Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals

Density functional theory (DFT) is having increasing success in predicting excitation energies using the methods of time-dependent DFT. As a result, it should be possible to generate potential energy surfaces for excited states by adding the excitation energy, as a function of geometry, to the ground-state energy. It is easier to find stationary points such as minima and transition states if the gradient of the energy is known. The present Letter extends earlier work on the gradients on excited-state surfaces using SCF and LDA (local density approximation) methods, to use gradient-corrected and hybrid functionals. Some examples of geometry optimisations are given.