New Permutationally Invariant Polynomial Potential Energy Surfaces for H ₅ O ₂ ⁺ with Fast Analytical Gradients Calculated Using Reverse Differentiation

Given the central importance of the protonated water dimer to the study of the hydrated proton, we report new fits to the previous CCSD(T) data set of Huang, Braams, and Bowman (HBB) that are more precise and, unlike HBB, provide fast gradients. The new fits, like the HBB one, are based on linear regression with permutationally invariant polynomials (PIPs). The fast gradients are provided via reverse differentiation. They cost roughly just three times the cost for an energy call and are roughly 20 times faster than the HBB numerical gradients. The two new PESs are fits to the original HBB data sets up to roughly 60,000 and to 110,000 cm^-1. Comparisons to the CCSD(T) benchmarks and to the HBB results for stationary points and Diffusion Monte Carlo ZPEs are reported and show good agreement.