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

Abstract

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.

Angular Jahn–Teller Effect and Photoluminescence of the Tetrahedral Coordinated Mn2+ Activators in Solids–A First-Principles Study

“…For a [Mn L 4 ] moiety with T d symmetry, the vibrational modes are given by Γ vib ( T d ) = a 1 + e + 2 t 2 , which contains a 1 + t 2 stretching modes and e + t 2 bond bending modes . The symmetrized bond bending coordinates of e -type symmetry for a tetrahedral [MnO 4 ] are given by , where R denotes the Mn–O bond length, and α denotes the O–Mn–O angle. The e -type Q ε and Q ϑ distortions separately decrease the symmetry of the [MnO 4 ] moiety from T d to D 2 d and D 2 .…”

“…For a [MnL 4 ] moiety with T d symmetry, the vibrational modes are given by Γ vib (T d ) = a 1 + e + 2t 2 , which contains a 1 + t 2 stretching modes and e + t 2 bond bending modes. 67 The symmetrized bond bending coordinates of e-type symmetry for a tetrahedral [MnO 4 ] are given by 28,67 1. These agree with previous works, 13,14,68 which demonstrate that in the 4 T 1 state of ZnS:Mn 2+ the strong Jahn−Teller coupling with e phonons takes place, while that with t 2 phonons is absent.…”

“…This agrees with the previous works, where the electron−lattice interaction shows greater strength for e-type distortion coupling with t 2 electrons than with e electrons in the d 1 systems of VF 4 , NbF 4 , and TaF 4 molecules. 28,67 Thus, for the 4 T 1 excited state, the unoccupied orbital of the majority spin with the d xy character is energetically favorable. However, the occupied orbital of the minority spin is the slightly higher one of the two e orbitals that has d x 2 -y 2 character and is likely due to the impact of the subtlety of the interplay between the ligand field and Coulomb interaction.…”

“…The transition metal molecules or clusters have been modeled by quantum chemistry calculations, − and various improvements have been reported to deal with the problem induced by carving a finite cluster from the bulk, which often involves cutting metal-linker bonds, and may lead to charged clusters and truncation artifacts, and thus the results may depend sensitively on the choice of the cluster. − On the other hand, the calculations based on density functional theory with the periodic supercell formalism have been successfully applied in the study of the stabilization and luminescence of activator centers, such as Ce 3+ , Bi 3+ , Mn 3+ , and Mn 4+ . For the excited states of the multielectron d 5 system in the framework of density functional theory, the spin contamination is a problem in particular to overcome, , which could especially be challenging for the excited states in tetrahedral coordinations due to the much weaker ligand-field splitting than the cases of octahedral or cubic coordinations.…”

Jahn–Teller Effect in Orthorhombic Manganites: Ab Initio Hamiltonian and Roto-vibrational Spectrum

“…Transition metal halides are also prone to JT effects due to the presence of high symmetry, open d-shell electronic configurations and degenerate electronic ground and/or excited states. Until now, several investigations have been made on the effect of various JT couplings for the vibronic spectra of many transition metal halides, such as, MnF 3 , , CoF 3 , , VF 3 , VF 4 , etc. In LaMnO 3 , along with the usual structural phase transition from the high-temperature pseudocubic perovskite ( Pm 3̅ m ) to the low-symmetry orthorhombic ( Pbnm ) structure at ∼780 K, the JT effect − also stabilizes the A -type antiferromagnetic spin order phase below the Néel temperature, T N ∼ 140 K. Such JT-driven phase transitions in perovskites are actually related to the distortions taking place in octahedral MnO 6 9– (cubic symmetry) units surrounded by positively charged rare-earth ions.…”