Performance of quantum Monte Carlo for calculating molecular bond lengths

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Molecular Modeling

Background:

• Accurate molecular geometries are crucial for understanding chemical properties and reactions.
• Traditional methods like Hartree-Fock (HF) and Density Functional Theory (DFT) have limitations in geometry prediction.
• Quantum Monte Carlo (QMC) methods offer a promising alternative for high-accuracy electronic structure calculations.

Purpose of the Study:

• To evaluate the accuracy of real-space Quantum Monte Carlo (QMC) methods for determining molecular geometries.
• To compare the performance of variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) against experimental data.
• To assess the impact of different trial wavefunctions on QMC accuracy for molecular bond lengths.

Main Methods:

• Calculated equilibrium bond lengths for 30 diatomic molecules using VMC and DMC.
• Employed trial wavefunctions including single determinants from HF and DFT (LDA, PBE, B3LYP) and multi-determinant expansions.
• Analyzed mean-absolute deviations (MADs) compared to experimental bond lengths.

Main Results:

• All DMC methods outperformed HF, DFT, and MCSCF in accuracy.
• DMC with a multi-determinant expansion achieved the lowest MAD of 3 ± 2 × 10⁻³ Å.
• VMC with a multi-determinant expansion yielded a comparable MAD of 4.0 ± 0.9 × 10⁻³ Å, demonstrating high efficiency.

Conclusions:

• QMC methods, particularly DMC, provide highly accurate molecular geometries.
• VMC offers a computationally efficient alternative for achieving accurate molecular geometries, suggesting its suitability for QMC force calculations.