  The lattice dynamics of TiO$_2$ in the rutile crystal structure was studied
by a combination of thermal diffuse scattering, inelastic x-ray scattering and
density functional perturbation theory. We experimentally confirm the existence
of an anomalous soft transverse acoustic mode with energy minimum at q = (1/2
1/2 1/4). The phonon energy landscape of this particular branch is reported and
compared to the calculation. The harmonic calculation underestimates the phonon
energies but despite this the shape of both the energy landscape and the
scattering intensities are well reproduced. We find a significant temperature
dependence in energy of this transverse acoustic mode over an extended region
in reciprocal space which is in line with a substantially anharmonic mode
potential-energy surface. The reported low energy branch is quite different
from the ferroelectric mode that softens at the Brillouin zone center and may
help explain anomalous convergence behavior in calculating TiO$_2$ surface
properties.
