Small polarons in real crystals: concepts and problems

Much of small polaron theory is based on highly idealized models, often essentially a continuum description with a single vibrational frequency. These models ignore much of the wealth of experimental data, which find interpretation in many atomistic simulations. We review here a range of properties of small polarons in real, rather than model, systems. The phenomena fall into three main classes: (i) the mechanisms and dynamics of self-trapping of polarons; (ii) static properties-the relative energies of large and small polarons, the optical transitions expected, their effect on positions of other ions and on lattice vibrations, their population in thermal equilibrium, and so on; (iii) small polaron hopping and diffusion. We discuss the key concepts and methods of calculation of polarons, and explore the properties of self-trapped holes and excitons in ionic crystals, and those of an excess electron in liquid water.