Spectroscopic Signatures of Thermally Distinguishable Polyhedral Shapes: Crystal Field Splitting and Normal-Mode Differentiation

We recently established the Thermally Distinguishable Polyhedral Shapes (TDPSs), discrete geometries that remain robust against thermal vibrations, for hexa- and hepta-coordinate complexes, employing graph enumeration and thermal smearing analysis of over 42,000 CSD structures.[1] Five TDPSs emerged for CN-6, including the not infrequent but previously overlooked Digonal Anticupola (DAC-6, C_2v), alongside fourteen novel CN-7 geometries. In the present work, we extend this framework by calculating the corresponding spectroscopic fingerprints for all TDPSs, both electronic (UV-Vis) and vibrational (IR/Raman). Electronic structures are obtained from a variational point-charge Crystal Field Theory (CFT) Hamiltonian, yielding orbital splitting diagrams. Vibrational levels are computed by means of Wilson's GF matrix approach with continuous angular coupling, with IR and Raman activities assigned through group-theoretical projection operators. The electronic model discloses ligand-field splitting, whereas the vibrational model reveals normal-mode differentiation. DAC-6 exhibits five non-degenerate orbital levels and six split stretching modes, breaking the Octahedron (OC-6, O_h) degeneracies.