Adiabat-to-Diabat Angle in Seam Space: Renner-Teller-Type and Pseudo-Jahn-Teller-Type Problems

In this study, we examine the adiabat-to-diabat (ATD) angles for trajectories in 2-dimensional vibrational subspace of the seam space of two degenerate states. In circulating around the tangential touching degeneracy center, the ATD angle is changed by2 π ${2\pi }$ or 0, similar to the Renner-Teller problem and the pseudo-Jahn-Teller problem, respectively. These ATD angle profiles may be indistinguishable from those of circulating multiple conical intersections or a pseudo-Jahn-Teller center. Methods to discern those seemingly indistinguishable cases are proposed. A sharp zigzag variation of the ATD angle is seen as a feature for trajectories that graze a pseudo-Jahn-Teller-type tangential touching center, in contrast to the monotonic steep variation for grazing a conical intersection or a Renner-Teller-type tangential touching center.

The Lack of Triplet Fusion for an Intramolecular Singlet Fission Chromophore: The Expected, the Unexpected, and a Reconciliation

Singlet fission (SF) has the potential to play a key role in photovoltaics since it generates a larger number of longer-lived triplet excitons after photoabsorption. Intramolecular SF (iSF) is of special interest since it enables tuning of SF efficiency by adjusting interchromophore configuration through covalent interaction. However, as elaborated in the present work, iSF chromophores are doomed to dissatisfy one general thermodynamic criterion for all SF chromophores, intramolecular or not: E(T2) ≥ 2E(T1), and therefore, the fusion of two triplet excitons to one triplet exciton is thermodynamically favorable. In our nonadiabatic quantum dynamics simulation for a model iSF chromophore, this expected fusion does not occur, because of the inefficient intersystem crossing hidden under the cover of internal conversion of the triplet fusion. A reconciliation is achieved between the dissatisfaction of E(T2) ≥ 2E(T1) and the large tetraradical character for general iSF chromophores.

The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

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.

Simulation of the photodetachment spectra of the nitrate anion (NO3-) in the B 2E' energy range and non-adiabatic electronic population dynamics of NO3

The photodetachment spectrum of the nitrate anion (NO3-) in the energy range of the NO3 second excited state is simulated from first principles using quantum wave packet dynamics. The prediction...

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.

The role of electron-nuclear coupling on multi-state photoelectron spectra, scattering processes and phase transitions

We present first principle based beyond Born-Oppenheimer (BBO) theory and its applications on various models as well as realistic spectroscopic and scattering processes, where the Jahn-Teller (JT) theory is brought in conjunction with the BBO approach on the phase transition of lanthanide complexes. Over one and half decades, our development of BBO theory is demonstrated with ab initio calculations on representative molecules of spectroscopic interest (NO2 radical, Na3 and K3 clusters, NO3 radical, C6H6+ and 1,3,5-C6H3F3+ radical cations) as well as triatomic reactive scattering processes (H+ + H2 and F + H2). Such an approach exhibits the effect of JT, Renner-Teller (RT) and pseudo Jahn-Teller (PJT) type of interactions. While implementing the BBO theory, we generate highly accurate diabatic potential energy surfaces (PESs) to carry out quantum dynamics calculation and find excellent agreement with experimental photoelectron spectra of spectroscopic systems and cross-sections/rate constants of scattering processes. On the other hand, such electron-nuclear couplings incorporated through JT theory play a crucial role in dictating higher energy satellite transitions in the dielectric function spectra of the LaMnO3 complex. Overall, this article thoroughly sketches the current perspective of the BBO approach and its connection with JT theory with various applications on physical and chemical processes.

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.