I will discuss our recent development of massively-parallel real-time time-dependent density functional theory (RT-TDDFT) method based on the planewave-pseudopotential formalism and its applications to modeling electronic stopping in condensed matters.

RT-TDDFT provides a convenient framework for numerically studying non- pertubative electron dynamics coupled with lattice (i.e. ions) movements in large systems. Because of the massively parallel nature of modern high-performance computers, development of new numerical algorithms is often not free from considering its parallelizability over large numbers of processors. We have developed a highly-scalable implementation of RT-TDDFT in qb@ll code for studying large extended systems. We will discuss performance of our new implementation over millions of processor cores, reaching the peta-flops performance. I will then discuss its application to the problem of electronic stopping. Electronic stopping describes the transfer of the kinetic energy from a highly- energetic ion to electrons in condensed matter. The projectile ions bear a highly localized electric field that is quite heterogeneous at the atomistic scale, and massive electronic excitations are produced in the process. Electronic stopping has been long studied within linear response theory framework (e.g. Bethe theory). I will discuss how non-equilibrium simulations based on RT-TDDFT enable us to study this electronic excitation process, in particular for the importance case of liquid water under proton irradiation. In addition to determining the energy transfer rate (i.e. electronic stopping power), our work reveals several key features in the excitation dynamics at the mesoscopic and molecular levels in liquid water under proton irradiation.

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