The development and applications of semiclassical initial value representation, a promising tool for tackling quantum dynamics

In this review we present an overview of the semiclassical initial value representation (SC-IVR) method, which is a powerful and promising tool for studying real-time quantum dynamics. We first introduce the origin, history, and basic ideas of it. Then its developments and applications in recent years are listed and discussed in detail, covering a range of fields including vibrational spectroscopy, correlation functions, reaction rate constants and nonadiabatic dynamics. By exploring and analyzing these different aspects of SC-IVR, we hope to provide a comprehensive foundational introduction and technical guidance for interested readers. We also hope that new inspirations and potential integration with other fields can be stimulated to further extend its applicability.