As two atoms approach, a potential energy 势能 curve captures the balance of attraction and repulsion. It dips to a minimum at the bond length 键长 (the stable separation) whose depth is the bond energy 键能. Shorter, stronger bonds sit in deeper, tighter wells; more shared pairs (double, triple bonds) give shorter, stronger bonds.
Potential energy is lowest at the bond length; the well depth is the bond energy
An ionic solid 离子固体 is a repeating 3-D lattice 晶格 of alternating cations and anions, held by strong electrostatic attraction. This explains their high melting points, brittleness, and why they conduct only when molten or dissolved (ions freed to move). The lattice energy rises with larger ion charges and smaller ions, so MgO (both $2+/2-$) melts far higher than NaCl (both $1+/1-$).
Ions pack into a giant lattice of alternating positive and negative ions
In a metal, cations sit in a lattice bathed in delocalized 离域 electrons, which explains conductivity, malleability, and luster. An alloy 合金 combines a metal with one or more other elements: a substitutional alloy swaps in similar-sized atoms; an interstitial alloy (like steel) fits small atoms into the gaps, making it harder.
Different-sized atoms in an alloy stop the layers sliding, so it is harderMetallic bonding: positive ions in a sea of delocalised electronsNative copper: metallic bonding gives a shiny, malleable solid with delocalised electrons
A Lewis diagram 路易斯结构 shows valence electrons as bonding pairs and lone pairs 孤对电子, giving most atoms an octet 八隅体 (8 valence electrons; H wants 2). Steps: count total valence electrons, connect atoms with single bonds, complete octets on outer atoms, then form multiple bonds if the central atom is short.
Dot-and-cross diagrams show the bonding pairs and lone pairs in a molecule
Worked example. Draw carbon dioxide, $\text{CO}_2$. Total valence electrons $=4+2(6)=16$. Put C in the centre; single bonds to each O use $4$ electrons and leave the outer O atoms short. Completing octets forces two double bonds, $\text{O}=\text{C}=\text{O}$: each O then has two lone pairs, C has none, and all $16$ electrons are placed with every atom at an octet.
When two or more valid Lewis diagrams differ only in electron placement, one delocalized electron distribution is represented by these contributors – resonance 共振. The molecule does not switch between them. Formal charge 形式电荷 (valence electrons minus lone-pair electrons minus half the bonding electrons) picks the best structure: the one with formal charges closest to zero, and any negative charge on the most electronegative atom.
Worked example. Assign formal charges in the nitrate ion, $\text{NO}_3^{-}$ (one double bond, two single bonds). For N (4 bonds, no lone pairs): $5-0-4=+1$. For the double-bonded O (2 lone pairs): $6-4-2=0$. For each single-bonded O (3 lone pairs): $6-6-1=-1$. The total is $+1+0+(-1)+(-1)=-1$, matching the ion's overall charge – a good check that the structure is drawn correctly. Because the three O atoms are equivalent by resonance, the real ion has three identical bonds.
Ozone has two resonance structures; the real molecule is their hybrid
VSEPR 价层电子对互斥 theory predicts shape: electron pairs (bonds and lone pairs) around a central atom spread out as far apart as possible. Counting electron domains gives the geometry (linear, trigonal planar, tetrahedral, …); lone pairs push bonds closer, bending the shape. Hybridization 杂化 ($sp$, $sp^2$, $sp^3$) describes the mixed orbitals matching that geometry. Molecular shape and bond polarity together decide whether the whole molecule is polar.
Hybridisation and shape: sp3 tetrahedral, sp2 planar, sp linearThe common VSEPR shapes and their bond angles
Worked example. Predict the shape of ammonia, $\text{NH}_3$. Nitrogen has $3$ bonding pairs and $1$ lone pair – four electron domains, so the electron geometry is tetrahedral and the hybridization is $sp^3$. The lone pair is invisible in the shape but still pushes the bonds together, so the molecular shape is trigonal pyramidal with a bond angle of about $107^{\circ}$ (a little less than the ideal $109.5^{\circ}$). The three N–H dipoles do not cancel, so the molecule is polar.
Bonds form when atomic orbitals overlap. Every single bond is one sigma bond σ键 – orbitals overlapping head-on along the line joining the two atoms. A multiple bond adds a pi bond π键, made by $p$ orbitals overlapping sideways above and below that line: a double bond is one sigma + one pi, a triple bond one sigma + two pi. Head-on overlap is more effective, so a sigma bond is stronger (higher bond energy) than a pi bond – which is why a double bond is stronger than a single bond but not twice as strong. A pi bond restricts rotation about the bond. A C=C double bond can give cis and trans forms – geometric isomers 几何异构体 – when each double-bonded carbon has two different attached groups. Ethene does not meet this condition.
Worked example. Count the bonds in ethene, $\text{H}_2\text{C}=\text{CH}_2$. The four C–H bonds are single bonds (one sigma each); the C=C is one sigma plus one pi. So ethene has 5 sigma and 1 pi bond, and that single pi bond is exactly what stops the two $\text{CH}_2$ ends from twisting relative to each other.
Common mistakes.
Naming the molecular shape from the electron geometry. Ammonia has four electron domains (tetrahedral electron geometry), but its molecular shape, which counts atoms only, is trigonal pyramidal; water is bent.
Saying a molecule with polar bonds must be polar. In $\text{CO}_2$ and $\text{CCl}_4$ the bond dipoles cancel by symmetry, so the molecule is non-polar.
Saying resonance structures flip back and forth. The real ion is one delocalized structure; in $\text{NO}_3^{-}$ all three N–O bonds are the same length.
Saying a double bond is twice as strong as a single bond. The extra pi bond is weaker than a sigma bond, so a double bond is stronger but less than twice as strong.
Reading a deeper well on a potential-energy curve as a longer bond. A deeper well means a stronger bond; the minimum's position gives the bond length, and stronger bonds between the same atoms are usually shorter.
Explaining the high melting point of MgO by "more bonds". MgO has larger ion charges ($2+$ and $2-$) and small ions, so the Coulombic attraction, and the lattice energy, is much larger.
Forgetting the ion's charge when counting valence electrons. For $\text{NO}_3^{-}$ add one electron; for a cation subtract them.
Decide the bond type from the atoms: ionic (metal + non-metal, electron transfer), covalent (non-metals, sharing), metallic (sea of delocalised electrons).
An ionic solid conducts only when molten or dissolved (ions free to move), never as a solid.
Draw Lewis structures to satisfy the octet (H wants 2), then use VSEPR — electron pairs spread as far apart as possible — to predict the shape.
Lone pairs take up space and push bonds closer, bending the shape (water is bent, ammonia pyramidal).
A molecule can have polar bonds yet be non-polar overall if its symmetry makes the dipoles cancel ($\text{CO}_2$).
A single bond is 1 sigma bond; a double bond is 1 sigma + 1 pi, a triple bond 1 sigma + 2 pi. Sigma is stronger than pi, and a pi bond blocks rotation, giving cis/trans geometric isomers.