Full and Ab Initio Multiple Spawning

This Chapter describes themethod for non-adiabatic quantum molecular dynamics called Full Multiple Spawning. The Full Multiple Spawning framework proposes to portray nuclear wave functions by linear combinations of classically-traveling multi-dimensional Gaussian functions, called trajectory basis functions. The number of trajectory basis functions can be adaptedwhen needed during the excited-state dynamics through a spawning algorithm, and all basis functions are coupled together. Hence, Full Multiple Spawning is a formally exact method for non-adiabatic dynamics in the limit of a large number of basis functions. Full Multiple Spawning can be extended to the description of light/matter interaction or the inclusion of spin-orbit coupling effects. Two controlled approximations can be performed on the Full Multiple Spawning equations and lead to the Ab InitioMultiple Spawning technique, which allows for on-the-fly non-adiabatic quantum dynamics of medium-size molecules. In addition to describing the formalism and algorithms of the Full- and Ab Initio Multiple Spawning, this Chapter presents a dissection of a typical Ab InitioMultiple Spawning dynamics run, aswell as different successful applications of this technique.