MesoHOPS: Size-invariant scaling calculations of multi-excitation open quantum systems.

The photoexcitation dynamics of molecular materials on the 10-100 nm length scale depend on complex interactions between electronic and vibrational degrees of freedom, rendering exact calculations difficult or intractable. The adaptive Hierarchy of Pure States (adHOPS) is a formally exact method that leverages the locality imposed by interactions between thermal environments and electronic excitations to achieve size-invariant scaling calculations for single-excitation processes in systems described by a Frenkel-Holstein Hamiltonian. Here, we extend adHOPS to account for arbitrary couplings between thermal environments and vertical excitation energies, enabling formally exact, size-invariant calculations that involve multiple excitations or states with shared thermal environments. In addition, we introduce a low-temperature correction and an effective integration of the noise to reduce the computational expense of including ultrafast vibrational relaxation in Hierarchy of Pure States (HOPS) simulations. We present these advances in the latest version of the open-source MesoHOPS library and use MesoHOPS to characterize charge separation at a one-dimensional organic heterojunction when both the electron and hole are mobile.

Formally Exact Simulations of Mesoscale Exciton Diffusion in a Light-Harvesting 2 Antenna Nanoarray.

The photosynthetic apparatus of plants and bacteria combine atomically precise pigment-protein complexes with dynamic membrane architectures to control energy transfer on the 10-100 nm length scales. Recently, synthetic materials have integrated photosynthetic antenna proteins to enhance exciton transport, though the influence of artificial packing on the excited-state dynamics in these biohybrid materials is not fully understood. Here, we use the adaptive hierarchy of pure states (adHOPS) to perform a formally exact simulation of excitation energy transfer within artificial aggregates of light-harvesting complex 2 (LH2) with a range of packing densities. We find that LH2 aggregates support a remarkable exciton diffusion length ranging from 100 nm at a biological packing density to 300 nm at the densest packing previously suggested in an artificial aggregate. The unprecedented scale of these formally exact calculations also underscores the efficiency with which adHOPS simulates excited-state processes in molecular materials.

Formally exact simulations of mesoscale exciton dynamics in molecular materials.

Excited state carriers, such as excitons, can diffuse on the 100 nm to micron length scale in molecular materials but only delocalize over short length scales due to coupling between electronic and vibrational degrees-of-freedom. Here, we leverage the locality of excitons to adaptively solve the hierarchy of pure states equations (HOPS). We demonstrate that our adaptive HOPS (adHOPS) methodology provides a formally exact and size-invariant (i.e., ) scaling algorithm for simulating mesoscale quantum dynamics. Finally, we provide proof-of-principle calculations for exciton diffusion on linear chains containing up to 1000 molecules.