04/14 Chemical Bonding and Molecular Structure

1. How atoms bond

Atoms bond because their valence electrons can be rearranged into lower-energy, more stable arrangements. Bonding models connect electron arrangement with observable properties such as formula, bond length, bond angle, polarity, melting point, conductivity, and magnetism.

In an ionic bond, electrons are transferred sufficiently that oppositely charged ions form. A neutral atom that loses electrons becomes a cation, while an atom that gains electrons becomes an anion. Ionic compounds usually involve metals and nonmetals and form extended three-dimensional crystal lattices rather than separate molecules.

For example:

The ions combine in a ratio that gives an electrically neutral formula unit:

The formula $\ce{MgCl2}$ means that the simplest ratio is one $\ce{Mg^{2+}}$ ion to two $\ce{Cl-}$ ions. Ionic solids are typically rigid, brittle, and poor electrical conductors because their ions are fixed in place. When molten or dissolved, their ions can move, allowing electrical conduction.

In a covalent bond, atoms share electron pairs. Covalent bonding commonly occurs between nonmetals and produces discrete molecules such as $\ce{H2O}$, $\ce{CO2}$, and $\ce{NH3}$. A single, double, or triple bond contains one, two, or three shared pairs, respectively. Sharing may be unequal when one atom attracts electrons more strongly; this produces a polar covalent bond.

Takeaway: Ionic bonding is dominated by attraction between ions, whereas covalent bonding is based on shared electron pairs. Both models relate electron behavior to material properties.

2. Building Lewis structures

A Lewis structure is a two-dimensional electron-bookkeeping model. It uses lines for shared electron pairs and dots for lone-pair electrons. It helps establish connectivity and electron-pair arrangements, but it does not directly show three-dimensional shape.

To count total valence electrons:

1. Add the valence electrons from every atom.

2. Add one electron for each negative charge.

3. Subtract one electron for each positive charge.

For $\ce{NO3^-}$, the total is

A practical construction sequence is:

1. Choose a skeletal arrangement. Hydrogen is terminal, and the least electronegative atom other than hydrogen is commonly central.

2. Connect atoms with single bonds.

3. Complete terminal-atom octets, remembering that hydrogen requires only two electrons.

4. Place remaining electrons on the central atom.

5. Form multiple bonds when needed to give the central atom an appropriate electron count.

6. Put an ion in brackets and label its overall charge.

7. Recount the electrons and check formal charges.

For water, the count is

Two electron pairs form the two $\ce{O-H}$ bonds, and the remaining four electrons form two lone pairs on oxygen. Thus, oxygen has four electron regions: two bonding regions and two lone-pair regions.

The octet rule is useful but not universal. $\ce{BeCl2}$ and $\ce{BF3}$ may have incomplete octets, $\ce{NO}$ has an odd number of electrons, and species such as $\ce{SF6}$ or $\ce{PCl5}$ may be drawn with expanded valence shells.

Takeaway: Build structures by controlling the total electron count, completing terminal atoms first, and checking both the overall charge and the central atom's electron arrangement.

3. Evaluating electron arrangements

Formal charge provides a consistent way to compare alternative electron arrangements. For an atom in a Lewis structure,

where $V$ is the valence-electron count of the isolated atom, $N$ is the number of nonbonding electrons assigned to the atom, and $B$ is the number of bonding electrons around it.

The formal charges must add to the species' overall charge. In one important Lewis structure for carbon monoxide, \ce{C#O}, each atom has one lone pair. The assignments are

Although this assignment may seem surprising, formal charge is a model-based accounting tool, not a direct measurement of partial charge.

When comparing valid structures, prefer arrangements that:

• use the correct total number of electrons;

• place formal charges as close to zero as possible;

• place negative formal charge on the more electronegative atom when possible;

• provide appropriate octets when possible.

Takeaway: Formal charge helps select the most plausible Lewis representation, but it should not be interpreted as proof that atoms in a covalent molecule carry isolated whole-number charges.

4. Resonance and electron delocalization

Some molecules and ions require more than one Lewis representation. Resonance structures have the same arrangement of atoms but different placements of electrons. Only lone pairs, multiple bonds, and formal charges move; the atoms do not move.

The nitrate ion, $\ce{NO3^-}$, can be represented by three equivalent structures in which the $\ce{N=O}$ double bond occupies a different position. The actual ion is a resonance hybrid, not a species that switches back and forth among separate structures. Its $\pi$ electrons and negative charge are delocalized over the three oxygen atoms.

As a result, all three $\ce{N-O}$ bonds are equivalent and have properties between those of typical single and double bonds. A useful average bond-order estimate is

The resonance hybrid is generally more stable than any one contributing structure. The same idea is useful for polyatomic ions, conjugated organic molecules, aromatic systems, and $\ce{O3}$.

Takeaway: Resonance is a model for electron delocalization. It changes electron placement while preserving atomic connectivity and total electron count.

5. Predicting molecular geometry

VSEPR theory treats each single bond, double bond, triple bond, or lone pair around a central atom as one electron region. These regions repel one another and arrange themselves as far apart as possible. Lone pairs usually repel more strongly than bonding pairs because their electron density is concentrated closer to the central atom.

The main electron-domain arrangements are:

• Two regions: linear, with an ideal angle of $180^\circ$.

• Three regions: trigonal planar, with an ideal angle of $120^\circ$.

• Four regions: tetrahedral, with an ideal angle of $109.5^\circ$.

• Five regions: trigonal bipyramidal, with angles of $90^\circ$, $120^\circ$, and $180^\circ$.

