Abstract
A numerically exact solution of the time-dependent Schr\odinger equation for noninteracting large-spin $(S=10)$ molecules in the presence of crystal-field anisotropy and time-dependent longitudinal magnetic field is performed. Crystal-field parameters and a field sweeping rate to fit experiment on ${\mathrm{Fe}}_{8}$ and ${\mathrm{Mn}}_{12}$ molecules are used. Magnetization steps are found for values of the sweeping field at which anticrossing of two energy levels occurs. The size of the step depends crucially on the field sweeping rate and on the presence of a transverse field. An efficient approximation is proposed in order to reduce the solution of the original $(2S+1)$-level problem to a sequence of two-level problems. This approach allows us to solve the time-dependent Schr\odinger equation with the experimental field sweeping rate, which is prevented in the original $(2S+1)$-level problem because of the huge computing time.
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