Diabatic representation

A diabatic representation describes coupled electronic states using a basis chosen to vary smoothly with nuclear geometry, often reducing the derivative couplings that appear in an adiabatic basis. In exchange, the electronic energy matrix generally has off-diagonal entries. It is a representation of coupled states, not a claim that the states never interact.

For a two-state example with nuclear coordinate $R$,The diagonal diabatic curves cross at $R=0$, while their coupled adiabatic eigenvalues have an avoided crossing when $V\ne 0$. This makes electron transfer and nonadiabatic reaction models easier to interpret. An exactly derivative-coupling-free basis need not exist globally for every multidimensional molecular problem.