Neodymium, samarium, and gadolinium complexes with terephthalic acid were synthesized for the first time, and it was found that, unlike complexes with phthalic acid, they are isostructural. A number of physical and chemical studies established their composition and chemical formula.Quantum-chemical semi-empirical calculation for neodymium, samarium and gadolinium complexes was carried out on the generalized Sparkle model, intended for lanthanide complexes on PM6, and the Sparkle/PM6 parameters for other trivalent lanthanides were also presented. The comparative analysis procedure took into account only qualitative crystallographic structures. The unsigned average errors (UME) of Sparkle/PM6, corresponding to all interatomic distances between neodymium, samarium, gadolinium ions and atoms directly coordinated with them, range from 0.066 to 0.086 Å, for Nd (III) – 0.086, Gd (III) – 0.066 and Sm (III) – 0.066, respectively. As a result of the application of Sparkle/PM6 to the synthesized lanthanide complexes, in particular, the values of the final heat of formation, the energy of repulsion of the nucleus-nucleus area and volume COSMO - (conductor-like screening model), the ionization potential, the energy of binding (homo) and antibonding (lumo) orbitals.