COMPUTATION METHODS EMPLOYED IN THE SELF-CONSISTENT TIME-DEPENDENT, HARTREE-FOCK CALCULATION FOR A REACTIVE MOLECULAR COLLISION

A fully self-consistent time-dependent Hartree-Fock calculation of the molecular reactive scattering system, collinear H+ + H2, has recently been shown to be a viable method for obtaining the reaction probability, charge exchange probability, and translational to vibrational energy transfer. The calculation couples the time-dependent Hartree-Fock equation for the electronic wavefunction, represented by a single Slater determinant, to the classical equations for the motion of the nuclei. This coupling is achieved by computing the force on the nuclei from the variation of the electronic energy at each time step. The nuclei's position and electronic wavefunction are co-propagated in time from the initial asymptotic scattering state until the collision products separate in the exit channel. In this self-consistent calculation one can identify four major parts that must be calculated concurrently. The first of these is the time propagation of the electronic wavefunction. The second is the determination of the forces on the nuclei from the variation of the electronic energy. The third is the solution of Poisson's equation for the electron-electron potential, V(e). The fourth is the propagation of the position and velocities of the nuclei according to the classical equations of motion. Each of these parts and their interrelation in the overall calculation is discussed here.