2 Theoretical concepts and techniques

Nowadays evaluating potential energy curves is the only obstacle to overcome to perform collisional calculations. Obtaining accurate values of these potential energy curves yield reliable relaxation parameters. The potential energy curves presented here have been calculated in the Born-Oppenheimer approximation (Born & Oppenheimer 1927) and obtained by methods of quantum chemistry (Schaeffer 1977; Jensen 1999). The electronic Schrödinger equation was solved by variational techniques for each internuclear distance giving the electronic energies as eigenvalues. The electronic wave function was obtained by using state average MultiConfiguration Self Consistent Field (MCSCF) method (Werner & Knowles 1985, 1988) which is a natural extension of the one-configuration Self Consistent Field (SCF) method.

At the SCF level, the electronic wave function is an antisymmetrical product of orbitals and electron spin functions and is given by a single determinant (Slater determinant) or configuration. Molecular orbitals that describe the wave function of each electron are determined by the field of the nuclei and the field arising from the average distribution of all the electrons. They are expanded in terms of atomic orbitals (LCAO method) built from a set of Gaussian functions (Boys 1950) in order to facilitate numerical integration. Optimization of the expansion coefficients for each internuclear distance is obtained by minimization of the energy of the electronic state. SCF wave functions give poor value for the relative energies, particularly for large internuclear distances.

To obtain a better accuracy, one must go beyond the SCF level. This can be done by using MCSCF wave functions given by a linear combination of determinants (configurations) built on a set of spinorbitals possibly larger than the set of orbitals occupied in the SCF configuration. Molecular orbitals as well as coefficients of the determinants are optimized at each internuclear distance. This MCSCF approach takes into account a large part of the correlation energy between electrons. In the case of very shallow potential energy curves (like $\Pi$ states of NaH), the more accurate MultiReference Configuration Interaction method (MRCI) that includes all the single and double excitations from the MCSCF wave function is used. All the results were obtained using the MOLPRO package.