What are bonds?

Lewis structures for ${\mathrm{H}}_2$${\mathrm{H}}_2$H_(2)\mathrm{H}_{2}${\mathrm{H}}_2$ and water:

Covalent bonding is a quantum phenomenon - it has no classical analog. Consider the $\mathrm{H}-\mathrm{H}$$\mathrm{H}-\mathrm{H}$H-H\mathrm{H}-\mathrm{H}$\mathrm{H}-\mathrm{H}$ bond in ${\mathrm{H}}_2$${\mathrm{H}}_2$H_(2)\mathrm{H}_{2}${\mathrm{H}}_2$. When two H atoms approach each other and their 1s orbitals overlap, a bond is formed. This means that the energy is lower when the nuclei are close together (but not too close), as shown in the graph. This energy lowering is the bond. The H-H bond is not a separate physical entity connecting the H atoms but is simply the low energy region of the energy-vs-distance curve at right.

Classical and quantum effects combine to lower the energy in the bonding region. Coulomb's Law gives the classical electrostatic force between charged particles (like charges repel, opposite charges attract). Two quantum effects are needed to make a covalent bond. One is the Heisenberg uncertainty principle, $\mathrm{\Delta }q\mathrm{\Delta }p\ge \hslash /2$$\mathrm{\Delta }q\mathrm{\Delta }p\ge \hslash /2$Delta q Delta p >= ℏ//2\Delta q \Delta p \geq \hbar / 2$\mathrm{\Delta }q\mathrm{\Delta }p\ge \hslash /2$, where $\mathrm{\Delta }q$$\mathrm{\Delta }q$Delta q\Delta q$\mathrm{\Delta }q$ is the spatial extent of the electron density (uncertainty in electron position), $\mathrm{\Delta }p$$\mathrm{\Delta }p$Delta p\Delta p$\mathrm{\Delta }p$ is the range of electron momenta, and $\hslash$$\hslash$ℏ\hbar$\hslash$ is

Planck's constant divided by $2\pi$$2\pi$2pi2 \pi$2\pi$. The size of the space in which electrons move ( $\mathrm{\Delta }q$$\mathrm{\Delta }q$Delta q\Delta q$\mathrm{\Delta }q$, orange regions) is larger in ${\mathrm{H}}_2$${\mathrm{H}}_2$H_(2)\mathrm{H}_{2}${\mathrm{H}}_2$ than in an H atom. This implies that $\mathrm{\Delta }p$$\mathrm{\Delta }p$Delta p\Delta p$\mathrm{\Delta }p$ is smaller in ${\mathrm{H}}_2$${\mathrm{H}}_2$H_(2)\mathrm{H}_{2}${\mathrm{H}}_2$ than in an H atom. Bond formation creates a space in which the average electron momentum $p$$p$pp$p$ is lower. This reduces the electronic kinetic energy ( $=p^2/2m$$=p^2/2m$=p^(2)//2m=p^{2} / 2 m$=p^2/2m$ ). As a result, molecules prefer to adopt geometries in which the electron density is delocalized (spread out), because a low energy molecule is formed with higher probability than an isomeric high energy molecule.

Octet Rule: A molecule is stable only if each atom shares 8 valence electrons.

• For a bond, each atom shares the electron pair. Both electrons are part of the octets of each atom.
• Both electrons of a lone pair are assigned to a single atom.
  

  

Atomic orbitals

s
${\mathbf{p}}_{\mathbf{x}}$${\mathbf{p}}_{\mathbf{x}}$p_(x)\mathbf{p}_{\mathbf{x}}${\mathbf{p}}_{\mathbf{x}}$
${\mathbf{p}}_{\mathbf{y}}$${\mathbf{p}}_{\mathbf{y}}$p_(y)\mathbf{p}_{\mathbf{y}}${\mathbf{p}}_{\mathbf{y}}$
${\mathrm{p}}_{\mathrm{z}}$${\mathrm{p}}_{\mathrm{z}}$p_(z)\mathrm{p}_{\mathrm{z}}${\mathrm{p}}_{\mathrm{z}}$

Ground states of $\mathrm{C},\mathrm{N}$$\mathrm{C},\mathrm{N}$C,N\mathrm{C}, \mathrm{N}$\mathrm{C},\mathrm{N}$ atoms

Nitrogen

$1\mathrm{s}\uparrow \downarrow$$1\mathrm{s}\uparrow \downarrow$1suarr darr1 \mathrm{~s} \uparrow \downarrow$1\mathrm{s}\uparrow \downarrow$

On each carbon atom, s and p AOs mix to form a pair of sp hybrid AOs:

