We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.

The sites, gap levels, and migration barriers of interstitial H in Si are predicted. The hydrogenation of C‐rich Si results in the formation of H2*(C) and C2H2, in contrast to FZ‐Si where H2 molecules dominate. The fully saturated vacancy (VH4) also forms. This complex is normally stable up to 650 °C. However, in C‐rich Si, VH4 anneals around 550 °C while the VH3HC complex appears. There, C replaces one of the four Si nearest‐neighbors to the vacancy. This implies that VH4 begins to diffuse at 550 °C, and then traps at Cs. This in turn implies that all the VHn complexes (n = 1, 2, 3, 4) are mobile at moderate temperatures. In this paper, we discuss the energetics of H in Si, summarize the key experimental and theoretical results about H interactions in C‐rich Si, and discuss the migration paths and activation energies of the four VHn complexes.

The most commonly used first-principles technique to predict the properties of impurities in semiconductors involves periodic supercells to represent the host crystal, classical molecular dynamics (MD) to describe the nuclear motion, with ab initio-type pseudopotentials and density-functional theory to treat the electronic problem. Calculating the entire dynamical matrix of the supercell is most useful. Indeed, the eigenvalues of this matrix give all the local, pseudolocal, and resonant vibrational modes associated with the impurity, and allow the calculation of the phonon density of states, from which the vibrational free energy can be obtained. Further, the eigenvectors of the dynamic matrix are used to quantify the ‘localization’ of specific vibrational modes and prepare the supercell in thermal equilibrium at a temperature T, up to a few hundred degrees kelvin. This supercell preparation allows non-equilibrium MD simulations to be performed. Applications include the calculation of vibrational lifetimes and of thermal conductivities. This paper describes the essential ingredients of such calculations.

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