First principle molecular dynamics are widely used in normal material simulations, in which smooth potential surface determined with quantum mechanical treatment of electronic states is used to govern the nuclear motion. The motions of electrons and nuclei are decoupled by the Born-Oppenheimer approximation. For hot dense plasma, the electronic excitation and ionization occurs very frequently and somehow randomly compared with the motion of nucleus, resulting in non-adiabatic energy exchange between nuclei and electrons. For non-thermal-equilibrium plasmas, the thermal energy exchange occurs too between electrons and nuclei. These kinds of non-adiabatic energy exchange between electrons and nuclei could be approximated by random electronic impacts on nuclei and taken into account by using Langiven equation for the nuclear motion with proper thermal friction and noise terms. It will be shown with examples that inclusion of these so-called electron collision induced friction and noise is essential for a proper converged ab initio molecular dynamics simulation of hot dense plasma.