Carbon-carbon triple bond

Carbon $\mathrm{s},{\mathrm{p}}_{\mathrm{x}}$$\mathrm{s},{\mathrm{p}}_{\mathrm{x}}$s,p_(x)\mathrm{s}, \mathrm{p}_{\mathrm{x}}$\mathrm{s},{\mathrm{p}}_{\mathrm{x}}$ and ${\mathrm{p}}_{\mathrm{y}}\mathrm{AOs}$${\mathrm{p}}_{\mathrm{y}}\mathrm{AOs}$p_(y)AOs\mathrm{p}_{\mathrm{y}} \mathrm{AOs}${\mathrm{p}}_{\mathrm{y}}\mathrm{AOs}$ combine to form $3{\mathrm{sp}}^2\mathrm{AOs}$$3{\mathrm{sp}}^2\mathrm{AOs}$3sp^(2)AOs3 \mathrm{sp}^{2} \mathrm{AOs}$3{\mathrm{sp}}^2\mathrm{AOs}$ in the $\mathrm{x}-\mathrm{y}$$\mathrm{x}-\mathrm{y}$x-y\mathrm{x}-\mathrm{y}$\mathrm{x}-\mathrm{y}$ plane.

Side view

Top view

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Carbon $\mathrm{s},{\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}},{\mathrm{p}}_{\mathrm{z}}$$\mathrm{s},{\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}},{\mathrm{p}}_{\mathrm{z}}$s,p_(x)p_(y),p_(z)\mathrm{s}, \mathrm{p}_{\mathrm{x}} \mathrm{p}_{\mathrm{y}}, \mathrm{p}_{\mathrm{z}}$\mathrm{s},{\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}},{\mathrm{p}}_{\mathrm{z}}$ combine to form four ${\mathrm{sp}}^3$${\mathrm{sp}}^3$sp^(3)\mathrm{sp}^{3}${\mathrm{sp}}^3$ hybrid AOs with tetrahedral symmetry.

Predicting hybridization, given the bond connectivity

1. Count the number of atoms + lone pairs bound to an atom
   ${\mathrm{sp}}^3$${\mathrm{sp}}^3$sp^(3)\mathrm{sp}^{3}${\mathrm{sp}}^3$ atoms + lone pairs = 4
   sp2 atoms + lone pairs = 3
   sp 2 atoms
2. Every hybridized atom is associated with a bond angle, which is a measurable quantity. Hybridization is uniquely defined only for atoms bound to $\ge 2$$\ge 2$>= 2\geq 2$\ge 2$ other atoms, which defines a bond angle.
   ${\mathrm{NH}}_3$${\mathrm{NH}}_3$NH_(3)\mathrm{NH}_{3}${\mathrm{NH}}_3$
   
   [NH]
   
   N 3 atoms +1 lone pair ${\mathbf{s}\mathbf{p}}^{\mathbf{3}}$${\mathbf{s}\mathbf{p}}^{\mathbf{3}}$sp^(3)\mathbf{s p}^{\mathbf{3}}${\mathbf{s}\mathbf{p}}^{\mathbf{3}}$
   
   [NH]N
   
   ${\mathrm{H}}_2\mathrm{O}$${\mathrm{H}}_2\mathrm{O}$H_(2)O\mathrm{H}_{2} \mathrm{O}${\mathrm{H}}_2\mathrm{O}$
   
   [OH2+]

• 2 atoms + 2 lone pairs ${\mathbf{s}\mathbf{p}}^{\mathbf{3}}$${\mathbf{s}\mathbf{p}}^{\mathbf{3}}$sp^(3)\mathbf{s p}^{\mathbf{3}}${\mathbf{s}\mathbf{p}}^{\mathbf{3}}$
  
  CC=NCO[TlH]
  
  
  CC=NC(C)O
  
  
  [13CH3][13CH2][13CH2]OCC=O

Common structures with octets on $\mathrm{C},\mathrm{N},\mathrm{O}$$\mathrm{C},\mathrm{N},\mathrm{O}$C,N,O\mathrm{C}, \mathrm{N}, \mathrm{O}$\mathrm{C},\mathrm{N},\mathrm{O}$ :

Drawing structures:
How to show bond connectivity

• Draw C-C bonds, leaving out C & H labels, except that H should be included if it is bound to a heteroatom (not C ).
• C atoms are located at corners (intersection of 2 or more $\mathrm{C}-\mathrm{C}$$\mathrm{C}-\mathrm{C}$C-C\mathrm{C}-\mathrm{C}$\mathrm{C}-\mathrm{C}$ bonds) and at the end of a chain.
• Number of H atoms bound to C is implied by the octet rule.

Molecule above:

CC/C=C1/CC2CC(C#N)CC2CC1=O

C#CCC1=CCNC(CC)C1

Revise the above 2 structures to include all $\mathrm{C}-\mathrm{H}$$\mathrm{C}-\mathrm{H}$C-H\mathrm{C}-\mathrm{H}$\mathrm{C}-\mathrm{H}$ bonds on each carbon.