Time-dependent density functional theory (TDDFT) is a powerful approach for absorption cross sections; however, due to the quadratic or cubic scaling of TDDFT, large scale simulations are very expensive. We developed and applied a method in which TDDFT is solved with significantly reduced computational costs. This method, labeled stochastic time-dependent density functional theory (sTDDFT), takes a statistical average of propagated purified stochastic orbitals, which eliminates the need for finding out Kohn-Sham orbitals. This results in a sublinear scaling O(<i>N</i><sup>0.5</sup>) of the method. The stochastic TDDFT method was used to solve for the absorption cross section of gold nano-clusters, containing up to ~10,000 electrons, by far the largest ever done quantum mechanically.

Fully quantum mechanical TDDFT for giant gold clusters with up to 10,000 electrons with stochastic TDDFT

251st National Meeting (2016)

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