One-dimensional tunneling calculations in the imaginary-frequency, rectilinear saddle-point normal mode

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Physics

Background:

• Quantum tunneling is crucial for chemical reaction rates.
• Accurate calculation of tunneling splitting is computationally challenging.
• Previous methods, like the reaction path Hamiltonian in the zero-curvature approximation, have limitations.

Purpose of the Study:

• To evaluate the accuracy of a newly developed one-dimensional Hamiltonian for tunneling calculations.
• To compare the performance of this new method against the traditional reaction path Hamiltonian.
• To investigate its application in systems like malonaldehyde and the D+H(2) reaction.

Main Methods:

• Utilizing tunneling calculations based on the reaction path Hamiltonian.
• Employing a novel one-dimensional Hamiltonian in the imaginary-frequency, rectilinear normal mode of a saddle point.
• Neglecting vibrational angular momentum terms in the calculations.

Main Results:

• The one-dimensional Hamiltonian demonstrated significantly higher accuracy compared to the zero-curvature approximation.
• Accurate predictions for ground-state tunneling splittings were achieved for H and D transfer in malonaldehyde.
• The method also proved effective for the three-dimensional D+H(2) reaction with zero total angular momentum.

Conclusions:

• The newly introduced one-dimensional Hamiltonian offers a more accurate approach for calculating quantum tunneling.
• This method provides a valuable tool for studying complex chemical reactions and molecular dynamics.
• It represents a significant advancement in theoretical chemistry for predicting reaction pathways.