The LaFe13-xSix (1.0 <= x <= 5.0) series is studied experimentally and theoretically to gain possible understanding for the relationships among geometrical structure, chemical composition, magnetic behavior, and physical properties as related to the magnetocaloric effect in these compounds. As the Si concentration increases, LaFe13-xSix exhibits a structural transformation from the cubic NaZn13 structure type to a tetragonal derivative due primarily to preferential ordering of Fe and Si atoms. At room temperature, LaFe13-xSix crystallize in the cubic structure for the range 1 <= x <= 2.6 and in the tetragonal for 3.2 <= x <= 5. In the range 2.6 <= x <= 3.2, it shows a two-phase mixture. Tempe ratu re-depen dent single-crystal X-ray diffraction experiments near the corresponding Curie temperatures were performed on the room-temperature cubic phases to examine the origin of the large isothermal magnetic entropy changes. A thorough statistical and structural analysis of the data indicates that the noncentrosym metric F (4) over bar 3c space group provides a more adequate atomic arrangement, than the centrosymmetric Fm (3) over barc space group. This change in space group leads to divergence for specific sets of Fe-Fe distances below the Curie temperature that arises from tilting of Fe-centered [Fe12-xSix] icosahedra. The no ncentrosym metric space group also agrees with the predominance of icosahedral clusters lacking local inversion symmetry. From extended HOckel and tightbinding linear muffin-tin orbital (TB-LMTO) electronic structure calculations on various model structures, the F (4) over bar 3c model is more energetically favorable than the Fm (3) over barc model, Extended HOckel calculations on various icosahedral [Fe12-nSin] (n = 1-5) clusters and TB-LMTO calculations on "LaFe13," LaFe11Si2, and LaFe9Si4 have also been carried out to study the effects of a main group element (Si) on stabilizing the cubic NaZn13-type structure, influencing the transformation between cubic and tetragonal symmetries, and to study relationships among their chemical bonding and magnetic properties.