Real-time time-dependent electronic structure theory

Real-time time-dependent electronic structure theory is one of the most promising methods for investigating time-dependent molecular responses and electronic dynamics. Since its first modern use in the 1990s, it has been used to study a wide variety of spectroscopic properties and electronic responses to intense external electromagnetic fields, complex environments, and open quantum systems. It has also been used to study molecular conductance, excited state dynamics, ionization, and nonlinear optical effects. Real-time techniques describe non-perturbative responses of molecules, allowing for studies that go above and beyond the more traditional energy- or frequency-domain-based response theories. Recent progress in signal analysis, accurate treatment of environmental responses, relativistic Hamiltonians, and even quantized electromagnetic fields have opened up new avenues of research in time-dependent molecular response. After discussing the history of real-time methods, we explore some of the necessary mathematical theory behind the methods, and then survey a wide (yet incomplete) variety of applications for real-time methods. We then present some brief remarks on the future of real-time time-dependent electronic structure theory. (C) 2017 Wiley Periodicals, Inc.