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Our knowledge of the low solar atmosphere, i.e., the photosphere and chromosphere, is based on the knowledge gained from the observations and the theoretical and numerical modeling of these layers. In this sense, the thermodynamical and magnetic semi-empirical models of the solar atmosphere have significantly contributed to the advance in the understanding of the physics of the Sun. In the past, many of these models have been used as a reference that helps us to, e.g., constrain the theoretical and numerical modeling, or to verify the goodness of physical parameters obtained from the inversion of the spectral lines. Nevertheless, semi-empirical models are quite limited by the assumptions that are inherent to the approach and do not necessarily provide an accurate view of the instantaneous and local thermodynamic conditions in the solar atmosphere. In this work, we provide an extensive collection of thermodynamic model atmospheres for active regions (ARs) obtained from the simultaneous inversion of 6 lines sensitive to changes in the thermodynamical conditions in the chromosphere, and another 6 lines sensitive to changes in the thermodynamical conditions in the photospere. These inversions were made using 320 representative profiles (RP) obtained by clustering the profiles in the umbra, penumbra, pore-like, plage, and surrounding quiet-sun in 126 active regions. Due to the simultaneous inversion of the selected lines, the resulting representative model atmosphere (RMA) samples the thermodynamics from the bottom of the photosphere to the top of the chromosphere. As a result, this database, named $IRIS^{2+}$ and formed by $40,320$ RP-RMA pairs, represents the most comprehensive collection of stratified-in-optical-depth thermodynamic models of the low solar atmosphere.