Where are the Excess Electrons in Subvalent Compounds? The Case of Ag7Pt2O7

Abstract

Subvalent compounds raise the question of where those valence electrons not belonging to chemical bonds are. In the limiting case of Ag₇Pt₂O₇, there is just one-electron excess in the chemical formula requiring the presence of Ag atoms with oxidation states below +1, assuming conventional Pt⁴⁺ and O^2- ions. Such a situation challenges the understanding of the semiconducting and diamagnetic behavior observed in this oxide. Previous explanations that localize pairwise the electron excess in tetrahedral Ag₄ interstices do not suffice in this case, since there are six silver tetrahedral voids and only an excess of nine electrons in the unit cell. Here, we provide an alternative explanation for the subvalent nature of this compound by combining interatomic distances, electron density-based descriptors, and orbital energetic analysis criteria. As a result, Ag atoms that do not participate in their valence electron are revealed. We identify excess electrons located in isolated subvalent silver clusters with electron-deficient multicenter bonds resembling pieces of metallic bonding in fcc-Ag and Ag₇Pt₂ alloy. Our analysis of the electronic band structure also supports the multicenter bonding picture. This combined approach from the real and reciprocal spaces reconciles existing discrepancies and is key to understanding the new chemistry of silver subvalent compounds.

Figure 1

Platinum-oxide (top panel) and silver-oxide (bottom panel) fragments of Ag₇Pt₂O₇. Platinum oxide octahedra and subvalent silver tetrahedra are highlighted. Red, green, and gray spheres stand for oxygen, platinum, and silver atoms, respectively.

Figure 2

ELF attractors positions in the Ag₇Pt₂ metallic sublattice. A1, A2, and A3 attractors are represented as black, orange, and purple spheres, respectively. In the labels, there are the number of electrons between brackets in each attractor. Pt atoms are shown in green and Ag atoms in gray. Zoom with the subvalent silver clusters is provided to facilitate the discussion in the main text.

Figure 3

ELF-2D heatmap along [001] and [0 1–1.273] lattice planes showing Pt–Pt bonds in the Ag₇Pt₂ metallic matrix.

Figure 4

Ag₄-T and Ag₄-R motifs of the silver fragment with their corresponding Ag atoms labeled. Ag–Ag distances are given in Å. The number of electrons in the A1 attractor is 0.12 e. ELF attractors are shown as black spheres.

Figure 5

View along the c-axis of the ELF attractor circuits (golden color) within one silver slab of the Ag₇Pt₂ alloy (top panel) and within the bulk of the Ag₇Pt₂O₇ (bottom panel). Ag₄-T and Ag₄-R units are represented by thin yellow lines. Gray, green, and red spheres stand for Ag, Pt, and O atoms, respectively.

Figure 6

Electronic band structure and the associated atomic and orbital projected density of states of the Ag₇Pt₂O₇ compound at PBE + U calculation level. The band at the Fermi level is highlighted in red. The Ag contribution to this band matches the value of the O barely allowing its observation in the PDOS picture.

Figure 7

Atomic, d-orbital, and s-orbital contributions of each type of silver atoms to the band crossing at the Fermi level from the projected electronic density of states.