Path integrals with higher order actions: Application to realistic chemical systems

Area of Science:

• Computational Quantum Chemistry
• Theoretical Physical Chemistry
• Statistical Mechanics

Background:

• Path Integral Monte Carlo (PIMC) simulations are crucial for determining quantum thermodynamic parameters.
• Standard PIMC methods become computationally intensive for highly quantum systems.
• Higher-order approximations to the thermal density matrix action can enhance PIMC efficiency.

Purpose of the Study:

• To compare the efficiency of different approximations to the action in PIMC simulations.
• To investigate the performance of numerically optimized higher-order actions for realistic molecular systems.
• To assess the impact of parameter choices on the efficiency of advanced PIMC methods.

Main Methods:

• Applied PIMC simulations using the primitive approximation (PA), Takahashi-Imada action (TIA), Suzuki-Chin action (SCA), and Chin action (CA).
• Utilized spectroscopically accurate potential energy surfaces for H2O and HCN-HNC, including three-body interactions.
• Numerically optimized parameters for the SCA and CA formalisms for each potential.

Main Results:

• Optimized Chin action (CA) demonstrated approximately twice the efficiency of Takahashi-Imada action (TIA) and an order of magnitude improvement over primitive approximation (PA).
• Optimized Suzuki-Chin action (SCA) showed comparable efficiency to CA for HCN-HNC but was less efficient than TIA for H2O at low temperatures.
• Optimal CA parameter (a1 ≈ 13) and SCA parameter (α ≈ 0.31) were identified, with significant performance degradation upon poor parameter selection.

Conclusions:

• Numerical optimization of SCA and CA parameters is essential for maximizing efficiency gains in PIMC simulations of realistic quantum systems.
• The harmonic approximation for CA parameters is suboptimal compared to numerically optimized values for these potentials.
• Optimized higher-order actions, particularly CA, offer significant computational advantages for quantum thermodynamic calculations.