The (E + A) × (e + a) Jahn-Teller and pseudo-Jahn-Teller Hamiltonian including spin-orbit coupling for trigonal...

Area of Science:

• Theoretical Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• Standard Jahn-Teller (JT) theory has limitations in describing complex molecular systems.
• Pseudo-Jahn-Teller (PJT) effects are crucial for understanding vibronic couplings in degenerate electronic states.
• Relativistic effects, particularly spin-orbit coupling, can significantly influence molecular properties.

Purpose of the Study:

• To develop an advanced theoretical framework for E × e JT and (E + A) × (e + a) PJT couplings in XY3 systems.
• To incorporate high-order expansions of the electrostatic Hamiltonian and spin-orbit coupling.
• To investigate the impact of relativistic effects on JT/PJT phenomena in molecules with C(3v) and D(3h) symmetry.

Main Methods:

• Developed a generalized Hamiltonian beyond standard JT theory, including bending modes of a and e symmetry.
• Replaced conventional Taylor expansions with high-order expansions in invariant polynomials for the electrostatic Hamiltonian.
• Extended spin-orbit coupling theory by expanding the Breit-Pauli operator up to second order in vibrational coordinates.

Main Results:

• Constructed an eighth-order, three-sheeted, three-dimensional ab initio potential-energy surface for PH3+.
• Identified a linear E × e JT effect of relativistic origin in C(3v) systems, which disappears at D(3h) geometry.
• Demonstrated that linear relativistic 2E – 2A PJT coupling persists in planar D(3h) geometry.

Conclusions:

• The developed high-order expansion method provides a more accurate description of vibronic couplings in XY3 systems.
• Relativistic effects introduce novel JT and PJT phenomena, dependent on molecular symmetry.
• The findings offer deeper insights into the electronic and vibrational dynamics of molecules exhibiting JT/PJT effects.