The one question that predicts a structure
You now hold all the pieces. Guide 1 gave you the radial story — the bonding-energy curve tells you how far apart two atoms settle and how deep the well is, that is, the bond length and the bond energy. Guides 2 and 3 gave you the cast of bonds: ionic, covalent, and metallic, plus the gentle secondary bonds. This guide layers one more question on top of all of them — not how far or how strong, but which way. Does the bond point?
That single question sorts every bond into two families. In the directional family — the covalent bond, and among the secondary bonds the hydrogen bond — the glue lives in a lobe of shared electrons that aims a definite way, so the bond has a preferred angle. In the non-directional family — metallic, ionic, and van der Waals — the pull is the same in every direction, like the field of a charged sphere. Bond directionality is the name of this master idea, and the claim of the whole guide is simple: directional bonds build open, low-coordination structures; non-directional bonds build dense, high-coordination ones.
Non-directional bonds: sphere-packing wins
Start with the non-directional family, because it is the easier half. If a bond pulls equally hard in every direction, then as far as its neighbours are concerned an atom is just a featureless sticky sphere. With no angles to honour, the only remaining question is a packing puzzle: how do you cram equal spheres together as tightly as possible? Nature's answer is close packing — exactly how a grocer stacks oranges into a pyramid, each new layer of fruit nestling into the hollows of the layer below.
Put numbers on it. Stack close-packed layers in the sequence ABCABC and you get the face-centred cubic pattern; stack them ABAB and you get the hexagonal close-packed one. Both give every atom twelve touching neighbours — a coordination number of 12 — and both fill 74 percent of space, an atomic packing factor of 0.74. That 0.74 is provably the densest equal spheres can ever be packed, so it is no surprise that most metals, held by the non-directional metallic bond, default straight to it: copper is face-centred cubic, magnesium is hexagonal close-packed.
The ionic bond is non-directional too, so it also plays sphere-packing — but with two extra rules. The crystal must stay electrically neutral, and it must stack two sizes of sphere, a small cation among larger anions. So ionic solids pack as tightly as those constraints allow, landing at somewhat lower coordination: in the rock-salt structure of NaCl each ion touches six of the other kind (coordination 6), while in caesium chloride the roomier caesium reaches eight. Still no angles are involved — how many neighbours fit is set by size, a size story guide 5 will tell in full.
Directional bonds: angles cost space
Now the directional half, where everything changes. A covalent bond is a shared pair of electrons sitting in a lobe that points from one atom straight at its partner. That lobe has a definite direction, and an atom's several lobes stand at definite angles to one another. Carbon forms exactly four bonds aimed at the corners of a tetrahedron, locked at 109.5 degrees. You cannot slip a fifth neighbour in by simply pushing harder, the way you could with sticky spheres — the electron geometry forbids it. The bonds behave like rigid struts of fixed length and fixed angle.
Follow those struts and you are forced into an open framework. In the diamond cubic structure every carbon bonds to only four others at those tetrahedral angles, so the coordination number is a mere 4 and the packing factor falls to just 0.34 — the atoms fill barely a third of space, against 0.74 for a close-packed metal. All that emptiness is the literal price of insisting on angles. The reward is ferocious stiffness and hardness: diamond is the hardest natural material precisely because those directional struts resist being bent or sheared.
The same directional logic can carve a two-dimensional motif instead of a three-dimensional one. In graphite each carbon reaches out to just three neighbours in one flat plane at 120 degrees, building an even more open honeycomb sheet with an in-plane coordination of only 3. Then, as guide 3 described, weak van der Waals forces merely stack those sheets. So directionality does its work whether the covalent framework fills space (diamond) or spreads a plane (graphite) — either way, pointing bonds mean open motifs and low coordination.
Same atoms, opposite structures
The sharpest proof that directionality — not chemistry alone — chooses the structure is a single element wearing two structures. Carbon is the famous one: directional tetrahedral bonding gives diamond (coordination 4, hard, an insulator), while a more spread-out bonding gives graphite (coordination 3 in-plane, soft, a conductor). Tin makes the point even more starkly: below about 13 degrees C, grey tin is diamond-cubic and directional (coordination 4, brittle); warm it above that and it becomes white tin, a denser metallic structure — the crumbling change old-timers called tin pest. Same atoms; flip the directionality of the bonding, and the whole architecture flips with it.
BOND DIRECTIONALITY -------------------------------> STRUCTURE directional (angles fixed) non-directional (a sphere's pull) | | covalent 3D covalent layers ionic (size-set) metallic diamond graphite sheet NaCl / CsCl copper (FCC) CN 4 CN 3 in-plane CN 6 / CN 8 CN 12 APF 0.34 open honeycomb medium density APF 0.74 <---- open, low coordination -------- dense, high coordination ---->
- Ask first whether the bond points. Shared, aimed electron pairs (covalent, or a hydrogen bridge) are directional; a pooled electron sea or a charged sphere (metallic, ionic, van der Waals) is not.
- If it points, expect fixed bond angles, so predict an open framework with low coordination — think diamond's 4 or graphite's in-plane 3, and a low packing factor.
- If it does not point, expect a sphere-packing puzzle, so predict a dense structure with high coordination — close-packed 12 for a metal, or 6 to 8 for an ionic solid once size is accounted for.
- Then sanity-check backwards: a hard, open, brittle solid hints at directional bonds; a dense, ductile, high-coordination one hints at non-directional bonds. The structure is a clue to the bond, and the bond a clue to the structure.
Honest limits — a tendency, not a law
Treat directionality as a powerful organising tendency, not an ironclad law, because it has honest exceptions. Not every non-directional metal packs to the maximum 0.74: iron and tungsten adopt the body-centred cubic structure, coordination 8 and packing factor 0.68, a touch looser than close-packed, because subtle electronic effects tune the balance. So 'non-directional means densest possible' is a strong rule of thumb with real exceptions, not a theorem.
Directionality also answers only half of the structural question. It tells you angles-or-no-angles; it does not by itself tell you how many neighbours fit. For a non-directional bond that count is set by size — the radius ratio of the two spheres — which is why NaCl chooses 6 and CsCl chooses 8 though both are equally non-directional. And most real bonds are not pure: mixed bonding means directionality is a dial, not a switch, so a bond can be partly directional and give an intermediate structure.
One last generalisation to keep the idea honest and wide: directionality is not only a primary-bond affair. The directional hydrogen bond of guide 3 props open ice into its low-density tetrahedral cage — the very same open, low-coordination logic, now acting through a secondary bond. That is why ice floats. Next, guide 5 turns to the other master control that directionality left unanswered: atomic size, radius, and how the radius ratio dictates coordination once you already know the bond does not point.