Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Physics

Background:

• Quantum tunneling is crucial for chemical reactions.
• Existing methods like instanton theory have limitations in accuracy.
• Anharmonic effects significantly impact tunneling rates.

Purpose of the Study:

• To introduce a novel perturbative correction (RPI+PC) to the ring-polymer instanton approximation.
• To enhance the accuracy of calculating tunneling splittings by incorporating higher-order terms.
• To improve the treatment of anharmonic effects in tunneling calculations.

Main Methods:

• Calculating perturbative corrections using higher-order terms in the asymptotic expansion in ℏ.
• Incorporating third and fourth derivatives of the potential along the tunneling path.
• Applying the RPI+PC method to full-dimensional malonaldehyde and its deuterated derivative.

Main Results:

• The RPI+PC method significantly improves accuracy for systems with low barriers and anharmonic modes.
• Reduced error in hydrogen transfer tunneling splitting from -11% to 2% for malonaldehyde.
• Achieved higher accuracy than diffusion Monte Carlo and path-integral molecular dynamics.

Conclusions:

• The RPI+PC approach provides a more accurate and computationally efficient method for tunneling calculations.
• This method offers a significant advancement over standard instanton theory.
• The RPI+PC method is applicable to complex molecular systems.