Chemical Bonding and Molecular Structure revision notes

Key Concepts & Definitions

Chemical Bond: The attractive force which holds various constituents (atoms, ions, etc.) together in different chemical species. Bonding lowers the energy of a system to attain stability.

Kössel-Lewis Approach & Octet Rule:

Lewis Symbols:

Notations representing valence electrons as dots around the chemical symbol. The group valence is equal to the number of dots or 8 minus the number of dots.

Octet Rule:

Atoms combine by transferring or sharing valence electrons to attain a stable outer shell of eight electrons (a noble gas configuration).

Langmuir's Contribution (1919):

Refined the Lewis postulations by abandoning the idea of the stationary cubical arrangement of the octet and introduced the term covalent bond.

Formal Charge (F.C.):

The difference between the valence electrons in an isolated atom and the electrons assigned to it in a Lewis structure. It helps keep track of valence electrons and select the lowest energy structure.JEE TIPThe lowest energy structure is generally the one with the smallest formal charges on the atoms.

Types of Bonds:

• Ionic (Electrovalent) Bond: Formed by the electrostatic attraction between positive and negative ions after a complete transfer of electrons.
• Covalent Bond: Formed by the sharing of an electron pair between two atoms. Multiple bonds involve sharing two (double bond) or three (triple bond) electron pairs.

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:

• Bond Length: The equilibrium distance between the nuclei of two bonded atoms.
• Covalent vs. van der Waals Radius: Covalent radius is half the distance between two similar bonded atoms (atom's core), while van der Waals radius is half the distance between two nonbonded atoms in adjacent molecules, representing the overall size including the valence shell.
• Bond Angle: The angle between orbitals containing bonding electron pairs around the central atom.
• Bond Enthalpy: Energy required to break one mole of a specific type of bond in the gaseous state.JEE TIPFor polyatomic molecules (like $\text{H}_2\text{O}$), bond dissociation enthalpies vary for identical bonds, so the average bond enthalpy is calculated.
• Bond Order: The number of bonds between two atoms.JEE TIPIsoelectronic molecules and ions (e.g., $\text{F}_2$ and $\text{O}_2^{2-}$) always have identical bond orders.

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

• JEE TIPCanonical structures have no real existence and there is no equilibrium between them. Resonance stabilizes the molecule; the resonance hybrid energy is always lower than any single canonical structure.

Bond Polarity & Dipole Moment:

• A polar covalent bond arises when the shared electron pair is displaced towards the more electronegative atom.
• Dipole Moment ($\mu$): The product of the magnitude of the charge and the distance of separation, expressed in Debye units ($1 \text{ D} = 3.33564 \times 10^{-30} \text{ C m}$). It is a vector pointing from positive to negative.

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.

• JEE TIPHydrogen bonding is maximum in the solid state and minimum in the gaseous state.
• Intermolecular H-bonding: Between different molecules (e.g., $\text{HF}$, $\text{H}_2\text{O}$).
• Intramolecular H-bonding: Within the same molecule (e.g., o-nitrophenol).

VSEPR Theory & Molecular Geometry

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 TIPLone 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 TIPThe 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 & Hybridisation

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 TIPThe 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 TIPPromotion 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., $\text{SF}_6$).

Molecular Orbital Theory (MOT)

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 TIPFor $\text{B}_2$, $\text{C}_2$, 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 TIPThey are experimentally known to exist specifically in the vapour phase.

Important Rules, Laws & Principles

• Kössel's Principle of Ionic Bonds: Highly electronegative halogens and electropositive alkali metals easily form negative and positive ions, stabilizing as an electrostatic lattice.
• Fajans' Rules (Covalent Character in Ionic Bonds):
  1. Smaller cation and larger anion increase covalent character.
  2. Greater charge on the cation increases covalent character.
  3. JEE TIPCations with a pseudo-noble gas transition metal configuration ($(n-1)d^n ns^0$) are more polarizing than cations with a noble gas configuration ($ns^2 np^6$) typical of s-block elements.
• LCAO Principle: Number of molecular orbitals equals the number of combining atomic orbitals. Electrons fill MOs following Aufbau, Pauli Exclusion, and Hund's rules.

Formulae & Equations

• Formal Charge (F.C.): $F.C. = [\text{Total valence } e^-] - [\text{Total non-bonding } e^-] - \frac{1}{2}[\text{Total bonding } e^-]$.
• Dipole Moment ($\mu$): $\mu = Q \times r$. (Expressed in Debye. $1 \text{ D} = 3.33564 \times 10^{-30} \text{ C m}$).
• Bond Order (B.O.): $\text{B.O.} = \frac{1}{2}(N_b - N_a)$. (Where $N_b$ = electrons in bonding MOs, $N_a$ = electrons in antibonding MOs).

