We have studied, by means of ab initio calculations, the energetics and the atomic and electronic structures of various reconstructions induced by rare-earth metals ($\text{RE}=\text{Eu}$, Nd, Sm, and Yb) and Ba on Si(100) in the coverage range up to 0.5 monolayer. It is shown that Si dimer buckling is an important structural element for such systems, leading frequently to oblique surface lattice symmetries. The strong metal atom---silicon binding favors the increased amount of metal atoms per unit surface area, i.e., the $(2\ifmmode\times\else\texttimes\fi{}3)$ reconstruction with two metal atoms per unit cell is found to be energetically unstable with respect to the $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstruction with three metal atoms per the same surface area [Eu/Si(100) and Yb/Si(100)]. The influence of the atomic size and the valence of the adsorbates is also investigated. In particular, it is found that an increase in atomic size stimulates the metal-metal repulsion, stabilizing the $(2\ifmmode\times\else\texttimes\fi{}3)$ configuration [Ba/Si(100)]. In the case of trivalent metals, the stabilization of the $(2\ifmmode\times\else\texttimes\fi{}3)$ is mediated by the loss of semiconducting state in the competing phases [Sm/Si(100) and Nd/Si(100)]. Our results demonstrate the importance of many factors, which account for the abundance of RE/Si(100) reconstructions. Finally, prominent atomic models are proposed for $(2\ifmmode\times\else\texttimes\fi{}3)$ and $(2\ifmmode\times\else\texttimes\fi{}6)$ reconstructions, and the character of the wavy ``$(1\ifmmode\times\else\texttimes\fi{}2)$'' reconstruction is discussed. The simulated scanning tunneling microscopy images for the proposed $(2\ifmmode\times\else\texttimes\fi{}6)$ reconstruction are in a particularly good agreement with the complex experimental images.
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