Tunneling splittings using modified WKB method in Cartesian coordinates: The test case of vinyl radical

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Spectroscopy

Background:

• Calculating tunneling splittings in multi-well systems is crucial for understanding molecular dynamics.
• Existing methods may be computationally expensive or limited in dimensionality.
• The WKB approximation offers a semi-classical approach to quantum mechanical problems.

Purpose of the Study:

• To re-derive and apply a modified Wentzel-Kramers-Brillouin (WKB) theory for tunneling splittings in full dimensionality.
• To assess the accuracy of the modified WKB theory by comparing its predictions to exact variational results.
• To investigate the theory's applicability to vinyl radical and its deuterated isotopologues.

Main Methods:

• Re-derivation of modified WKB theory using Cartesian coordinates, emphasizing its foundation on wavefunctions exact for harmonic potentials.
• Application of the theory to calculate tunneling splittings in vinyl radical and its isotopologues across various vibrational states.
• Comparison of calculated tunneling splittings with exact variational results for validation.

Main Results:

• The modified WKB theory reproduces exact variational results within a factor of 2 for most states.
• Large enhancements in tunneling splittings, up to three orders of magnitude, are accurately reproduced.
• The theory correctly distinguishes between localized and delocalized tunneling states in asymmetrically deuterated vinyl radical.

Conclusions:

• Modified WKB theory provides a computationally inexpensive and accurate method for calculating tunneling splittings in full dimensionality.
• The theory's accuracy is demonstrated for vinyl radical systems, offering insights into its performance for larger molecular systems.
• This method is a valuable tool for studying tunneling phenomena in complex molecular systems.