Quantum Monte Carlo with density matrix: potential energy curve derived properties

Area of Science:

• Quantum Chemistry
• Computational Physics
• Molecular Spectroscopy

Background:

• Conventional quantum Monte Carlo methods rely on wave functions formed by determinant products.
• Newer density matrix-based quantum Monte Carlo methods offer alternative approaches.
• Accurate potential energy curves are crucial for understanding molecular behavior.

Purpose of the Study:

• To evaluate the accuracy of density matrix-based diffusion quantum Monte Carlo (d-DMC) and variational quantum Monte Carlo (d-VMC) methods.
• To determine the potential energy curve (PEC) and spectroscopic constants for the ground state of the H2 molecule.
• To assess the robustness of d-DMC against variations in basis set size.

Main Methods:

• Utilized diffusion quantum Monte Carlo with density matrix (d-DMC) and variational quantum Monte Carlo with density matrix (d-VMC).
• Calculated the potential energy curve (PEC) for the H2 molecule.
• Performed calculations using two distinct basis sets to analyze size influence.
• Obtained spectroscopic constants, including dissociation energy and rotational constant.

Main Results:

• The d-DMC method provided a highly accurate PEC for the H2 molecule.
• Spectroscopic constants, such as dissociation energy and rotational constant, were successfully obtained using d-QMC methods for the first time.
• The accuracy of the PEC described by d-DMC was consistent across different basis set complexities.
• Results from d-DMC were found to be in excellent agreement with the most accurate literature values.

Conclusions:

• Density matrix-based quantum Monte Carlo methods, particularly d-DMC, offer a robust and accurate approach for describing molecular potential energy curves.
• These methods provide reliable spectroscopic constants for molecules like H2.
• The accuracy of d-DMC is largely independent of the basis set size, highlighting its efficiency and reliability.