Application de la mecanique quantique a la resolution de problemes de spectroscopie: Developpement de methodes pour le calcul de proprietes d'etats metastables

In the present thesis we develop numerical methods to extract information on properties of metastable states. First, we study the photodissociation of gazeous HF in a strong, chirped electromagnetic field. The evolution of the system can be characterized by the time dependant Schrodinger equation. We propose here a novel scheme for solving the equation based on the direct numerical integration in the interaction representation using a cleverly defined preconditioner.;Second, we study the energies and wavefunctions of metastable states of the acetylene-vinylidene system, which is one of the simplest isomerization reaction. These vibrational metastable states are at very high energy (57 kcal/mol) and have therefore not yet been characterized exactly. We have developed a new iterative method based on the Lanczos algorithm in combination with a particular contracted basis in order to simultaneously obtain eigenvalues and eigenvectors of the Hamiltonian. We have adapted and parallelized a recently published method as well as implemented a local reorthogonalization scheme. The longest lived vinylidene states have been obtained at what is believed to be spectroscopic accuracy.;Third, we develop a method for studying resonance states of HCO. A complex absorbing potential (CAP) is usually needed in order to remove the asymptotic part of their wavefunction. We have developed, based on recently published ideas, a method that renders the calculation of resonance states efficient while avoiding complex arithmetic. A basis of damped eigenvectors is obtained from a variant of the Lanczos algorithm and used to minimize the perturbation of the Hamiltonian by the CAP. The new scheme is very robust and a "black box" generalization of the ideas is proposed for solving general real unsymmetric eigenproblems.;Keywords: Molecular dynamics, theoretical spectroscopy, method development, metastables state, resonance, photodissociation, isomerization.