High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes

TL;DR

This paper demonstrates that hierarchical equations of motion (HEOM) can be efficiently solved for larger light-harvesting systems using GPU acceleration, enabling detailed studies of energy transfer with memory effects at physiological temperatures.

Contribution

The authors develop a GPU-accelerated implementation of HEOM, allowing for large-scale simulations of energy transfer in light-harvesting complexes beyond small systems.

Findings

HEOM can be efficiently solved for larger systems with GPU acceleration.

Memory effects significantly influence energy transfer efficiency.

Approximate methods may not accurately capture the dynamics compared to HEOM.

Abstract

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require to consider time non-local propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments (J. Chem. Phys., 130, p. 234111, 2009), which plays a significant role in photosynthetic electronic energy transfer. HEOM are often used as a reference for other approximate methods, but have been implemented only for small systems due to their adverse computational scaling with the system size. Here, we show that HEOM are also solvable for larger systems, since the underlying algorithm is ideally suited for the usage of graphics processing units (GPU). The tremendous reduction in computational time due to the GPU allows us to perform a systematic study of the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO) light-harvesting complex at physiological temperature under full consideration of memory-effects. We find that approximative methods differ qualitatively and quantitatively from the HEOM results and discuss the importance of finite temperature to achieve high energy-transfer efficiencies.