Ab initio molecular dynamics simulations were performed to study the initiation of decompositionand formation of first products of two molecular crystals pentaerythritol tetranitrate (PETN) and 5-nitro-2,4-dihydro-1,2,4-triazole-3-one (NTO) under thermal decomposition temperature (475 K for PETN and 531 Kfor NTO) coupled with different pressures (1-5 GPa). The pressure effects on the initial decomposition stepsand initially generated products on PETN and NTO were very different. PETN was triggered by C-H... O intermolecular hydrogen transfer. The initial decomposition mechanism was independent of the pressure. ForNTO, two different initial decomposition mechanisms were found. At 1, 2, and 3 GPa, it was triggered by NH....O intermolecular hydrogen transfer, while at 4 and 5 GPa, it was triggered by N-H.....N intermolecularhydrogen transfer. This indicates that the initial decomposition mechanism was dependent on the pressure.Our study may provide new insights into initial mechanisms and decomposition reactions of molecular crystalexplosives under thermal decomposition temperature coupled with different pressures with details at atomiclevel.