= 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 $R$,
$$
H_d(R)=\begin{pmatrix}aR&V\\V&-aR\end{pmatrix},\qquad
E_\pm(R)=\pm\sqrt{a^2R^2+V^2}.
$$
The diagonal diabatic curves cross at $R=0$, while their coupled adiabatic eigenvalues have an <avoided crossing> when $V\ne0$. 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.
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