Thermohaline instability and rotation-induced mixing. III - Grid of stellar models and asymptotic asteroseismic quantities from the pre-main sequence up to the AGB for low- and intermediate-mass stars at various metallicities

The availability of asteroseismic constraints for a large sample of stars from the missions CoRoT and Kepler paves the way for various statistical studies of the seismic properties of stellar populations. In this paper, we evaluate the impact of rotation-induced mixing and thermohaline instability on the global asteroseismic parameters at different stages of the stellar evolution from the Zero Age Main Sequence to the Thermally Pulsating Asymptotic Giant Branch to distinguish stellar populations. We present a grid of stellar evolutionary models for four metallicities (Z = 0.0001, 0.002, 0.004, and 0.014) in the mass range between 0.85 to 6.0 Msun. The models are computed either with standard prescriptions or including both thermohaline convection and rotation-induced mixing. For the whole grid we provide the usual stellar parameters (luminosity, effective temperature, lifetimes, ...), together with the global seismic parameters, i.e. the large frequency separation and asymptotic relations, the frequency corresponding to the maximum oscillation power {\nu}_{max}, the maximal amplitude A_{max}, the asymptotic period spacing of g-modes, and different acoustic radii. We discuss the signature of rotation-induced mixing on the global asteroseismic quantities, that can be detected observationally. Thermohaline mixing whose effects can be identified by spectroscopic studies cannot be caracterized with the global seismic parameters studied here. But it is not excluded that individual mode frequencies or other well chosen asteroseismic quantities might help constraining this mixing.