First-principles study of large-amplitude dynamic Jahn-Teller effects in vanadium tetrafluoride

Transition metal tetrahalides are a class of highly symmetric molecules for which very few spectroscopic data exist. Exploratory ab initio calculations of electronic potential energy functions indicate that the equilibrium molecular geometries of the vanadium, niobium, and tantalum tetrafluorides (i.e., VF₄, NbF₄, and TaF₄) exhibit strong distortions from the tetrahedral configuration in their electronic ground state (²E) and first excited state (²T₂) along the nuclear displacement coordinates of e symmetry. The distortions result from the E × e and T₂ × e Jahn-Teller (JT) effects, respectively. In addition, there are weaker distortions in the ²T₂ state along the coordinates of t₂ symmetry due to the T₂ × t₂ JT effect. The description of the large-amplitude dynamics induced by these JT effects requires the construction of JT Hamiltonians beyond the standard model of JT theory, which is based on Taylor expansions up to second order in normal-mode displacements. These higher-order JT Hamiltonians were constructed in this work by expansions of the electronic potentials of the title molecule in terms of symmetry invariant polynomials in symmetry-adapted nuclear displacement coordinates for the bending modes of VF₄. A multi-configuration electronic structure method was employed to determine the coefficients of these high-order polynomial expansions from first principles. Using these large-amplitude Jahn-Teller Hamiltonians, the vibronic spectra of VF₄ were computed. The spectra illustrate the effects of large-amplitude fluxional nonadiabatic dynamics due to exceptionally strong E × e and T₂ × e JT couplings. In addition, the vibronic spectrum of the T₂ × (e + t₂) JT effect, including the bending mode of t₂ symmetry, was computed. The spectrum displays strong inter-mode coupling effects exhibiting a vibronic structure, which is substantially different from that predicted by independent-mode approximation. These results represent the first ab initio study of dynamical Jahn-Teller effects in VF₄.