Chemical+dynamics

Once the electronic and nuclear variables are separated (within the Born–Oppenheimer representation), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator (physics) associated to the time-dependent Schrödinger equation (for the full molecular Hamiltonian). In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism. The potential representing the interatomic interaction is given by the potential energy surfaces. In general, the potential energy surfaces are coupled via the vibronic coupling terms. The most popular methods for propagating the wave packet associated to the molecular geometry are:
 * the split operator technique ,
 * the Chebyshev (real) polynomial,
 * the multi-configuration time-dependent Hartree method (MCTDH),
 * the semiclassical method.