Using molecular dynamic simulations of an extended-simple-point-charge model of water, we investigated the effect of translation-rotation coupling on the motion of the hydrogen atom in a water molecule in low temperature water. We introduce a translation-rotation probability distribution P-CM,P-Omega(r,theta(R),t), where r(t) is the scalar displacement of the center of mass from origin at time t starting from the origin at t=0; and theta(R)(t)=arccos[b(t).b(0)/b(2)] is the angle of rotation of the vector, b, connecting the center of mass of the water molecule to the hydrogen atom position. We developed a procedure to determine P-CM,P-Omega(r,theta(R),t) starting from the van Hove self-correlation function of the center of mass, G(s)(CM)(r,t), taking into account the translation-rotation coupling effect. In the long time region, we use a translation-rotation coupling parameter, Q(*), to determine the angular dependence of P-CM,P-Omega(r,theta(R),t) from G(s)(CM)(r,t). Thus, the dynamics of the hydrogen atoms in a water molecule is fully determined by the van Hove self-correlation function of the center of mass and by the value of the translation-rotation coupling parameter. In particular, we show that the self intermediate scattering function of the hydrogen atom can be calculated with a better accuracy than using the traditional decoupling approximation. The model can be used to analyze incoherent quasielastic neutron scattering spectra of water in the future. (C) 2003 American Institute of Physics.