Numerical Methods for Quantum Dynamics and their Applications in Chemistry

Abstract

As chemistry advances into ultrafast and complex molecular processes, understanding quantum effects in reactions like electron and energy transfer is crucial. Developing new computational methods to simulate quantum dynamics in realistic systems and their complex environments is essential.Chemical systems are inherently quantum many-body systems, making their exact simulation a formidable challenge due to the exponential scaling of computational resources required. Tensor network approaches to quantum many-body systems have emerged as efficient representations of quantum states in these systems. In this work, we developed matrix product states in the chain-mapped interaction picture and demonstrated that this approach is computationally superior to the conventional chain mapping method.We develop advanced numerical tools, including tensor networks, path integral resummation methods, and quantum master equations, to enable accurate modeling of quantum coherence, entanglement, and environmental effects in systems ranging from small molecules to large assemblies. These methods are applied to simulate processes such as electron and energy transfer in multi-acceptor systems, which are critical to materials science, catalysis, and biological systems. Our results reveal how quantum effects and molecular structure interplay to enhance or regulate chemical processes. By bridging theory and experiment, these computational advances offer chemists powerful tools to predict, interpret, and design complex chemical systems.