Locating excited states, i.e. SADDLE POINTS in wave function space, by MINIMIZATION
What is it about?
Stable species (like water or carbon dioxide), in order to be reused, must be activated by electronic excitation (like in photosynthesis). And in order to understand which electrons are going to interact, not only the excitation energy, but also the excited state wave function is needed. It is demonstrated that even in the simplest system of helium atom, the standard computation methods (which are proven that in principle yield incorrect excited state wave functions), need large expansions in order to approach the exact answer, whereas the reported method approaches correctly the exact answer even if the truncated wave function is small, (thus, allowing study of larger systems, like catalysts).
Why is it important?
The reported method computes excited state truncated (either large or small) wave functions that approach the exact, without using orthogonality to lower-lying approximants (that would necessarily yield incorrect excited state wave functions). It also recognizes "flipped roots" in energy avoided crossings. It can also be used to immediately improve ground state approximants.