We present simulations for a design of a high-energy single-stage mid-IR difference frequency generation adapted to a two-color Ti:sapphire amplifier system. The optimized mixing process is based on chirped pulse difference frequency generation (CP-DFG), allowing for a higher conversion efficiency and reduced two-photon absorption losses. The numerical start-to-end simulations include stretching, chirped pulse difference frequency generation and pulse compression. Realistic design parameters for commercially available nonlinear crystals (GaSe, AgGaS2, LiInSe2, LiGaSe2) are considered. Compared with conventional unchirped DFG directly pumped by Ti:sapphire technology, we predict a threefold increase in the quantum efficiency. Our CP-DFG scheme provides up to 340 mu J pulse energy directly at 7.2 mu m when pumped with 8 mJ and supports a bandwidth of up to 350 nm. The resulting 240 fs mid-IR pulses are inherently phase stable.