Interpolated potential energy surfaces: How accurate do the second derivatives have to be?

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Molecular Modeling

Background:

• Accurate potential energy surfaces (PES) are crucial for molecular simulations.
• The modified Shepard interpolation scheme is a robust method for constructing global PES.
• Ab initio calculations can introduce errors in derivative data, impacting PES accuracy.

Purpose of the Study:

• To construct a global potential energy surface for the water dimer.
• To assess the impact of second derivative accuracy on quantum diffusion Monte Carlo (QDMC) simulations.
• To determine the required precision of second derivative data for accurate PES representation.

Main Methods:

• Utilized the modified Shepard interpolation scheme for PES construction.
• Employed ab initio calculations to obtain energy and derivative data.
• Performed truncation of exact second derivatives to approximate series.
• Conducted quantum diffusion Monte Carlo (QDMC) simulations to evaluate PES accuracy.

Main Results:

• The accuracy of the second derivative matrix was tested by truncation.
• Convergence of zero-point energy and wave function histograms was achieved.
• Inclusion of three significant figures or three decimal places in second derivatives was sufficient for convergence.
• Results converged within the numerical uncertainty of the QDMC simulation.

Conclusions:

• The modified Shepard interpolation scheme is effective for water dimer PES construction.
• Precise second derivative data is essential for reliable QDMC simulations.
• A specific level of precision (three significant figures/decimal places) in second derivatives ensures accurate simulation outcomes.