Electron Counting Rules and Electronic Structure in Tetrameric Transition-Metal (T)-Centered Rare-Earth (R) Cluster Complex Halides (X)

Abstract

Electron partition schemes are a beneficial means to systematize bonding networks and to identify structure-bonding relationships in polar intermetallics. One prolific class of polymetal networks with simple counterions is the broad family of transition-metal (T)-centered rare-earth metal (R) cluster halides (X), which can be isolated or condensed to oligomers and chains. While the electronic structures of R cluster monomers and chains encapsulating T atoms have been studied systematically, the band structures of oligomers, in particular, the most frequent Friauf-type {T(4)R(16)} tetramers, have been investigated to a lesser extent. Therefore, the band structures of prototypical compounds with {T(4)R(16)}-type tetramers, while maintaining different compositions, were analyzed employing density functional theory based methods. Furthermore, these theoretical examinations provide insight into the origin of the 15 electron rule, which is significant for this class of compounds and correlates with the closed-shell configurations for these structures. Additional research focused on the band structure of monoclinic {Ru(4)Gd(16)}Br(23), which is composed of rhomboid-shaped {Ru(4)Gd(16)} tetramers.

The Crystal Orbital Hamilton Population (COHP) Method as a Tool to Visualize and Analyze Chemical Bonding in Intermetallic Compounds

“…An examination [65] of the hitherto identified rare-earth transition-metal halides whose crystal structures comprise such tetramers suggested that the maximum numbers of CBEs for intracluster bonding are attained for totals of 15 electrons per transition-metal centered rare-earth octahedron. Examinations [66] of the electronic structures for diverse halides composed of these tetramers bared that the Fermi levels fall into gaps corresponding to closed-shell configurations in halides for which CBE counts of 15 electrons per [TR 6 ] cluster are achieved. An additional bonding analysis [66] based on the COHP curves and their integrated values (Table 1) indicates that the majority of the bonding interactions reside between the heteroatomic R−T as well as R−X separations, whereas the homoatomic R−R and T−T interactions play minor, but evident roles.…”

“…Examinations [66] of the electronic structures for diverse halides composed of these tetramers bared that the Fermi levels fall into gaps corresponding to closed-shell configurations in halides for which CBE counts of 15 electrons per [TR 6 ] cluster are achieved. An additional bonding analysis [66] based on the COHP curves and their integrated values (Table 1) indicates that the majority of the bonding interactions reside between the heteroatomic R−T as well as R−X separations, whereas the homoatomic R−R and T−T interactions play minor, but evident roles. [70] (Figure 1).…”

Revealing the Nature of Chemical Bonding in an ALn2Ag3Te5-Type Alkaline-Metal (A) Lanthanide (Ln) Silver Telluride

“…The following orbitals were employed as basis sets in the computations (downfolded [63] orbitals in parentheses): Rb-5s/(-5p)/(-4d)/(-4f ); Pr-6s/(-6p)/-5d; Ag-5s/-5p/-4d/(-4f ); Te-5s/-5p/(-5d)/(-4f ) with the corresponding WS radii (Å): Rb, 4.73; Pr, 3.58; Ag, 2.86-2.89; Te, 3.24-3.35. The praseodymium 4f states were treated as core-like states-a procedure that has been widely used elsewhere [34,35,64,65]. More specifically, the aforementioned handling of the rare-earth-metal 4f states has been substantiated by previous explorations [34,35,[65][66][67] on the electronic structures of rare-earth-containing compounds.…”

Revealing Tendencies in the Electronic Structures of Polar Intermetallic Compounds

“…A survey of all hitherto discovered ternary rare-earth transition-metal halides comprising these [T 4 R 16 ] tetramers implied that the maximum amounts of cluster-based electrons (CBEs) are accomplished for counts of 15 electrons per [TR 6 ] octahedron [58]. An examination of the first-principles-based electronic band structure calculations for a series of rare-earth transition-metal halides containing the tetramers revealed that the majority of the bonding populations resides between the heteroatomic R-X and R-T contacts, while homoatomic R-R and T-T bonding plays a subordinate role (Table 2) [59]. Further research on the energy regions near the Fermi levels in these halides revealed the presence of gaps corresponding to closed-shell-configurations for CBE counts of 15 electrons as electronically favorable situations whose accomplishments can be considered as the driving forces of the tendency to achieve totals of 15 CBEs per [TR 6 ] octahedron [59].…”

“…Further research on the energy regions near the Fermi levels in these halides revealed the presence of gaps corresponding to closed-shell-configurations for CBE counts of 15 electrons as electronically favorable situations whose accomplishments can be considered as the driving forces of the tendency to achieve totals of 15 CBEs per [TR 6 ] octahedron [59]. Table 2 have been reported elsewhere [59]. One prolific group of ternary rare-earth transition-metal halides containing cluster chains is the class of those halides with the net formula [TR 3 ]X 3 , for which five different types of structure have been reported [60][61][62][63].…”