The static and dynamic properties of interstitial H2, HD and D2molecules in crystalline silicon are obtained from ab initiomolecular-dynamics simulations with atomic-like basis sets. The static(T = 0) calculations agree with those of most other authors: the centre ofmass (CM) of H2 is at the tetrahedral interstitial (T) site, the moleculeis a nearly-free rotator, and the activation energy for diffusion is 0.90 eV.However, these results fail to explain a number of experimental observations,such as why H2 is infrared (IR) active, why the expectedortho/para splitting is not present, why the symmetry isC1, why the piezospectroscopic tensors of H2 and D2 are identical orwhy the exposure to an H/D mix results in a single HD line which is not onlyat the wrong place but also much weaker than expected. In the present work, weextend the static calculations to include the constant-temperature dynamics for H2 in Si. At T>0 K, the CM of the molecule no longerremains at the T site. Instead, H2 `bounces' off the walls of itstetrahedral cage and exchanges energy with the host crystal. The averageposition of the CM is away from the T site along ⟨100⟩. Underuniaxial stress, the CM shifts off that axis and the molecule has C1symmetry. The H-H stretch frequency calculated from the Fourier transform ofthe v-v autocorrelation function is close to the measured one. Since thepotential energy experienced by H2 in Si near the T site is very flat, weargue that H2 should be a nearly free quantum mechanical rotator. Up toroom temperature, only the j = 0 and j = 1 rotational states are occupied,H2 resembles a sphere rather than a dumbbell, the symmetry is determined bythe position of the CM and HD is equivalent to DH in any symmetry. The rapidmotion of the CM implies that an ortho-to-para transition will occur if alarge magnetic moment is nearby. Several candidates are proposed. Sincenuclear quantum effects are not included in our calculations, we cannotaddress the possibility that the observed vibrational spectrum of H2results from a tunnelling excitation as proposed by Stoneham.