Exploring Jahn-Teller distortions: a local vibrational mode perspective

Abstract

The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case, ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$ / ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$ , as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case, ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$ / ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$ . We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$ to ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$ there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$ to ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$ we observed an increase in covalency without altering the bond nature. Distinct $\pi$ back-donation disparity could be confirmed by comparison with the isolated CN ${}^{-}$ system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.

Keywords: CNM/ACS protocol; Jahn-Teller effect; Local vibrational mode theory; Vibrational spectroscopy.