Atoms & Chemical Bonds

Tiny building blocks of everything!

Junior level — plain language, no maths

Everything around you - the air you breathe, the food you eat, the water you drink - is built from unimaginably tiny particles called atoms. They're so small that a single drop of water holds more atoms than there are grains of sand on every beach on Earth put together.

Atoms are joiners. They latch onto one another to make molecules, held together by a chemical bond - think of it as a pair of tiny invisible hands gripping tight. Two hydrogen atoms clasp one oxygen atom and you get water, H₂O; a sodium atom grabs a chlorine atom and you get table salt, NaCl.

The real magic is that the same atoms, arranged differently, become wildly different things. Pure carbon is the soft, slippery graphite in your pencil - or, bonded another way, diamond, the hardest natural material there is. Nothing changed but the pattern of the bonds. In the simulation below, watch atoms bounce, attract, and snap together into molecules.

Covalent and Ionic Bonds: electron sharing vs electron transfer

Student level — the core equations

Atoms bond for one reason: it lowers their energy. Most crave a full outer shell of electrons - the octet rule - and how they get there depends on how greedily each atom pulls on electrons, a property called electronegativity \(\chi\). The gap \(\Delta\chi\) between two atoms sets the whole character of the bond they form.

When the gap is small, atoms share. A covalent bond is two atoms pooling a pair of electrons in the space between them: in H₂ each hydrogen chips in one electron, the shared pair settles in the middle, and the molecule sheds ~436 kJ/mol in the process. Pool two pairs and you get a double bond, three a triple - each shorter and stronger than the last. When the gap is large, one atom simply takes. In NaCl chlorine strips an electron clean off sodium, and the resulting \(\text{Na}^+\) and \(\text{Cl}^-\) then cling by raw electrostatic pull, \(U = -\dfrac{k\,Q_1 Q_2}{r}\), stacking into a crystal lattice.

This is the secret behind "like dissolves like." Water is bent and lopsided, carrying a dipole moment \(\mu = 1.85\ \text{D}\), so it eagerly surrounds ions and other polar molecules - but leaves oil, which has no such charge to grab, entirely alone. And however winding a route a reaction takes, its heat is fixed in advance: Hess's law says \(\Delta H\) depends only on the start and end states, \(\Delta H_{\text{rxn}} = \sum \Delta H_f(\text{products}) - \sum \Delta H_f(\text{reactants})\), never on the path in between.

Quantum mechanics of bonding: MO theory and reaction dynamics

Scholar level — full mathematical depth

01A bond is interfering waves

At bottom, a chemical bond is a quantum interference pattern. Molecular orbital theory builds a molecule's electron waves by adding atomic ones - the LCAO recipe, \(\psi = c_A \phi_A + c_B \phi_B\). Bring two hydrogen 1s orbitals together and they can add in phase or out of phase, and which one the electrons occupy is the whole difference between a molecule and two separate atoms. Bonding is not a metaphor about sharing; it is literally constructive interference of matter waves.

02Bonding and antibonding

The two combinations split in energy. The in-phase sum \(\sigma = (\phi_A + \phi_B)/\sqrt{2+2S}\) piles electron density between the nuclei, screening their repulsion and dropping the energy - a bonding orbital. The out-of-phase difference carves a node between them and raises the energy - antibonding, marked with a star. Fill the bonding level and skip the antibonding one and the atoms stick; the net tally, \(\text{BO} = (N_b - N_a)/2\), is exactly why He₂ doesn't exist while H₂ does.

03Freezing the nuclei: potential energy surfaces

Electrons are thousands of times lighter than nuclei and move accordingly faster, which lets the Born–Oppenheimer approximation pin the nuclei in place and solve for the electrons at each fixed geometry. Do that everywhere and you trace out a potential energy surface - a landscape of valleys (stable molecules) and passes between them. Chemistry becomes topography: a reaction is a trajectory across this surface from one valley to another.

04Over the pass: transition states and Arrhenius

Between reactant and product valleys sits a mountain pass - the transition state, a saddle point of the surface - and its height is the activation energy \(E_a\). Only molecules with enough thermal energy clear it, and since the fraction that can rises steeply with temperature, the rate follows Arrhenius, \(k = A\,e^{-E_a/RT}\). The transition state itself flickers into existence for barely \(10^{-13}\) s, yet femtosecond lasers can now photograph a molecule mid-passage across the pass.

05The wavefunction that's too big to store

The dream of solving the Schrödinger equation for a real molecule founders on scale: the wavefunction of \(N\) electrons lives in \(3N\) dimensions, and its cost explodes exponentially - a few dozen atoms and no computer that will ever exist could store it. For most of the 20th century, quantitative quantum chemistry was stuck against this wall. The way through was to stop tracking the wavefunction at all.

06DFT: density instead of wavefunction

Density Functional Theory made the impossible routine. The Hohenberg–Kohn theorems prove that the humble electron density \(\rho(r)\) - a function of just 3 coordinates - secretly determines every ground-state property, so you never need the monstrous \(3N\)-dimensional wavefunction. The Kohn–Sham equations turn the interacting swarm into tractable one-electron problems, hiding the hard many-body physics inside an exchange-correlation functional. DFT is now the workhorse behind catalyst design, battery materials and drug discovery - quantum mechanics, made affordable.