  Electron-positron interactions have been utilized in various fields of
science. Here we develop time-dependent multi-component density functional
theory to study the coupled electron-positron dynamics from first principles.
We prove that there are coupled time-dependent single-particle equations that
can provide the electron and positron density dynamics, and derive the formally
exact expression for their effective potentials. Introducing the adiabatic
local density approximation to time dependent electron-positron correlation, we
apply the theory to the dynamics of a positronic lithium hydride molecule under
a laser field. We demonstrate the significance of electron-positron dynamical
correlation by revealing the complex positron detachment mechanism and the
suppression of electronic resonant excitation by the screening effect of the
positron.
