Context. Asteroseismology is a powerful tool used to infer the evolutionary status and chemical stratification of white dwarf stars and to gain insights into the physical processes that lead to their formation. This is particularly true for the variable hydrogen-rich atmosphere (DA) white dwarfs, known as DAV or ZZ Ceti stars. They constitute the most numerous class of pulsating white dwarfs. Aims. We present a new grid of white dwarf models that take into account advances made over the last decade in modeling and input physics of both the progenitor and the white dwarf stars. As a result, it is possible to avoid several shortcomings present in the set of white dwarf models employed in the asteroseismological analyses of ZZ Ceti stars that we carried out in our previous works. Methods. We generate white dwarf stellar models appropriate for ZZ Ceti stars with masses from ∼0.52 to ∼0.83 M⊙, resulting from the whole evolution of initially 1.5–4.0 M⊙ mass star models. These new models are derived from a self-consistent way with the changes in the internal chemical distribution that result from the mixing of all the core chemical components induced by mean molecular-weight inversions, from 22Ne diffusion, Coulomb sedimentation, and from residual nuclear burning. In addition, the expected nuclear-burning history and mixing events along the progenitor evolution are accounted for, in particular the occurrence of third dredge-up, which determines the properties of the core and envelope of post-AGB and white dwarf stars, as well as the white dwarf initial-final mass relation. The range of hydrogen envelopes of our new ZZ Ceti models extends from the maximum residual hydrogen content predicted by the progenitor history, log(MH/M⊙)∼ − 4 to −5, to log(MH/M⊙) = − 13.5, thus allowing for the first stellar models that would enable the search for seismological solutions for ZZ Ceti stars with extremely thin hydrogen envelopes – if, indeed, they do exist in nature. We computed the adiabatic gravity(g)-mode pulsation periods of these models. Calculations of our new evolutionary and pulsational ZZ Ceti models were performed with the LPCODE stellar evolution code and the LP-PUL stellar pulsation code. Results. Our new hydrogen-burning post-AGB models predict chemical structures for ZZ Ceti stars that are substantially different from those we used in our previous works, particularly in connection with the chemical profiles of oxygen and carbon near the stellar centre. We also discuss the implications of these new models for the pulsational spectrum of ZZ Ceti stars. Specifically, we find that the pulsation periods of g modes and the mode-trapping properties of the new models differ significantly from those characterizing the ZZ Ceti models of our previous works, particularly for long periods. Conclusions. The improvements in the modeling of ZZ Ceti stars we present here lead to substantial differences in the predicted pulsational properties of ZZ Ceti stars, which are expected to impact the asteroseismological inferences of these stars. This is extremely relevant in view of the abundant amount of photometric data from current and future space missions, resulting in discoveries of numerous ZZ Ceti stars.