Types of Hybridisation and Geometry of Molecules

sp hybridisation — BeCl₂ (linear). Beryllium's ground-state valence configuration is 2s² (2p empty). To form two equivalent Be-Cl bonds, one of the paired 2s electrons is promoted ('excited') into an empty 2p orbital, giving the excited-state configuration 2s¹ 2p¹. The one 2s orbital and one 2p orbital now MIX (hybridise) to produce TWO equivalent sp hybrid orbitals, each with 50% s-character and 50% p-character, oriented in exactly OPPOSITE directions (180° apart) (Fig 10.22). Each sp orbital then overlaps linearly with a chlorine 3pz orbital to form a Be-Cl σ bond -- giving BeCl₂ its observed LINEAR shape.

sp² hybridisation — BF₃ (trigonal planar). Boron's ground-state valence configuration is [He]2s² 2p¹ -- only ONE unpaired electron, but boron needs THREE unpaired electrons to form three covalent bonds with three fluorine atoms. One of the paired 2s electrons is promoted to the empty 2p_y orbital, giving the excited-state configuration 2s¹ 2pₓ¹ 2p_y¹. The one 2s orbital and TWO 2p orbitals (2pₓ, 2p_y) now mix to generate THREE equivalent sp² hybrid orbitals, lying in the same (xy) plane, each separated from its neighbours by 120° (Fig 10.23). Each sp² orbital overlaps axially with a fluorine 2pz orbital, giving BF₃ its TRIGONAL PLANAR shape.

sp³ hybridisation — CH₄ (tetrahedral). Carbon's ground-state valence configuration is [He]2s² 2pₓ¹ 2p_y¹ (2p_z empty). To form four covalent bonds with four hydrogens, one of the paired 2s electrons is promoted to the empty 2p_z orbital, giving the excited-state configuration 2s¹ 2pₓ¹ 2p_y¹ 2p_z¹ -- four unpaired electrons. The one 2s orbital and all three 2p orbitals mix to give FOUR equivalent sp³ hybrid orbitals, oriented tetrahedrally, with an angle of 109°28' between any two of them (Fig 10.24). The 1s orbitals of the four hydrogen atoms overlap linearly with these four sp³ orbitals, giving four equivalent C-H σ bonds and methane's tetrahedral shape.

sp³d hybridisation — PCl₅ (trigonal bipyramidal). In molecules such as PCl₅, the central phosphorus atom is covalently bonded to FIVE chlorine atoms -- more than an ordinary octet allows. Phosphorus's ground-state valence configuration is [Ne]3s² 3pₓ¹ 3p_y¹ 3p_z¹ (three unpaired p electrons already, plus a paired 3s). One of the paired 3s electrons is promoted into a VACANT 3d orbital (specifically 3d_z²), giving five unpaired electrons across one 3s, three 3p, and one 3d orbital. These five orbitals mix to give FIVE equivalent sp³d hybrid orbitals, whose overall orbital geometry is TRIGONAL BIPYRAMIDAL (Fig 10.25). Each sp³d orbital overlaps linearly with a chlorine 3pz orbital, giving five P-Cl σ bonds.

sp³d² hybridisation — SF₆ (octahedral). In sulphur hexafluoride, the central sulphur atom extends its octet further still, undergoing sp³d² hybridisation to generate SIX equivalent hybrid orbitals, accounting for six equivalent S-F bonds. Sulphur's ground-state valence configuration is [Ne]3s² 3pₓ² 3p_y¹ 3p_z¹. One electron each from the 3s orbital and from a paired 3p orbital is promoted into TWO vacant 3d orbitals (3d_z² and 3d_(x²−y²)), giving six unpaired electrons across one 3s, three 3p, and two 3d orbitals. These six orbitals mix to give SIX equivalent sp³d² hybrid orbitals, whose orbital geometry is OCTAHEDRAL (Fig 10.26). Each overlaps linearly with a fluorine 2pz orbital, giving six equivalent S-F σ bonds.

Bonding in ethylene (C₂H₄). Ethylene's molecular formula is C₂H₄; carbon's valency is 4. Carbon's ground-state valence configuration ([He]2s² 2pₓ¹ 2p_y¹, 2p_z empty) is first promoted to 2s¹ 2pₓ¹ 2p_y¹ 2p_z¹ to satisfy this valency, exactly as for methane. But in ethylene, EACH carbon undergoes sp² hybridisation -- mixing only 2s, 2pₓ and 2p_y into three coplanar sp² orbitals (120° apart, lying in the xy plane) -- and leaves the 2p_z orbital UN-hybridised, standing perpendicular to that plane.

• σ-bond formation: one of the sp² orbitals on each carbon, lying along the molecular (x) axis, overlaps LINEARLY with the corresponding sp² orbital on the other carbon, forming a C-C σ bond. The other two sp² orbitals on each carbon overlap linearly with the 1s orbitals of two hydrogen atoms, giving two C-H σ bonds per carbon (four in total).
• π-bond formation: the two UN-hybridised 2p_z orbitals (one on each carbon), lying perpendicular to the molecular axis, cannot overlap head-on -- they can only overlap SIDEWAYS. This lateral overlap forms a π bond between the two carbons. Together, the C-C σ bond plus this C-C π bond give ethylene's C=C double bond, and the molecule is planar (Fig 10.27). …