Strong static and dynamic Jahn-Teller and pseudo-Jahn-Teller effects in niobium tetrafluoride

We present a first-principles study of the static and dynamic aspects of the strong Jahn-Teller (JT) and pseudo-JT (PJT) effects in niobium tetrafluoride, NbF₄, in the manifold of its electronic ground state, ²E, and its first excited state, ²T₂. The complex topography of the full-dimensional multi-sheeted adiabatic JT/PJT surfaces is analyzed computationally at the complete-active-space self-consistent-field (CASSCF) and multireference second-order perturbation levels of electronic structure theory, providing a detailed characterization of minima, saddle points, and minimum-energy conical intersection points. The calculations reveal that the tetrahedral (T_d) configuration of NbF₄ undergoes strong JT distortions along the bending mode of e symmetry, yielding tetragonal molecular structures of D_2d symmetry with T_d → D_2d stabilization energies of about 2000 cm^-1 in the X̃²E state and about 6400 cm^-1 in the òT₂ state. In addition, there exists strong X̃²E-òT₂ PJT coupling via the bending mode of t₂ symmetry, which becomes important near the crossing seam of the X̃²E and òT₂ potential energy surfaces. A five-state five-mode JT/PJT vibronic-coupling Hamiltonian is constructed in terms of symmetry-invariant polynomial expansions of the X̃²E and òT₂ diabatic potential energy surfaces in the e and t₂ bending coordinates. The parameters of the Hamiltonian are determined by a least-squares fit of its eigenvalues to the CASSCF ab initio data. The vibronic spectra and the time evolution of adiabatic electronic population probabilities are computed with the multi-configuration time-dependent Hartree method. The complexity of the spectra reflects the effects of the exceptionally strong E × e and T₂ × e JT couplings and (E + T₂) × (e + t₂) PJT coupling. The time evolution of the populations of the adiabatic electronic states after the initial preparation of the òT₂ state reveals the femtosecond nonadiabatic dynamics through a multidimensional seam of conical intersection. These results represent the first study of the static and dynamical JT/PJT effects in the X̃²E and òT₂ electronic states of NbF₄.