Dynamics of interstitial hydrogen molecules in crystalline silicon

The static and dynamic properties of interstitial H₂, HD and D₂ molecules in crystalline silicon are obtained from ab initio molecular-dynamics simulations with atomic-like basis sets. The static (T = 0) calculations agree with those of most other authors: the centre of mass (CM) of H₂ is at the tetrahedral interstitial (T) site, the molecule is 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 expected ortho/para splitting is not present, why the symmetry is C₁, why the piezospectroscopic tensors of H₂ and D₂ are identical or why the exposure to an H/D mix results in a single HD line which is not only at the wrong place but also much weaker than expected. In the present work, we extend the static calculations to include the constant-temperature dynamics for H₂ in Si. At T > 0 K, the CM of the molecule no longer remains at the T site. Instead, H₂ 'bounces' off the walls of its tetrahedral cage and exchanges energy with the host crystal. The average position of the CM is away from the T site along <100>. Under uniaxial stress, the CM shifts off that axis and the molecule has C₁ symmetry. The H-H stretch frequency calculated from the Fourier transform of the v-v autocorrelation function is close to the measured one. Since the potential energy experienced by H₂ in Si near the T site is very flat, we argue that H₂ should be a nearly free quantum mechanical rotator. Up to room temperature, only the j = 0 and j = 1 rotational states are occupied, H₂ resembles a sphere rather than a dumbbell, the symmetry is determined by the position of the CM and HD is equivalent to DH in any symmetry. The rapid motion of the CM implies that an ortho-to-para transition will occur if a large magnetic moment is nearby. Several candidates are proposed. Since nuclear quantum effects are not included in our calculations, we cannot address the possibility that the observed vibrational spectrum of H₂ results from a tunnelling excitation as proposed by Stoneham.