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Mathematics for Physics

222 Chemical Bonding

A strong, lasting attraction between atoms that is used to hold them together as stable molecules and solid crystals.

The electrostatic origin of the bond. Atoms stick together because positive nuclei and negative electrons attract each other. The bonded pair has lower energy than the separated atoms. This principle is used to define a chemical bond as an energy well in the internuclear potential.

The bond dissociation energy is

\[ D_{e} = E(\infty) - E(R_{e}) \]

where

  • \(D_{e}\) is the electronic dissociation energy.
  • \(E(\infty)\) is the energy of the separated atoms.
  • \(E(R_{e})\) is the energy at the equilibrium bond length.
  • \(R_{e}\) is the equilibrium internuclear distance.

Shared electron density. When atoms come close, outer electrons feel both nuclei and gather between them. This principle is used to describe a covalent bond as shared electron density that lowers the energy.

The equilibrium bond length. The bond settles at the distance where attraction and repulsion balance and the energy is lowest. This principle is used to fix the equilibrium bond length.

The equilibrium bond-length condition is

\[ \Bigl(\dfrac{dE}{dR}\Bigr)_{R_{e}} = 0 \]

where

  • \(E\) is the internuclear potential energy.
  • \(R\) is the internuclear distance.
  • \(R_{e}\) is the equilibrium bond length.

The opposite-spin requirement. Electrons that share the space between the nuclei must have opposite spins. Matching spins raise the energy and push the atoms apart. This principle is used to explain why a covalent bond holds two electrons of opposite spin.

The repulsive wall. Forcing atoms closer than \(R_{e}\) raises the energy sharply because the nuclei and electron clouds resist further compression. This principle is used to explain the steep repulsive wall of the potential curve.

Note: The opposite-spin requirement is the Pauli restriction on a bonding pair.

222.1 References

  1. Levine, I. N. Physical Chemistry. Ch. 19 — molecular electronic structure.
  2. Atkins, P., de Paula, J., & Keeler, J. Atkins’ Physical Chemistry. Focus 9 — molecular structure.
  3. Feynman, R. P., Leighton, R. B., & Sands, M. The Feynman Lectures on Physics. Vol. I Ch. 12 and Ch. 14; Vol. III Ch. 4 and Ch. 10.