Detection of a\nPlanar Tetracoordinate Hydrogen within\nthe Indium Framework by Quantum Dynamics Theory

In this work, we consider the question\nhow to detect\nthe planar\ntetracoordination hydrogen geometry which was recently proposed by\nelectronic structure calculations on the In<sub>4</sub>H<sup>+</sup> system (<i>Angew. Chem. Int. Ed.</i> <b>2024</b>, <i>63</i>, e202317312; e202400927; e202403214). Keeping\nthe <i>C</i><sub>4v</sub> symmetry, a two-dimensional model\nof In<sub>4</sub>H<sup>+</sup> is designed to build the nonadiabatic\nHamiltonian operator with the lowest-lying singlet and triplet states\ncoupled with spin–orbit coupling. The electronic energies in\nfitting the potential energy matrix are computed at either the MRCI\nor CCSD (T) level. Having constructed Hamiltonian, the multiconfigurational\ntime-dependent Hartree product method predicts vibrational eigenstates\nfor spectrum and recrossing probability of the proton. These quantum\ndynamics calculations predict a period of ∼60 fs for the proton\nrecrossing the In<sub>4</sub> moiety and further indicate that experimental\nobservation of the <i>D</i><sub>4h</sub> geometry for the\ntriplet state is highly probable at room temperature even though the\npresent MRCI and previous CASPT2 calculations (<i>Angew. Chem.\nInt. Ed.</i> <b>2024</b>, <i>63</i>, e202400927)\nboth predict the <i>C</i><sub>4v</sub> symmetry. To measure\nthe <i>C</i><sub>4v</sub> geometry, a low temperature of\n≲30 K could be adopted. Despite the low temperature, the experiment\nmight still miss the <i>C</i><sub>4v</sub> geometry due\nto the nonzero recrossing probability of H at the low kinetic energy\nregion. Further, a new type of hydrogen bonding in the <i>D</i><sub>4h</sub> geometry is proposed to explain the interaction between\nthe <i>C</i><sub>4v</sub> geometries.