A continuous spawning method for nonadiabatic dynamics and validation for the zero-temperature spin-boson problem

A four-dimensional spin-boson model is used to study the convergence and accuracy of the full multiple spawning (FMS) method using two spawning algorithms. The original spawning algorithm, based on the idea of effective non-adiabatic coupling, is expected to be optimal when the coupling between electronic states is either spatially or temporally localized. The new "continuous spawning" algorithm ensures that at all times there is a (user defined) minimal overlap between a basis function traveling on one electronic state and one (or more) basis functions traveling on the other electronic state. The algorithm is expected to be numerically efficient when the electronic states are coupled by a constant, position- independent term, as is the case in spin-boson models. The fast convergence of the algorithm is demonstrated by direct comparison to numerically converged results obtained using the multi -configuration time-dependent Hartree method. The results of the FMS dynamics are also compared to the more classical surface-hopping and Ehrenfest methods. The surface-hopping and Ehrenfest methods are shown to be sensitive to the particular method used to choose the trajectory initial conditions (quasi-classical vs. Wigner), while the FMS method is not very sensitive to this choice.