape: Traps comparing electron geometry to molecular shape (e.g., differentiating between tetrahedral electron geometry and bent shape for $\text{H}_2\text{O}$, or distorted see-saw for $\text{SF}_4$).
• Dipole Moment Comparisons: Explaining net zero dipole moments in symmetric molecules ($\text{BF}_3$, $\text{CO}_2$, $\text{BeF}_2$) versus non-zero in angular/pyramidal ones ($\text{H}_2\text{O}$, $\text{NH}_3$).
• Axial vs Equatorial bonds: Identifying structural differences in $sp^3d$ hybridization ($\text{PCl}_5$).
• Bonding in Non-Existent Molecules: Applying MOT to prove $\text{He}_2$ and $\text{Be}_2$ do not exist because their bond order is zero.