  First-principles density functional theory methods are used to investigate
the structure, energetics, and vibrational motions of the neutral vacancy
defect in diamond. The measured optical absorption spectrum demonstrates that
the tetrahedral $T_d$ point group symmetry of pristine diamond is maintained
when a vacancy defect is present. This is shown to arise from the presence of a
dynamic Jahn-Teller distortion that is stabilised by large vibrational
anharmonicity. Our calculations further demonstrate that the dynamic
Jahn-Teller-distorted structure of $T_d$ symmetry is lower in energy than the
static Jahn-Teller distorted tetragonal $D_{2d}$ vacancy defect, in agreement
with experimental observations. The tetrahedral vacancy structure becomes more
stable with respect to the tetragonal structure by increasing temperature. The
large anharmonicity arises mainly from quartic vibrations, and is associated
with a saddle point of the Born-Oppenheimer surface and a minimum in the free
energy. This study demonstrates that the behaviour of Jahn-Teller distortions
of point defects can be calculated accurately using anharmonic vibrational
methods. Our work will open the way for first-principles treatments of dynamic
Jahn-Teller systems in condensed matter.
