Sharing electrons gives atoms a bond.
In a covalent bond, electrons are shared between atoms. We will first see what a shared pair means, then build the three bonds in C≡C, and finally ask why bonded nuclei settle at a particular separation.
01One pair, attracted by two nuclei
Hydrogen has one proton and one electron. Two hydrogen atoms can form H₂ by sharing two electrons. The shared negative charge is attracted by both positive nuclei; the arrows below show the resulting attraction on the nuclei towards the shared region. A single bond line stands for one shared pair.
02Build a triple bond: one σ and two π
Our molecule is ethyne, H–C≡C–H. Focus on the two carbons in its centre. An orbital describes the possible distribution of an electron, rather than a track. In this bonding model, each carbon uses inward-pointing sp orbitals for σ bonding and two perpendicular p orbitals for π bonding. We reveal these contributions in order so that you can inspect them.
σ — end-on overlap
Pronounced “sigma”. Density surrounds the line joining the nuclei. Each single bond is a σ bond in this model. The central C–C σ pair is shared along the axis.
π — side-on overlap
Pronounced “pi”. Each π orbital has a plane of zero density containing the nuclear axis. Its two lobes together describe one orbital, not two separate bonds. Ethyne has two perpendicular π orbitals.
Six electrons, not six dots
The C–C bond contains 6 electrons. Two C–H bonds contain 4 more valence electrons. Each carbon also has two inner 1s electrons, omitted from the density display. No electron is created by making a bond.
The sequential reveal is a teaching sequence, not a claim that real ethyne forms these bonds one after another in time. Clouds use smooth Gaussian orbital shapes, not a molecular quantum-chemistry calculation; C–H densities and carbon core electrons are omitted. Colour identifies the orbital, not its phase. The apparent edge is not a hard boundary.
03Why do we draw opposite spins?
An electron has an intrinsic quantum property called spin. Relative to a chosen measurement axis, we label its two possible spin outcomes ↑ and ↓. The Pauli exclusion principle says that no two electrons in a system can have the same complete quantum state. Therefore the same spatial orbital can hold at most two electrons, and their spins must be opposite.
Opposite spin is the occupancy condition for a pair in one orbital; it is not a promise that any two opposite-spin electrons will form a bond. Stable bonding also requires a suitable orbital and a lower total energy. The next experiment makes that energy condition visible.
04Why does a bond have a particular length?
Return to the simpler H₂ molecule. The nuclei repel one another, as do the electrons; nuclei and electrons attract. Quantum electronic energy also changes strongly at short distances. In atoms with occupied inner shells, Pauli restrictions on overlapping occupied states add an important short-range contribution. All of these contributions determine the total potential-energy curve. The lowest point gives the equilibrium separation between nuclei: the bond length.
Watch bond vibration keeps the mechanical energy: the two nuclei oscillate on either side of the potential minimum. Drag and release adds damping to show energy passing to an imagined environment. Motion is greatly slowed and uses a classical teaching potential, not a quantum simulation of H₂.
The electrical starting point
For two point charges, force magnitude grows with charge and falls with separation squared. Opposite signs attract; like signs repel. q₁ and q₂ are charges, r their separation, and k the Coulomb constant.
Force is not energy
With zero energy at infinite separation, a two-charge pair has this electrical potential energy. Force tells us how energy changes with position. Molecular energy includes many interactions and quantum motion, so this one formula is not the whole bond.
A minimum is stable
On either side of the minimum, a small displacement produces a restoring force. Real bonds vibrate around equilibrium. At large separation, attraction becomes weak; atoms do not snap back from any arbitrary distance. The displayed H₂ equilibrium distance is approximately 74 pm.
Check: do the upper and lower π lobes contain a pair each?
No. Together they belong to one spatial π orbital, occupied by two electrons in total. Ethyne’s other π pair occupies a second orbital in a perpendicular plane.