There is, however, no longer a need to restrict oneself to purely classical simulations. In the last decades, progress has been made towards pushing the limits imposed by the computational cost of exact or nearly exact quantum mechanical approaches (like time-dependent wavepacket methods, e.g., the multiconfiguration time-dependent Hartree, and even exact spectroscopic methods ). Less expensive but more approximate computational methods are also available, such as semiclassical initial value representation, 8 approximated path-integral methods, nonadiabatic ring-polymer molecular dynamics and nonadiabatic quantum instanton theory -all of which have been applied to nonadiabatic processes.