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The collective dynamics in liquid water is an active research topicexperimentally, theoretically and via simulations. Here, ab initio moleculardynamics simulations are reported in heavy and ordinary water at temperature323.15 K, or 50$^\circ$C. The simulations in heavy water were performed bothwith and without dispersion corrections. We found that the dispersioncorrection (DFT-D3) changes the relaxation of density-density time correlationfunctions from a slow, typical of a supercooled state, to exponential decaybehaviour of regular liquids. This implies an essential reduction of themelting point of ice in simulations with DFT-D3. Analysis of longitudinal (L)and transverse (T) current spectral functions allowed us to estimate thedispersions of acoustic and optic collective excitations and to observe the L-Tmixing effect. The dispersion correction shifts the L and T optic (O) modes tolower frequencies and provides by almost thirty per cent smaller gap betweenthe longest-wavelength LO and TO excitations, which can be a consequence of alarger effective high-frequency dielectric permittivity in simulations withdispersion corrections. Simulation in ordinary water with the dispersioncorrection results in frequencies of optic excitations higher than in D$_2$O,and in a long-wavelength LO-TO gap of 24 ps$^{-1}$ (127 cm$^{-1}$).

Ab initio molecular dynamics study of collective excitations in liquid H$_2$O and D$_2$O: Effect of dispersion corrections