Which mathematical model is used to represent the potential energy of a diatomic covalent bond as a function of bond length?

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To begin, consider what each model represents when describing the potential energy as a function of bond length in a diatomic covalent bond.
Option a: Hooke's Law. This is the simplest harmonic approximation, where the potential energy increases quadratically with displacement from the equilibrium bond length. It works well for small vibrations near the minimum but does not capture anharmonic effects, bond dissociation, or the correct asymptotic behavior at large bond lengths.
Option b: Morse potential. This model introduces anharmonicity by using an exponential term that smoothly approaches a finite dissociation energy as the bond length grows, providing a more accurate description of bond stretching, including bond breaking and the correct curvature near the minimum.
Option c: Lennard-Jones potential. This potential is typically used to describe nonbonded interactions between neutral atoms, particularly van der Waals forces, combining a short-range repulsion and a long-range attraction. It is not tailored to covalent bond formation and dissociation in a diatomic molecule.
Option d: Coulomb's Law. This law quantifies static electrostatic forces between charged particles. While it can be relevant for ionic interactions, it does not capture the covalent bonding energy curve, particularly the bond formation energy or the correct short- and long-range behavior for a neutral diatomic covalent bond.

In summary, the harmonic Hooke model (a) is too simplistic for real bond stretching, the Lennard-Jones potential (c) is intended for intermolecular forces rather than a covalent bond’s internal potential, and Coulomb's Law (d) describes electrostatic interactions that do not govern covalent bond energies. The Morse potential (b) stands out as the appropriate functional form because it models anharmonicity and bond dissociation more faithfully, aligning with how diatomic covalent bonds behave as the bond length varies.

PHAS0006_24-25 Week 4 Quiz

Which mathematical model is used to represent the potential energy of a diatomic covalent bond as a function of bond length?

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