Relativistic Jahn-Teller effects in the photoelectron spectra of tetrahedral P4, As4, Sb4, and Bi4

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.

Formation of the elusive tetrahedral P3N molecule

The tetrahedral 1,2,3-triphospha-4-azatricyclo [1.1.0.0^2,4] butane (P₃N) molecule-an isovalent species of phosphorus (P₄)-was prepared in low-temperature (5 K) phosphine-nitrogen ices and was identified in the gas phase through isomer-selective, tunable, soft photoionization reflectron time-of-flight mass spectrometry. Theoretical calculations reveal that the substitution of a single phosphorus atom by nitrogen in the P₄ molecule results in enhanced spherical aromaticity while simultaneously increasing the strain energy from 74 to 195 kJ mol^-1. In P₃N, the P─P bond is shortened compared to those in P₄ by 3.6 pm, while the P─N─P bond angle of 73.0° is larger by 13.0° compared to the P─P─P bond angle of 60.0° in P₄. The identification of tetrahedral P₃N enhances our fundamental understanding of the chemical bonding, electronic structure, and stability of binary, interpnictide tetrahedral molecules and reveals a universal route to prepare ring strained cage molecules in extreme environments.

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.

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.