Pair approximating the action for molecular rotations in path integral Monte Carlo.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Statistical physics

Background:

• Path integral Monte Carlo (PIMC) methods commonly use primitive approximations for path probability densities.
• Existing methods can be computationally intensive, requiring many imaginary time steps for convergence.

Purpose of the Study:

• To develop and validate the pair discrete variable representation (pair-DVR) approach for studying molecular rotations.
• To enhance the efficiency and accuracy of path integral simulations for systems with pairwise interactions.

Main Methods:

• Developed the pair-DVR approach by combining pair factorization with a discretized path integral ground state paradigm.
• Applied the method to a chain of planar rotors with pairwise dipole interactions.
• Utilized Wigner-Kirkwood density expansion for asymptotic analysis and compared convergence with primitive propagators.

Main Results:

• The pair propagator shows improved accuracy, requiring fewer imaginary time steps for convergence compared to primitive Trotter paths.
• Energetic and structural properties, including correlation functions and Binder ratios, were computed as functions of coupling strength.
• The pair-DVR method demonstrated effective behavior near criticality.

Conclusions:

• The pair-DVR approach offers a more efficient and accurate alternative to primitive approximations in PIMC for molecular rotations.
• This method is well-suited for systems with pairwise potentials, providing reliable benchmarks for complex molecular systems.