Computational Methods: Transition Metal Clusters

Abstract

Cluster chemistry is dominated by structural aspects. Indeed, structure and bonding are strongly related to stability and properties, and cluster structures are particularly diverse and often complex. Thus, electron‐counting rules, which relate structure to electron count, have been the key to the development of cluster chemistry as a distinct area of chemistry. These rules have been set up progressively along time with the help of quantum chemistry. This article deals with the recent progress on transition metal and mixed main group/transition metal cluster chemistry arising from the contribution of modern computational theory to the rationalization of structures. This article focuses on “viable” species, i.e., molecules that are isolable under reasonable conditions and deals with the exploration of the limitations of the classical electron‐counting rules as well as the establishment of new rules for new structural types with the help of quantum chemical calculations.

Supramolecular Frameworks Built up from Red‐Phosphor­escent trans‐Re6 Cluster Building Blocks: One Pot Synthesis, Crystal Structures, and DFT Investigations

“…[73] In the approximation of O h symmetry, the molecular orbital (MO) diagram shows a set of twelve metal-metal bonding molecular orbitals (a 1g , t 1u , t 2g , t 2u and e g ) for the [{M 6 L i 8 }L a 6 ] unit leading to a closed shell configuration with a metallic electron, i.e. electrons available for metal-metal bonding, count of 24.…”

Combined theoretical and time-resolved photoluminescence investigations of [Mo6Bri8Bra6]2−metal cluster units: evidence of dual emission

“…Facecapped octahedral transition metal cluster units have been the subject of various theoretical investigations. 31 From a qualitative point of view, the electronic structures of groups 6 and 7 transition metal M 6 clusters are very similar regardless of the nature of the capping and apical ligands: twelve molecular orbitals (MOs) mainly centered on metals have mainly a metalmetal bonding character and to a lesser extent a metal-ligand antibonding one. They are well separated from the antibonding MOs by a significant energy gap.…”

“…The first unoccupied MOs are the antibonding metalmetal MO counterparts, still presenting metal-ligand antibonding (d/p*) character. 31 The octahedral symmetry of the isolated [Mo 6 Br i 8 Br a 6 ] 2À unit is undoubtedly the ground state (S 0 ) structural arrangement (in vacuum at 0 K). Nevertheless, experimentally, the anisotropy of the cluster environment induces slight deviations from O h symmetry.…”

Polyhedral [M2B5] Metallaborane Clusters and Derivatives: An Overview of Their Structural Features and Chemical Bonding

“…Note that, organometallic chemists often use the cluster valence electron (cve) count in addition to the sep count. The cve count was obtained by adding the valence electrons of the cluster atoms and the electrons brought by the surrounding ligands [ 1 , 12 ]. Thus, the 7-sep closo-octahedral species [B 6 H 6 ] 2− and [Ru 6 (CO) 18 ] 2− possess 26 [6 × 3 (B) + 6 × 1 (H) + 2 (charge)] and 86 [6 × 8 (Ru) + 18 = × 2 (CO) + 2 (charge)] cves, respectively.…”

“…To get more precise information about the shape and the electron count of these ‘rule-breakers’, theoretical computations are generally needed [ 1 , 12 ]. These calculations are useful to illustrate and discuss: (i) about the shape itself, (ii) which isomer is energetically preferred, (iii) about their bonding, electronic structure, electronic properties, etc.…”