Building molecules

Chapter 3 named which electrons matter: the outermost ones. Chapter 4 showed what they do: share or tug. This chapter turns those electrons into a notation you can write on paper, and then into a builder you can use to assemble real molecules.

5.1 Dots for the outermost

The electrons that actually do chemistry are the valence electrons: the ones in the outermost $s$ and $p$ subshells. Everything deeper is buried too close to the nucleus to participate in bonding. In 1916, Gilbert Lewis proposed a notation as compact as the idea itself: write the element's symbol, and then draw one dot around it for each valence electron. Place a single dot on each of the four sides first, then start doubling up. That's all there is to it.

Notice that each column of the periodic table gives the same number of dots: every alkali metal has one, every halogen has seven. That isn't a coincidence. Lewis's notation is just the periodic table's group number, drawn around the symbol.

5.2 Eight is full

The magic number eight is not arbitrary. The outer layer of any shell is made of exactly one $s$ subshell and one $p$ subshell. The $s$ holds one orbital and the $p$ holds three, so the outer layer has $1 + 3 = 4$ orbitals total. Pauli says each orbital can hold at most two electrons, which gives $4 \times 2 = 8$. Eight is the largest number of valence electrons a shell can fit, and filling all eight is the noble-gas state you met in chapter 3 - the reason the noble gases sit at the right edge of each row.

Every atom is pulled toward that full-shell state for the same reason electrons do anything else: it's the lowest energy available. So atoms share or transfer electrons with their neighbors until each one can count eight in its outer shell. Hydrogen is the one exception. Its only shell is shell 1, which has just the $1s$ orbital, so its full shell holds only two electrons. Hydrogen's target is a duet, not an octet.

Here is the move that makes the whole thing work. When two atoms share a pair of electrons, both atoms get to count that pair as part of their own outer shell. Neither atom owns the pair outright, but each one includes those two electrons in its own total. That double-counting is what a covalent bond is, on paper.

5.3 Lines are pairs

Drawing two dots between every pair of bonded atoms gets tedious fast, so chemists replaced the shared dots with a single line. The rule is simple: one line means one shared pair, which means one bond. Pairs that stay on a single atom instead of being shared are still drawn as two dots side by side, and those are called lone pairs.

The recipe runs the same way every time. First, add up the valence electrons each atom brings - that's the total you have to work with. Second, put the least-electronegative atom in the center, since the center holds the most bonds; hydrogen is never central, because its full shell is only two and it can manage just one bond. Third, draw a single bond from the center to each outer atom. Fourth, place any leftover electrons as lone pairs, filling the outer atoms first and then the center. Fifth, if any atom still falls short of eight, slide one of its neighbor's lone pairs into the gap between them to make a double or triple bond.

5.4 The builder

Now you do it. The atoms are already placed in a sensible skeleton, and your job is to decide the bonds and the lone pairs. Click in the gap between two atoms to cycle the bond order through $0 \to 1 \to 2 \to 3 \to 0$; click directly on an atom to add a lone pair, which cycles through $0, 1, 2, 3, 4$ pairs and then wraps. Each atom glows green when its count reaches its target (8 for everything past hydrogen, 2 for hydrogen) and rose if you overshoot. The molecule is done when every electron is placed and every atom is satisfied.

5.5 Double and triple are shorter and stronger

Some molecules, like CO₂, O₂, and N₂, force you to draw double or triple bonds because there aren't enough electrons to go around otherwise. A double bond isn't a different kind of bond; it's just two shared pairs sitting in the same gap between two atoms instead of one. A triple bond is three pairs. More shared pairs in the gap means more negative charge holding the two positive nuclei together, which lets the nuclei sit closer without their mutual repulsion winning out, and it takes more energy to pull them apart again. Both effects show up clearly in the numbers for carbon–carbon bonds:

Triple bonds are the reason nitrogen gas, $\text{N}_2$, is famously inert. Pulling two nitrogen atoms apart costs 945 kJ/mol, which is nearly three times the energy of a single O–H bond. About four-fifths of the air around you is N₂, and almost none of it reacts with anything at room temperature. The entire atmosphere is held in place by a triple bond.

5.6 What the dots can't say

Lewis structures are flat bookkeeping. They get which atoms are bonded and how many pairs sit where, and they get those things exactly right. But they are silent about everything else. They don't tell you that the four C–H bonds in methane aim outward to the corners of a tetrahedron rather than lying flat in a square. They don't tell you that water bends at an angle of about 105 degrees instead of sitting in a straight line, or that water molecules stick to each other through small extra attractions called hydrogen bonds - the attractions that make ice float, hold DNA in shape, and keep your blood liquid at body temperature.

Geometry and stickiness live behind the door this notation just opened for you. This course stops here, and the next one picks up there.

5.7 What you now have

• Lewis dot symbols: the valence count drawn around the element's symbol, dots placed singly before they pair (Hund's rule, in ink).
• The octet (or duet for hydrogen): one $s$ orbital plus three $p$ orbitals in the outer layer, capped at two electrons each by Pauli, add up to a full shell of eight - the noble-gas state every atom slides toward.
• A bond is a shared pair both atoms count in their own shells. Two pairs in the same gap make a double bond, three make a triple, and each step pulls the nuclei closer and makes the bond harder to break.
• The Lewis structure of any small molecule is recoverable from rules alone: count valence, lay down single bonds, spread the leftovers as lone pairs, promote bonds wherever atoms fall short.

Five chapters ago the question was where an electron lives, and the answer was a probability cloud labeled by three quantum numbers. From there, Pauli and Hund seated the electrons inside each atom, shielding decided what order the seats filled in, the seating chart unfolded into the periodic table, and the outermost seats - the valence electrons - explained why the columns of the table share their chemistry. Then two atoms met, the energy well between them explained why bonding happens at all, a single continuum from covalent to polar to ionic collapsed the old zoo of bond types into one axis, and those same valence electrons became a working notation for assembling molecules.

One rule did all of that work, applied honestly at every step: electrons go to the lowest energy available, given the constraints in front of them. The constraints kept changing - one nucleus, then many electrons, then many atoms - but the rule never did. That is what made this a single course instead of five.