Lanthanide complexes with eight coordinating atoms can exhibit several coordination geometries. The most common geometries for eight-coordinate lanthanide complexes are:1. Square antiprismatic SAP geometry: In this geometry, the lanthanide ion is surrounded by eight ligands, forming two squares that are rotated by 45 degrees relative to each other. The ligands are arranged in an alternating fashion above and below the central ion.2. Dodecahedral DD geometry: In this geometry, the lanthanide ion is surrounded by eight ligands, forming a polyhedron with 12 faces. Each face is a pentagon, and the ligands are arranged in a way that the central ion is equidistant from all of them.3. Bicapped trigonal prismatic BCTP geometry: In this geometry, the lanthanide ion is surrounded by eight ligands, forming a trigonal prism with two additional ligands capping the top and bottom faces. The central ion is in the center of the prism, and the ligands are arranged in a way that they form a triangular base and top.In contrast, eight-coordinate transition metal complexes typically exhibit different coordination geometries, such as:1. Cubic geometry: In this geometry, the transition metal ion is surrounded by eight ligands, forming a cube. The ligands are arranged in a way that the central ion is equidistant from all of them.2. Square antiprismatic SAP geometry: This geometry is also common in transition metal complexes, similar to lanthanide complexes.3. Dodecahedral DD geometry: This geometry is less common in transition metal complexes compared to lanthanide complexes.The differences in coordination geometries between lanthanide and transition metal complexes can be attributed to the differences in their electronic configurations and the nature of their bonding. Lanthanide ions have larger ionic radii and exhibit weaker crystal field effects compared to transition metal ions. As a result, lanthanide complexes tend to have more flexible coordination geometries and can accommodate a wider range of ligands. In contrast, transition metal complexes often have more rigid coordination geometries due to the stronger crystal field effects and the involvement of d-orbitals in bonding.