Thermochemical models of detonation are widely used to estimate energy delivery, but they are based on the assumption that the carbon-rich condensates (soot) formed during detonation are very similar to bulk carbon. We present an analytic equation of state (EOS) based on experimental detonation data for soot formed during the detonation of triaminotrinitrobenzene (TATB)-based high explosives. X-ray photoelectron spectra of several detonation soots are used to determine the elemental nitrogen abundance, with surprisingly high values for TATB. The proposed TATB soot EOS is highly compressible at low pressures and shares some features of glassy carbon, exhibiting graphite- and diamond-like behavior as a function of pressure. We demonstrate the influence of formed soot on detonation performance, including a lowering of the detonation velocity at typical charge densities, and a more compressive product Hugoniot at overdriven conditions. The soot model improves the accuracy of thermochemical calculations for TATB-based explosives across a wide range of states. Detonation velocity predictions for HMX (cyclotetramethylene-tetranitramine)-TATB blends with 80% or more TATB content, as well predictions for 1,3-diamino-2,4,6-trinitrobenzene (DATB) and 3-nitro-1,2,4-triazol-5-one (NTO), which share some features with TATB, are also improved.