#### Title

Molecular Orbital Calculations for [Mo(CN)₈]⁴⁻ an Investigation of Eight Coordination Geometries

#### Document Type

Thesis - Open Access

#### Award Date

1974

#### Degree Name

Master of Science (MS)

#### Department

Chemistry

#### Abstract

Until the last twenty years only a few discrete 8-coordinate transition metal complexes were known. Increased interest in 8-coordination has led to the synthesis and characterization of a great many 8-coordinate compounds. Application of 3-dimensional X-ray analysis has made structural determination of these complexes much simpler. Two configurations dominate the stereochemistry of discrete 8-coordination, the D4d square antiprism and the D2d triangular dodecahedron. Both of these structures can be obtained by distorting the cube, a configuration not commonly observed. A 45° rotation of one square face of a cube about the perpendicular axis through that face results in the antiprism structure shown in Figure 1a. Figure 1b shows that the dodecahedron is a more complicated distortion of the cube, requiring essentially a twist of about 35° and a fold in each of the remaining square faces. One may consider the dodecahedron to be a combination of two distorted tetrahedra, one elongated, the other flattened, with 4 vertices in each of two perpendicular planes. This distortion, shown in Figure 2, demonstrates that the dodecahedron has two sets of 4 equivalent vertices. No completely satisfactory explanation has been given for the occurrence of the specific geometries found in 8-coordinate compounds. Among the factors influencing the spatial distribution of the ligands about the central metal are ligand-central metal interaction, ligand-ligand repulsions, nonbonded electron repulsions, and constraints of polydentate ligands. In early theoretical work both the dodecahedron and the antiprism were studied through application of a-bonding directed valence orbitals. In these calculations the greatest bond strengths were computed for the antiprism, but the difference in going to the dodecahedron was not great. More recently, theoretical treatments of 8-coordination have been applications of ligand field theory, the investigators regarding ligand-ligand repulsions as the chief factor influencing the geometry. Results from computing ligand-ligand repulsions and from crystal field stabilization energy calculations show that the potential energy minima corresponding to the square antiprism and to the dodecahedron are very similar and that these stereochemistries are relatively easy to distort.

#### Library of Congress Subject Headings

Quantum chemistry

Molecular rotation

Molecular orbitals

#### Format

application/pdf

#### Number of Pages

193

#### Publisher

South Dakota State University

#### Recommended Citation

Herman, Patty S., "Molecular Orbital Calculations for [Mo(CN)₈]⁴⁻ an Investigation of Eight Coordination Geometries" (1974). *Electronic Theses and Dissertations*. 4721.

https://openprairie.sdstate.edu/etd/4721