Theory of Nonadiabatic Tunneling Splitting

Area of Science:

• Quantum mechanics
• Theoretical chemistry
• Computational physics

Background:

• Estimating tunneling splittings is a significant challenge in quantum mechanics, often limited by experimental and computational precision.
• Existing methods primarily calculate ground-state tunneling splittings for symmetric or asymmetric potentials.
• Very small splittings, below a wavenumber, push the boundaries of current detection and calculation capabilities.

Purpose of the Study:

• To develop a unified theoretical approach for calculating tunneling splittings.
• To extend calculations to excited states and near energy crossings.
• To enable analytic approximations and provide new insights into semiclassical theory.

Main Methods:

• A two-state approximation is employed for unified application to symmetric and asymmetric potentials.
• The approach is applicable to diabatic potential crossings and excited states.
• Incorporates vibrational perturbation theory and an instanton-based steepest descent expression.

Main Results:

• The unified method provides reliable estimates for tunneling splittings, even for excited states near energy crossings.
• It facilitates analytic approximations for model potential systems.
• Offers new perspectives on semiclassical tunneling theory.

Conclusions:

• The developed theoretical approach offers a significant advancement in calculating tunneling splittings.
• It provides a robust framework for future multidimensional applications.
• Numerical tests show promising results, paving the way for broader implementation.