  The real-time electronic dynamics on material surfaces is critically
important to a variety of applications. However, their simulations have
remained challenging for conventional methods such as the time-dependent
density-functional theory (TDDFT) for isolated and periodic systems. By
extending the applicability of TDDFT to systems with open boundaries, we
achieve accurate atomistic simulations of real-time electronic response to
local perturbations on material surfaces. Two prototypical scenarios are
exemplified: the relaxation of an excess electron on graphene surface, and the
electron transfer across the molecule-graphene interface. Both the transient
and long-time asymptotic dynamics are validated, which accentuates the
fundamental importance and unique usefulness of an open-system TDDFT approach.
The simulations also provide insights into the characteristic features of
temporal electron evolution and dissipation on surfaces of bulk materials.
