Using Gradients in Permutationally Invariant Polynomial Potential Fitting: A Demonstration for CH₄ Using as Few as...

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Quantum Chemistry

Background:

• Developing accurate high-dimensional potential energy surfaces (PES) is crucial for understanding molecular dynamics.
• Traditional methods often require extensive computational resources and large datasets.

Purpose of the Study:

• To introduce novel software for constructing accurate PES.
• To assess the benefits of incorporating both electronic energies and gradients in PES development.
• To evaluate the efficiency of the method with limited data.

Main Methods:

• Utilizing a permutationally invariant polynomial basis set.
• Employing direct dynamics with the B3LYP/6-31+G(d) level of theory to obtain energies and gradients.
• Training and testing on datasets of varying sizes (from 50 to 9000 configurations).
• Performing root-mean-square fitting error analysis, normal-mode analysis, and diffusion Monte Carlo calculations.

Main Results:

• The developed software effectively incorporates energies and gradients for PES construction.
• Accurate potential surfaces can be achieved with as few as 50-100 configurations when using both energies and gradients.
• Incorporating gradients significantly enhances the fidelity of the fitted potential surfaces.
• Fits using all data from direct-dynamics trajectories, though more demanding, yielded encouraging results.

Conclusions:

• The new software provides an efficient and accurate approach to developing high-dimensional potential energy surfaces.
• The inclusion of gradients alongside energies dramatically reduces the data requirements for precise PES fitting.
• This method holds significant promise for advancing molecular dynamics simulations and theoretical chemical studies.