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# Real‐time time‐dependent electronic structure theory

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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. WIREs Comput Mol Sci 2018, 8:e1341. doi: 10.1002/wcms.1341 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods
Comparison of time convergence for Fourier (left column) and Padé acceleration (right column), for the total z‐dipole contribution to the absorption spectrum (top row), two representative MO contributions to the spectrum (middle), and the resulting total absorption spectrum (bottom row). Note the high spectral density in the Padé accelerated technique, along with the rapid convergence with respect to simulation time. In all, Padé converges seven times faster than conventional Fourier transform—a considerable computational savings. (Reprinted with permission from Ref . Copyright 2016 American Chemical Society.)
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Absorption spectra of acetylene modeled with RT‐TDDFT (green) and non‐Hermitian RT‐TDDFT with an imaginary absorbing potential (orange) compared with an EELS experimental spectrum (blue). The gray lines denote DFT Koopmans’ ionization potentials. The absorbing potential adds a finite lifetime to resonance states and shows dramatic improvement when compared against the experimental spectrum. (Reprinted with permission from Ref . Copyright 2013 American Chemical Society.)
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Absorption spectra for atomic mercury obtained with real‐time electron dynamics. The dynamics utilized an X2C Hamiltonian, which contains an ab initio treatment of spin–orbit coupling. This allows for the observation of the otherwise spin‐forbidden 3P1 transition. (Adapted from Ref with the permission of AIP Publishing.)
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