⚠️ EXCEPTIONS & ANOMALIES

• Exceptions to the Octet Rule:
  1. Incomplete Octet: Central atom has less than 8 valence electrons (e.g., $\text{LiCl}$, $\text{BeH}_2$, $\text{BCl}_3$, $\text{AlCl}_3$, $\text{BF}_3$).
  2. Odd-electron Molecules: Molecules like $\text{NO}$ and $\text{NO}_2$ do not satisfy the octet rule for all atoms.
  3. Expanded Octet: Central elements in the 3rd period and beyond can utilize $3d$ orbitals for bonding, exceeding 8 electrons (e.g., $\text{PF}_5$ has 10, $\text{SF}_6$ has 12, $\text{H}_2\text{SO}_4$ has 12).
• 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.

Trends & Comparisons

• 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).

Previous Year JEE Topics

• 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.

Top 10 JEE MCQ Traps

Trap 1 - Hybridisation Requires Empty/Half-Filled Orbitals

• Misconception: Only half-filled orbitals or orbitals where an electron has been excited/promoted can undergo hybridisation.
• Correct Understanding:JEE TIPPromotion of an electron is NOT an essential condition. Fully filled valence orbitals (like the lone pairs in $\text{NH}_3$ and $\text{H}_2\text{O}$) freely participate in hybridisation.

Trap 2 - $\text{C}_2$ Double Bond Composition

• Misconception: Every double bond in nature is composed of $1 \sigma$ bond and $1 \pi$ bond.
• Correct Understanding:JEE TIPThe diatomic Carbon molecule ($\text{C}_2$) in the vapour phase possesses a double bond made of $0 \sigma$ bonds and $2 \pi$ bonds.

Trap 3 - Significance of $(+)$ and $(-)$ in Orbital Overlap

• Misconception: The (+) and (-) lobes in $p$-orbital diagrams represent regions of positive and negative electrical charge.
• Correct Understanding:JEE TIPThe signs represent the phase of the orbital wave function ($\psi$). Constructive overlap (bonding) only occurs when identical phases (e.g., + and +) overlap.

Trap 4 - VSEPR Angle of $\text{H}_2\text{O}$ vs $\text{NH}_3$

• Misconception: Since both $\text{H}_2\text{O}$ and $\text{NH}_3$ are $sp^3$ hybridized, their bond angles are compressed equally from $109.5^\circ$.
• Correct Understanding:JEE TIP$\text{H}_2\text{O}$ has two lone pairs, causing higher $lp-lp$ repulsion. Therefore, water's bond angle gets compressed down to $104.5^\circ$, which is much smaller than ammonia's $107^\circ$ (which only has one lone pair).

Trap 5 - Stability of Octet Rule Violators

• Misconception: Molecules that violate the octet rule ($\text{PCl}_5$, $\text{SF}_6$, $\text{BF}_3$) are highly unstable.
• Correct Understanding:JEE TIPThese molecules exist at room temperature and are highly stable. The octet rule is a useful guideline, but minimizing formal charge and optimizing lattice/bond enthalpy are the true drivers of chemical stability.

Trap 6 - Resonance Equilibrium

• Misconception: A molecule like Ozone ($\text{O}_3$) rapidly flips back and forth (is in equilibrium) between its two Lewis canonical structures.
• Correct Understanding:JEE TIPCanonical forms have NO real physical existence and there is no equilibrium. The molecule exists constantly and permanently as a single resonance hybrid.

Trap 7 - MOT Sequence for Nitrogen vs. Oxygen

• Misconception: The MOT energy filling order is identical for all homonuclear diatomic molecules.
• Correct Understanding:JEE TIPFor $\text{O}_2$ and $\text{F}_2$, $\sigma 2p_z$ fills before $\pi 2p_x/\pi 2p_y$. For $\text{B}_2, \text{C}_2,$ and $\text{N}_2$, $2s-2p$ mixing occurs, pushing the $\sigma 2p_z$ orbital above $\pi 2p_x$ and $\pi 2p_y$.

Trap 8 - Dipole Moment of Highly Symmetric Geometries

• Misconception: A molecule with strongly polar bonds must be a polar molecule overall.
• Correct Understanding:JEE TIPPolyatomic molecules with symmetric geometries ($\text{BeF}_2$ - linear, $\text{BF}_3$ - trigonal planar, $\text{CCl}_4$ - tetrahedral) perfectly cancel out individual polar bond vectors, resulting in a net dipole moment of exactly zero.

Trap 9 - Nature of Ionic vs Covalent Bonds

• Misconception: A bond between a metal and nonmetal is 100% ionic.
• Correct Understanding:JEE TIPNo bond is 100% ionic. High positive charge, small cation size, or pseudo-noble gas configurations ($(n-1)d^{10}ns^0$) highly polarise the anion, introducing significant covalent character (Fajans' Rules).

Trap 10 - $\text{He}_2$ Stability

• Misconception: $\text{He}_2$ exists because Helium is stable, or it fails to exist purely because it is a noble gas.
• Correct Understanding:JEE TIP$\text{He}_2$ mathematically does not exist because its Bond Order is exactly $0$. The number of bonding electrons (2 in $\sigma 1s$) is exactly canceled by the number of antibonding electrons (2 in $\sigma^* 1s$), resulting in net zero stabilizing force.