Université de Cergy-Pontoise, France.
On the Computation of Excited
States with MCSCF Methods
We discuss the theoretical and practical problems arising when
trying to compute excited states of electons in a molecular system, by
multiconfiguration (MCSCF) methods. These nonlinear models approximate the
linear Schrödinger model. Due to the MCSCF nonlinearity, a theoretical
definition of what should be a MCSCF excited state is not clear at all. We
compare various definitions used in Quantum Chemistry. We in particular
stress that some defects may lead to important computational problems,
already observed in Quantum Chemistry (root flipping).
We then propose a definition of MCSCF excited states based on a solid
mathematical ground and compare it with the most used methods. We finally
provide numerical results for two-electron systems.