Potential Energy Surfaces for Diatomic Molecules

We saw in section 3.1 that the potential energy surface of a molecular system is defined as the electronic potential energy including nuclear repulsion, at a given nuclear configuration (equation (3.8)). This is found by solving the electronic Schrödinger equation (equation (3.6), see also equation (3.4) for the electronic Hamiltonian operator) for a given nuclear configuration (inter-nuclear distances and angles).
A potential energy surface is the result of solving equation (3.6) for many nuclear configurations – giving the electronic potential energy including nuclear repulsion of the system as a function of the nuclear coordinates.

In a diatomic molecule AB, there is only one nuclear coordinate; the inter-atomic distance R_AB. In this case, the potential energy ‘surface’ is more accurately termed a potential energy curve. It describes the potential energy of the system, U(R), as the two atoms are brought closer to, or moved away from, one another (Figure 4.1).

Figure 4.1 - Potential energy curve for a bound electronic state of a diatomic molecule

The point at which the curve flattens out at large inter-atomic distances is termed the dissociation limit, and represents a state where the molecule is no longer bound, being instead, two separate atoms.
The dissociation energy, D_e, is the vertical distance between the dissociation limit and the base of the curve, found at the equilibrium bond length, R_eq.
The following Flash animation (Figure 4.2) illustrates the change in energy (watch the slider on the left) and inter-atomic distance (watch the atoms on the right) at different points along the curve:

The curve may not be a bound state – many excited states are unbound, the typical shape of these curves is exponential decay-like, with no minima (Figure 4.3, below).

Figure 4.3 - Potential energy curve for an unbound electronic state of a diatomic molecule