Rapid, far-from-equilibrium processes involving excitation of electronic, vibrational, spin, photon, topological, and other degrees of freedom form the basis of modern technologies, including electronics and optoelectronics, solar energy harvesting and conversion to electrical and chemical energy, quantum information processing, spin- and valleytronics, chemical detection, and medical therapies. Such processes are studied experimentally with various time-resolved spectroscopies that allow scientists to track system's evolution on ultrafast time scales and at close to atomistic level of detail. The availability of various forms of lasing has made such measurements easily accessible to many experimental groups worldwide, to study atoms and small molecules, nanoscale and condensed matter systems, proteins, cells, and mesoscopic materials. The experimental work necessitates parallel theoretical efforts needed to interpret the experiments and to provide insights that cannot be gained through measurements due to experimental limitations.Non-adiabatic (NA) molecular dynamics (MD) allows one to study processes at the atomistic level and in the time domain most directly mimicking the time-resolved experiments. Atomistic modeling takes full advantage of chemical intuition and principles that guide design and fabrication of molecules and materials. It provides atomistic origins of quasi-particles, such as holes, excitons, trions, plasmons, phonons, polarons, polaritons, spin-waves, momentum-resolved and topological states, electrically and magnetically polarized structures, and other abstract concepts. An atomistic description enables one to study realistic aspects of materials, which necessarily contain defects, dopants, surfaces, interfaces, passivating ligands, and solvent layers. Often, such realistic features govern material properties and are hard to account for phenomenologically. NA-MD requires few approximations and assumptions. It does not need to assume that atomic motions are harmonic, that electrons are Drude oscillators, that coupling between different degrees of freedom is weak, that dynamics is Markovian or has short memory, or that evolution occurs by exponential kinetics of transitions between few states. The classical or semiclassical treatment of atomic motions constitutes the main approximation of NA-MD and is used because atoms are 3-5 orders of magnitude heavier than electrons. NA-MD is limited by system size, typically hundreds or thousands of atoms, and time scale, picoseconds to nanoseconds. The quality of NA-MD simulations depends on the electronic structure method used to obtain excited state energies and NA couplings.NA-MD has been largely popularized and advanced in the chemistry community that focuses on molecules. Modeling far-from-equilibrium dynamics in nanoscale and condensed matter systems often has to account for other types of physics. At the same time, condensed phase NA-MD allows for approximations that may not work in molecules. Focusing on the recent NA-MD developments aimed at studying excited state processes in nanoscale and condensed phases, this Account considers how the phenomena important on the nanoscale can be incorporated into NA-MD and what approximations can be made to increase its efficiency with complex systems and processes.
99