The Potential Energy Curve and Chemical Bonding

The nuclei in a molecule move in the force field created by the electrons. The motion of the light electrons is separable from that of the slow nuclei; The force felt by the nuclei may be used to define a potential energy which is a function of position only, U(r)

where F is the force exerted on the nuclei by the effective field of the electrons in a given electronic state. Every molecule can exist in more than one electronic state and has a unique potential function for each state. Normally, only the lowest electronic state of a molecule is populated at room temperature . This state is called the electronic ground state. The molecule can be excited from the ground state to another electronic state which will have greater energy and a completely different potential surface. Chemical reactions sometimes cause a molecule to be created in an excited electronic state, we will use a laser for this purpose.

Examine the potential curves for two states in the I₂ molecule. The ground state of the molecule is labeled by its electronic symmetry as . An excited state can be produced by the absorption of visible light. The two states even correspond to different dissociation products with the excited state correlating to one ground and one excited iodine atom.

The potential function defines for us the nature of a particular bond: where the nuclei would rest if the molecule were not vibrating (the equilibrium bond length, r_e), how much energy is required to break the bond (the dissociation energy, D_e or D₀ depending on whether you mean from the bottom of the potential or the lowest vibrational level), and the stiffness of the bond (the vibrational frequency, _e). Note that each electronic state of the molecule has its own dissociation limit, bond length and vibrational frequency.