The main focus of this work was to investigate substitution effects on the chemical bonding in compounds of AlB 2 -type and related structure types. Delocalization indices within the QTAIM approach and the topological analysis of the ELI functionals were used as tools to describe the bonding situation in digallides and diborides. Digallides of AlB 2 -type were found only within group I and II; for CaGa 2 (meta-stable phase), SrGa 2 , BaGa 2 , YGa 2 and LaGa 2 compounds. Within these compounds, QTAIM analysis showed similar trend as previously found in diborides. That is, along the period in the Periodic Table, metal-triel interactions increase at the expense of in-plane (triel-triel) ab interactions (Tr=triel).
However, transition metal diborides adopt the AlB 2 -type up to group VI. To understand this difference, we simulated transition metal (TM) digallides and diborides up to group VI in the AlB 2 -type. Additionally, the puckered variants diborides ReB 2 and OsB 2 were also simulated in the AlB 2 -type. With filling of d shell, there is a delicate balance between increase of TM–Tr and decrease of in-plane (Tr–Tr) ab electron sharing. This balance is maintained as long as interlayer interactions in the c direction (Tr–Tr ) c and (TM–TM ) c are not relatively too high in comparison to in-plane electron sharing. In contrast to TM B 2 of AlB 2 -type, digallides in the same structure type build up strong interlayer interactions for early transition metal elements.
Our results showed that within digallides, a relatively strong increase in interlayer electron sharing (Ga–Ga) c and (TM–TM ) c takes place. Such increase occurs already for ScGa 2 and TiGa 2 . On the other hand, diborides show a steady increase in electron sharing of TM –B and (TM–TM ) c , but not of (B–B) c . Therefore, it is reasonable to suggest that diborides will tend to adopt a 3D network composed of boron and transition metal atoms (ReB 2 and RuB 2 types). The additional high (Ga–Ga) c interlayer interactions indicate a tendency for digallides to form 3D networks composed only by gallium atoms, characteristic of CaGa 2 (CaIn 2 -type) and ScGa 2 (KHg 2 -type). The counterbalancing bonding effects of in-plane and out-of-plane interactions that give the chemical flexibility of the AlB 2 -type in diborides is thus disrupted in AlB 2 -type digallides by a further enhanced degree of interlayer interactions (Ga–Ga) c and (TM –TM ) c . This results in a smaller number of digallides than that of diborides in AlB 2 -type.
The most conspicuous difference between diborides and digallides of AlB 2 -type is in the representation of the B – B and Ga – Ga bonds revealed by the ELI- D topology. Whereas AlB 2 -type diborides exhibit one ELI-D attractor at the B – B midpoint, AlB 2 -type digallides exhibit two ELI-D attractors symmetrically opposite around the Ga – Ga bond midpoint. We utilized the E 2 H 4 (E=triel, tetrel ) molecular series in the D 2h point group symmetry as model systems for solid state calculations. In particular, we addressed the appearance of ELI- D double maxima for Ga – Ga, by using orbital decomposition within the ELI framework. The ELI-D topology changes along the 13th group T r 2 H 4 series. Whereas B 2 H 4 and Al 2 H 4 exhibit one ELI-D attractor representing the Tr–Tr bond, Ga 2 H 4 and In 2 H 4 give rise to two ELI-D attractors. Partial ELI-D allows the orbital decomposition of the electron density. Partial ELI-q gives access to the decomposition of a two-particle property, which is given by the Fermi-hole curvature. We have found that the d-orbitals enable the formation of the two ELI-D attractors through pairing contributions. This has a net effect of lowering electron localizability at the Ga – Ga bond midpoint. Namely, the different ELI-D topology of Ga – Ga and B – B bonds stems from the contributions of d-orbitals to orbital pairing. We have also investigated the bonding situation in transition metal diborides of ReB 2 -type (MnB 2 , TcB 2 , ReB 2) and RuB 2 -type (OsB 2 , RuB 2). One can consider these two structure types as an extension of the trend found in TM B 2 of AlB 2 -type: an increase in TM –B interactions and an enhanced three-center bonding. The change in the structure type results in a puckered layer of boron atoms with electrons equally shared between B – B and TM –B. However, TM –B bonds exhibit a high three-center character. The ELI-D/QTAIM intersection technique also revealed a high participation of TM in the B – B bonding basin population. Moreover, ELI-D topology in the ReB 2 -type also discloses a seemingly important Re 3 three-center interaction along the flat layer of Re atoms.
Such basin is absent in MnB 2 , which coincides with the fact that MnB 2 was only observed in the AlB 2 -type. In this regard, we concluded that the 3D network consists not only of covalent B – B bonds, but also of TM –B bonds.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:30868 |
| Date | 05 March 2018 |
| Creators | Quaresma Faria, Joao Rodolfo |
| Contributors | Grin, Juri, Ruck, Michael, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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