Shapes and forces

A sigma bond forms by head-on overlap along the line joining the nuclei. It can use s-s overlap (H₂), s-p overlap (HCl) or p-p overlap. A pi bond forms by sideways overlap of parallel p orbitals, with electron density above and below the internuclear axis. A single bond is sigma; a double bond is one sigma plus one pi; a triple bond is one sigma plus two pi.

VSEPR places electron domains as far apart as possible to reduce repulsion. Around a central atom, a single, double or triple bond counts as one bonding domain. Lone pairs also repel, but are omitted from the name of the molecular shape. Lone-pair/bond-pair repulsion is greater than bond-pair/bond-pair repulsion, compressing some angles.

The table follows the same repulsion argument throughout: two bonding domains point in opposite directions (linear), three spread in one plane (trigonal planar), and four point towards the corners of a tetrahedron. Six equivalent domains point along three perpendicular axes (octahedral). NH₃ and H₂O both start from four electron domains. Replace one tetrahedral bonding direction by a lone pair to obtain a pyramidal atom arrangement; replace two to obtain a bent arrangement. Lone pairs occupy more angular space near the central atom, so they compress the remaining bond angles.

Sulfur in SF₆ has twelve outer electrons, but oxygen in the same group never goes past eight. An element in Period 3 or below has empty d orbitals in its outer shell (3d for Period 3). They are close enough in energy to be used, so the central atom can hold five or six electron domains. A Period 2 atom such as N, O or F has only 2s and 2p orbitals, so it is limited to four domains and eight electrons. That is why PCl₅ and SF₆ exist, but NCl₅ and OF₆ do not. This is called expanding the octet.

Where the lone pairs go decides the shape. With five domains, the three equatorial positions are 120 degrees apart, while the two axial positions are at 90 degrees to three others. A lone pair takes an equatorial position, where it has fewer close neighbours at 90 degrees. So one lone pair gives a see-saw, two give a T-shape and three give a straight line. With six domains every position is the same, so one lone pair gives a square pyramid. A second lone pair goes opposite the first, as far from it as possible, which leaves a square plane.

Ethene contains five sigma bonds in total (four C-H and one C-C) plus one C-C pi bond. Sideways overlap requires the two p orbitals to remain aligned, so the double bond cannot rotate freely without disrupting that overlap. This explains later cis-trans isomerism.

Electronegativity describes an atom's attraction for a bonding electron pair. In H-Cl, Cl attracts the pair more strongly: H is partially positive and Cl partially negative. These are partial charges within a covalent bond, not full H⁺ and Cl^- ions. The molecular dipole is the combined effect of all bond dipoles in three dimensions.

Instantaneous dipole-induced dipole attractions occur in all particles: a momentary uneven electron distribution induces a dipole in a neighbouring particle, and the nearby opposite partial charges attract electrostatically. They are the principal intermolecular attraction in Br₂ and the attraction between noble-gas atoms. Larger, more easily polarised electron clouds usually give stronger attractions. CHCl₃ also has permanent dipole-permanent dipole attraction between oppositely charged ends of neighbouring molecules.

Hydrogen bonding is an electrostatic attraction between the partially positive H covalently bonded to N, O or F and a lone pair on N, O or F in a neighbouring particle. Water provides O-H donors and oxygen lone pairs; ammonia provides N-H donors and a nitrogen lone pair. Merely containing hydrogen is insufficient: methane cannot hydrogen-bond to itself.

The same possible attractions exist in a gas and its liquid, but gas particles are usually far apart. Cooling reduces kinetic energy and compression brings particles closer, allowing attractions to hold particles in a liquid. A larger attraction generally makes liquefaction easier. Pressure alone does not guarantee liquefaction at every temperature; this is a qualitative explanation, not an ideal-gas calculation.

Hydrogen bonding makes water's boiling point relatively high for such a small molecule because substantial energy is needed to separate molecules. In ordinary ice, each water molecule hydrogen-bonds to four neighbours in an open, approximately tetrahedral network: its two O-H groups donate two hydrogen bonds and its two oxygen lone pairs accept two. On melting, some of that open arrangement collapses, so liquid water is denser than ice and ice floats. The covalent O-H bonds remain intact.