# New Permutationally Invariant Polynomial Potential Energy Surfaces for H5O2 + with Fast Analytical Gradients Calculated Using Reverse Differentiation

## TL;DR

This paper introduces new, precise potential energy surfaces for H5O2+ with fast analytical gradients using reverse differentiation, improving on previous methods.

## Contribution

The paper presents new, more precise potential energy surfaces with fast analytical gradients for H5O2+ using reverse differentiation.

## Key findings

- The new fits are more precise and provide fast gradients compared to the HBB method.
- Reverse differentiation enables gradients that are 20 times faster than HBB numerical gradients.
- The new PESs agree well with CCSD(T) benchmarks and HBB results for stationary points and ZPEs.

## Abstract

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.