• Six regions: octahedral, with angles of $90^\circ$ and $180^\circ$.

Electron-domain geometry includes both bonding and lone-pair regions. Molecular geometry describes only the positions of the atoms. Common examples include:

• $\ce{CO2}$: two regions and linear geometry.

• $\ce{BF3}$: three regions and trigonal planar geometry.

• $\ce{CH4}$: four regions and tetrahedral geometry.

• $\ce{NH3}$: four regions, three bonds and one lone pair, giving trigonal pyramidal geometry with angles near $107^\circ$.

• $\ce{H2O}$: four regions, two bonds and two lone pairs, giving bent geometry with angles near $104.5^\circ$.

• $\ce{PCl5}$: five regions and trigonal bipyramidal geometry.

• $\ce{SF6}$: six regions and octahedral geometry.

For $\ce{NH3}$, nitrogen has three $\ce{N-H}$ bonds and one lone pair. The electron-domain geometry is tetrahedral, but the molecular geometry is trigonal pyramidal because the lone pair is not counted as an atom position. Its stronger repulsion compresses the $\ce{H-N-H}$ angles below $109.5^\circ$.

Takeaway: Count electron regions first, identify the electron-domain geometry, and then ignore lone pairs when naming the molecular geometry.

6. Connecting shape to polarity

A bond is polar when its electrons are shared unequally. The more electronegative atom has a partial negative charge, $\delta^-$, while the less electronegative atom has a partial positive charge, $\delta^+$. A bond dipole points toward the more electronegative atom.

Molecular polarity depends on the vector sum of all bond dipoles, so three-dimensional shape matters as much as electronegativity.

• $\ce{CO2}$ has polar $\ce{C=O}$ bonds, but its linear shape makes the dipoles cancel; the molecule is nonpolar.

• $\ce{H2O}$ has polar $\ce{O-H}$ bonds and a bent shape, so its dipoles do not cancel; the molecule is polar.

• $\ce{CCl4}$ is tetrahedral and nonpolar overall because its four identical bond dipoles cancel symmetrically.

• $\ce{CH3Cl}$ is polar because replacing one H in methane with Cl removes the symmetry needed for cancellation.

To determine Molecular polarity:

1. Draw the Lewis structure.

2. Determine the molecular geometry.

3. Identify polar bonds using electronegativity differences.

4. Add the bond dipoles as vectors.

5. Decide whether the net vector is zero.

Polarity helps explain differences in solubility, boiling point, intermolecular forces, and molecular interactions.

Takeaway: Polar bonds do not guarantee a polar molecule. The net molecular dipole depends on both bond polarity and molecular symmetry.

7. Molecular orbitals and magnetic behavior

Lewis structures and VSEPR theory are localized models. Molecular orbital theory extends the description by treating electrons as occupying orbitals that can spread over the entire molecule.

When two atomic orbitals combine with suitable energies, symmetry, and spatial overlap, they produce two molecular orbitals:

• a lower-energy bonding molecular orbital formed by constructive overlap;

• a higher-energy antibonding molecular orbital formed by destructive overlap, commonly marked with an asterisk, such as $\sigma^*$ or $\pi^*$.

Sigma orbitals, written $\sigma$, have electron density concentrated along the internuclear axis. Pi orbitals, written $\pi$, have electron density above and below that axis. Molecular orbitals are filled from lower to higher energy, with no more than two electrons per orbital and with unpaired electrons maximized among equal-energy orbitals.

Bond order is calculated by

For $\ce{H2}$, both electrons occupy a bonding $\sigma_{1s}$ orbital:

For hypothetical $\ce{He2}$, two electrons would occupy a bonding orbital and two would occupy an antibonding orbital:

Thus, the model does not predict a stable ordinary covalent bond for $\ce{He2}$. A larger bond order generally corresponds to a shorter, stronger bond.

MO theory also explains why oxygen is paramagnetic. In $\ce{O2}$, two electrons occupy separate antibonding $\pi^*$ orbitals and remain unpaired, so oxygen is attracted to a magnetic field.

Takeaway: Lewis structures efficiently describe connectivity and electron counting, while molecular orbital theory gives deeper explanations for bond order, delocalization, stability, and magnetism.

8. An integrated problem-solving workflow

Use the following sequence to solve a bonding problem systematically:

1. Identify the species and its charge.

2. Count total valence electrons.

3. Construct a valid Lewis structure.

4. Calculate formal charges.

5. Check for resonance.

6. Count electron regions around each central atom.

7. Assign electron-domain and molecular geometries.

8. Evaluate bond polarity and the vector sum of dipoles.

9. If needed, use molecular orbital theory to calculate bond order or explain magnetism.

10. Relate the model to measurable properties such as bond length, boiling point, conductivity, or magnetic response.

For $\ce{NH4+}$, the electron count is

Nitrogen forms four $\ce{N-H}$ single bonds and has no lone pair. Four bonding regions give a tetrahedral molecular geometry with bond angles near $109.5^\circ$. Nitrogen has formal charge

Each hydrogen has formal charge zero, so the total charge is $+1$, as required.

This workflow prevents common errors: omitting the charge when counting electrons, confusing electron-domain geometry with molecular geometry, treating a resonance hybrid as a rapidly changing structure, or assuming that every polar bond makes the entire molecule polar.

Final takeaway: Start with electrons and connectivity, then progress through charge, delocalization, shape, polarity, and—when necessary—molecular orbitals. Each model answers a different part of the bonding problem.