Detection of a Planar Tetracoordinate Hydrogen within the Indium Framework by Quantum Dynamics Theory

In this work, we consider the question how to detect the planar tetracoordination hydrogen geometry which was recently proposed by electronic structure calculations on the In₄H⁺ system (Angew. Chem. Int. Ed. 2024, 63, e202317312; e202400927; e202403214). Keeping the C_4v symmetry, a two-dimensional model of In₄H⁺ is designed to build the nonadiabatic Hamiltonian operator with the lowest-lying singlet and triplet states coupled with spin-orbit coupling. The electronic energies in fitting the potential energy matrix are computed at either the MRCI or CCSD (T) level. Having constructed Hamiltonian, the multiconfigurational time-dependent Hartree product method predicts vibrational eigenstates for spectrum and recrossing probability of the proton. These quantum dynamics calculations predict a period of ∼60 fs for the proton recrossing the In₄ moiety and further indicate that experimental observation of the D_4h geometry for the triplet state is highly probable at room temperature even though the present MRCI and previous CASPT2 calculations (Angew. Chem. Int. Ed. 2024, 63, e202400927) both predict the C_4v symmetry. To measure the C_4v geometry, a low temperature of ≲30 K could be adopted. Despite the low temperature, the experiment might still miss the C_4v geometry due to the nonzero recrossing probability of H at the low kinetic energy region. Further, a new type of hydrogen bonding in the D_4h geometry is proposed to explain the interaction between the C_4v geometries.