In this paper, the wireless communication over indoor Terahertz (THz) channels is studied. The physical mechanisms governing a wireless transmission in the 0.1-10 THz band are a very high molecular absorption and spreading loss which result in a very high and frequency-selective path loss for the line-of-sight (LOS) links. For the non-line-of-sight (NLOS) propagation, a very high reflection loss depending on the shape, material, and roughness of the reflecting surface affects the THz wave propagation. Taking these peculiarities of the THz radiation into account and applying a ray tracing approach for scattered rays, a novel deterministic equivalent channel model is developed that accounts for both the LOS and NLOS propagation cases. Furthermore, the channel capacity of the proposed model is investigated. Simulation results demonstrate that for distances, up to 1 m, data rates in the order of Terabit per second (Tbps) are obtained for a transmit power of 1 Watt. Moreover, the capacity of only the NLOS component is around 100 Gigabit per second (Gbps). These results are highly motivating to develop future wireless THz communication systems.