Charge carrier mobility is at the center of organic electronic devices. The strong couplings between electrons and nuclear motions lead to complexities in theoretical description of charge transport, which pose a major challenge for the fundamental understanding and computational design of transport organic materials. This tutorial review describes recent progresses in developing computational tools to assess the carrier mobility in organic molecular semiconductors at the first-principles level. Some rational molecular design strategies for high mobility organic materials are outlined.

Developed 25 years ago, Tully's fewest switches surface hopping (FSSH) has proven to be the most popular approach for simulating quantum-classical dynamics in a broad variety of systems, ranging from the gas phase, to the liquid and solid phases, to biological and nanoscale materials. FSSH is widely adopted as the fundamental platform to introduce modifications as needed. Significant progress has been made recently to enhance the accuracy and efficiency of the surface hopping technique. Various limitations of the standard FSSH-associated with quantum nuclear effects, interference and decoherence, trivial or "unavoided" crossings, superexchange, and representation dependence-have been lifted. These advances are needed to allow one to treat many important phenomena in chemistry, physics, materials, and related disciplines. Examples include charge transport in extended systems such as organic solids, singlet fission in molecular aggregates, Auger-type exciton multiplication, recombination and relaxation in quantum dots and other nanoscale materials, Auger-assisted charge transfer, nonradiative luminescence quenching, and electron-hole recombination. This Perspective summarizes recent advances in the surface hopping formulation of nonadiabatic dynamics and provides an outlook on the future of surface hopping.

An optimal single-photon source should deterministically deliver one and only one photon at a time, with no trade-off between the source's efficiency and the photon indistinguishability. However, all reported solid-state sources of indistinguishable single photons had to rely on polarization filtering which reduced the efficiency by 50%, which fundamentally limited the scaling of photonic quantum technologies. Here, we overcome this final long-standing challenge by coherently driving quantum dots deterministically coupled to polarization-selective Purcell microcavities-two examples are narrowband, elliptical micropillars and broadband, elliptical Bragg gratings. A polarization-orthogonal excitation-collection scheme is designed to minimize the polarization-filtering loss under resonant excitation. We demonstrate a polarized single-photon efficiency of 0.60(2), a single-photon purity of 0.991(3), and an indistinguishability of 0.973(5). Our work provides promising solutions for truly optimal single-photon sources combining near-unity indistinguishability and near-unity system efficiency simultaneously.Single photons are appealing candidates for quantum communications 1,2 , quantumenhanced metrology 3,4 and quantum computing 5,6 . In view of the quantum information applications, the single photons are required to be controllably prepared with a high efficiency into a given quantum state. Specifically, the single photons should possess the same polarization, spatial mode, and transform-limited spectro-temporal profile for a high-visibility Hong-Ou-Mandel-type quantum interference 1,7 .Self-assembled quantum dots show so far the highest quantum efficiency among solid-state quantum emitters and thus can potentially serve as an ideal single-photon source 8-15 . There has been encouraging progress in recent years in developing highperformance single-photon sources 11 . Pulsed resonant excitation on single quantum dots has been developed to eliminate dephasing and time jitter, which created single photons with near-unity indistinguishability 15 . Further, by combining the resonant excitation with Purcell-enhanced micropillar 16,17 or photonic crystals 18,19 , the generated transform-limited 20,21 single photons have been efficiently extracted out of the bulk and funneled into a single mode at far field. Despite the recent progress 16-22 , the experimentally achieved polarized-single-photon efficiency (defined as the number of single-polarized photons extracted from the bulk semiconductor and collected by the first lens per pumping pulse) is ~33% in ref. 16 and ~15% in ref. 17, still fell short of the minimally required efficiency of 50% for boson sampling to show computational advantage to classical algorithms 23 , and was below the efficiency threshold of 67% for photon-loss-tolerant encoding in cluster-state models of optical quantum computing 24 . It should be noted that a <50% single-photon efficiency would render nearly all linear optical quantum computing schemes 1,5 not scalable.The indistinguishable single-photon...

The mechanism of charge transport in organic materials is still controversial from both experimental and theoretical perspectives. At room temperature, molecular deformations interact strongly with the charge carrier both through intermolecular and intramolecular phonons, suggesting a thermally activated hopping mechanism as described by the Marcus electron transfer theory. However, several experimental measurements have indicated that the electronic transport behaves in a "bandlike" manner, as indicated by a decrease in mobility with increasing temperature, in contradiction to the Marcus description. Bandlike first-principles calculations based on the Holstein-Peierls model tend to overestimate the charge mobility by about 2 orders of magnitude. Here, a hopping model is derived that not only quantitatively describes the charge mobility but also explains the observed bandlike behavior. This model uses the quantum version of charge-transfer theory coupled with a random-walk simulation of charge diffusion. The results bridge the gap between the two extreme mechanisms. This first-principles method predicts the room-temperature hole mobilities to be 2.4, 2.0, and 0.67 cm(2)/V s, for rubrene, pentacene, and tetracene, respectively, in good agreement with experiment