On the rearrangement and dissociation mechanism of SiH4+ in its triply-degenerate ground state

An ab initio molecular orbital study has been performed to explore the structural rearrangement and dissociation of SiH4+ radical cation at the X̃2T2 ground electronic state. All stationary points located on the lowest adiabatic sheet of Jahn-Teller (JT) split X̃2T2 state are fully optimized and characterized by performing harmonic vibrational frequency calculations. The structural rearrangement is predicted to start with JT distortions involving the doubly-degenerate (e) and triply-degenerate (t2) modes. The e mode reduces the initial Td symmetry of the SiH4+ ground state to a D2d saddle point, which eventually dissociates into the SiH3+(2A1) + H products via C3v local minimum. In turn, an e-type bending of αH-Si-H yields the SiH2+(2A1) + H2 products through the first C3v local minimum and then the Cs(2A') global minimum. In the alternative pathway, the t2 mode distorts the initial Td symmetry into a loosely bound C3v local minimum, which further dissociates into the SiH3+(2A1) + H asymptote via totally symmetric Si-H stretching mode, and SiH2+(2A1) + H2 products via H-Si-H bending (e) mode through the Cs(2A') global minimum. It is further predicted that the Cs global minimum interconverts equivalent structures via a C2v transition structure. In addition, the two dissociation products are found to be connected by a second C2v transition structure.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in tetrahedral and octahedral symmetries

Heavy element compounds with high symmetries often feature both spin-orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be three-fold degenerate and experience complicated Jahn-Teller and pseudo-Jahn-Teller interactions. To accurately describe these interactions, high quality spin-orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin-orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes, and generates Hamiltonian expansion formulas of arbitrarily high order.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibrational modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E₃^″⊗e₁^' Jahn-Teller interaction is used to demonstrate the correctness of the formalism. A Python program is developed to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems and interface the expansions to the MCTDH quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn-Teller and pseudo-Jahn-Teller problems. Also it is the only one.

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.

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO₃⁻.

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.