Accuracy of Embedded Fragment Calculation for Evaluating Electron Interactions in Mixed Valence Magnetic Systems: Study of 2e- Reduced Lindqvist Polyoxometalates ; Accurate quantum chemical calculations on real-world magnetic systems are challenging, the inclusion of electron correlation being the bottleneck of such task. One method proposed to overcome this difficulty is the embedded fragment approach. It tackles a chemical problem by dividing it into small fragments, which are treated in a highly accurate way, surrounded by an embedding included at an approximate level. For the vast family of medium-to-large sized polyoxometalates, two-electron-reduced systems are habitual and their magnetic properties are interesting. In this paper, we aim at assessing the quality of embedded fragment calculations by checking their ability to reproduce the electronic spectra of a complete system, here the mixed-metal series [MoxW6−xO19]4− (x = 0−6). The microscopic parameters extracted from fragment calculations (electron hopping, intersite electrostatic repulsion, local orbital energy, etc.) have been used to reproduce the spectra through model Hamiltonian calculations. These energies are compared to the results of the highly accurate ab initio difference dedicated configuration interaction (DDCI) method on the complete system. In general, the model Hamiltonian calculations using parameters extracted from embedded fragments nearly exactly reproduce the DDCI spectra. This is quite an important result since it can be generalized to any inorganic magnetic system. Finally, the occurrence of singlet or triplet ground states in the series of molecules studied is rationalized upon the interplay of the parameters extracted.